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- Evolution of Defects in Amorphized Silicon
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- CAMERON, ADRIAN EWAN ( Author, Primary )
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Silicon ( jstor )
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EVOLUTION OF DEFECTS IN AMORPHIZED SILICON
By
ADRIAN EWAN CAMERON
A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE
UNIVERSITY OF FLORIDA
2006
Copyright 2006
By
Adrian Ewan Cameron
To Mom, Dad, Evins, and Bill.
ACKNOWLEDGMENTS
The author would like to thank his parents for their unwavering support throughout
his academic career. He would also like to thank his advisor, Dr. Mark Law, for his
direction and guidance as well as Dr. Kevin Jones for his work on TEM and his insight
and knowledge of this area. The author would also like to thank the SWAMP group for
their help, especially Renata, Ljubo, Russ, Danny, Michelle, Diane, Erik, Serge, and
everyone else who has helped prepare samples, answer questions, take TEM pictures, and
teach the author how to use lab equipment. Thanks are also extended to Dr. Scott
Thompson for serving on the thesis defense committee. The author would like to thank
Zoe for her help and for proofreading. A huge thank you goes to Teresa for keeping the
SWAMP group moving and organized so well.
TABLE OF CONTENTS
A C K N O W L E D G M E N T S ................................................................................................. iv
LIST OF TABLES ............. ................ ...................... .... ................. vii
LIST OF FIGURES ............. ............................ ........ .................viii
A B STR A C T ................................................. ..................................... .. x
CHAPTER
1 IN TR OD U CTION ............................................. ... .. ....... .... .............. .
1.1 Background and M motivation ....................................................... ............... 1
1.2 Ion Im plantation ......... ..... .............................................................. ........ .. .. ....
1.2.1 Ion Stopping ............................................. ..................... 5
1.2.2 Am orphization and Im plant D am age ........................................ ................6
1.3 D am ag e A n n ealin g ....................................................................... .......... .. .. .8
1.3.1 Solid-P hase E pitaxy .......... ........................................ ............ .... ......... 8
1.3.2 End-O f-R ange D effect Evolution ........................................ ..................... 9
1.3.3 Transient Enhanced Diffusion.................... ...................10
1.4 Scope and Approach of this Study................................. .. ............... .......... 11
2 EXPERIMENTAL AND DATA EXTRACTION PROCEDURES..............................13
2 .1 O v erv iew .................. ...................................................................................... 13
2.2 TEM and Sample Preparation..................................................... ..... ......... 13
2.3 PTEM Analysis and Data Extraction ..................... ............... 14
2.4 Procedures for Simulation Experiments ...........................................................15
3 DOSE AND ENERGY DEPENDENCE EXPERIMENT............................................17
3 .1 O v erview ...................................... .............................. ................. 17
3.2 R results for 750C A nneals......................................................... ............... 17
3.3 D discussion and A nalysis............................................... ............................ 18
3.4 Summary ................................... ............... ......19
4 EFFECTS OF THE SURFACE ON SIMULATED END-OF-RANGE DAMAGE ......29
4.1 Overview .................. .......... .................................................. 29
4.2 Surface Reaction Rate Effects on {311}'s ................................. .......... ........ 29
4.3 Effects of a Surface Field on {311 }'s...................................... ..................... .... 32
4 .4 S u m m ary ............. ............ .. .................................................... 3 4
5 CONCLUSIONS AND FUTURE WORK ............ .........................................39
5.1 O overview ............................................................... ................... .... 39
5.2 Dose and Energy Dependence Experiment .................................. ............... 39
5.3 Simulated Effects of the Surface on {311} Evolution..............................40
5 .4 F u tu re W ork ................................................... ................ 4 1
APPENDIX
A PTEM IM A G E S A N D D A TA ............................................................ .....................42
B FLOOPS MODIFICATIONS BY SEEBAUER ET AL.........................................47
L IST O F R E F E R E N C E S ......... ............... .....................................................................56
B IO G R A PH IC A L SK E TCH ..................................................................... ..................59
LIST OF TABLES
Table page
1.1 ITRS values for the next several technology nodes for key parameters of interest.
MPU is a logic, high-performance, high-production chip. ........................................3
3.1 List of implants done in this work and relevant previous work by Gutierrez. A
starred (*) condition indicates work done by Gutierrez......... ........................24
3.2 Decay rates and R2 values (a measure of how well the curve fits the data) for each
im p lan t ............. ......... .. .. ......... .. .. ..................................................2 5
4.1 Values for Figure 4.1. Values are in m inutes.................................... ..................35
A.1 Data set used for graphing figures 3.1-3.8. ...................................... ...............46
LIST OF FIGURES
Figure page
1.1 Cross section of a CMOS transistor. (A) Transistor with deep junctions. Depletion
regions of source and drain will encroach on channel, shortening effective
channel length. (B) Transistor with shallow junctions. Smaller depletion regions
lengthen the effective channel and reduce short-channel effects. Courtesy of
Paul R ackary of Intel ........... ...... .. ...... .... ............ ...............
1.2 Examples of behavior on implanted ions. A) Tunneling when the ion is not
stopped. B) Nuclear stopping, which displaces a lattice atom and can cause
secondary damage. C) Non-local electronic stopping of electrical drag on an ion
in a dielectric medium. D) Local electronic stopping involving collisions of
electrons. All figures from Plummer et al. ...................................... ...............6
1.3 Evolutionary path for Si+ self-implantation in the EOR damage region by Jones. ...10
3.1 Defect density dissolution and curve fit for 5e14 10keV implant. The curve
equation is listed on the graph ........................ ............................ ............ ... 20
3.2 Defect density curve for 2e15 10keV implant. The curve equation is listed on the
graph ............... ...................................................... ... .. ....... .. 2 1
3.3 Decay curve for 2e15 5keV implant. The curve equation is listed on the graph........22
3.4 Dissolution curve for 5e15 5keV implant. The curve equation is on the graph.
Note that this curve has the smallest R2 value (.7456) of the five implants.............23
3.5 Dissolution curve for 5e15 10keV implant. The curve equation is listed on the
g ra p h ...................................... ....................................................... 2 4
3.6 Decay rates for each implant condition. Note that there is no apparent trend in
dose or energy ..................................................... ................. 2 5
Figure 3.7 Graph of data set for all implants together. Curve fit equation and R2 value
is on the graph. Note that a fit of the average value at each anneal time yields
about the same decay rate but an R2 value of 0.9913...............................................26
3.8 Comparison of data from this work and previous work by Gutierrez. The data sets
follow similar trends with the exception of the 5e14 5keV implant by Gutierrez.
The reader is referred to Table 3.1 for which implants were performed for this
w o rk ......... .. ................. ................. ................................................... 2 7
3.9 Germanium implant defect evolution tree. This is an alternate path to the high
energy implants which form stable loops and {311 }'s. The highlighted grey
path is the observed path both here and by Gutierrez. .............................................28
4.1 Effect of changing "ksurf' for each implant energy on the dissolution time of
{3 11} defects............................................................................. ....... 35
4.2 Schematic of band bending energy diagram for p-type silicon showing a narrow
space-charge region and its influence on charged particles. ...................................36
4.3 Potential curve created from a low energy B implant into silicon..............................37
4.4 Effect of surface pinning value on the dissolution rate of {311 }'s created by a lel5
cm-2, 40keV Si+ implant into silicon. There is no apparent trend in the effect of
the surface pin on the dissolution tim e .......................................... ............... 38
A.1 PTEM micrographs of a 5e14 10keV implant and 750C anneal. Each image is
approximately 20tm across. A) 5 minutes, B) 15 minutes C) 30 minutes D) 45
m minutes, E) 60 m minutes ............................................ .... .... .... .. ...... .... 42
A.2 PTEM micrographs for a 2el5 5keV implant annealed at 750C. Each image is
approximately 20tm across. A) 5 minutes, B) 15 minutes C) 30 minutes, D) 45
m minutes, E) 60 m minutes ............................................ .... .... .... .. ...... .... 43
A.3 PTEM micrographs for a 2e15 10keV implant and 750C anneal. Each image is
approximately 20tm across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45
m minutes, E) 60 m minutes ............................................ .... .... .... .. ...... .... 44
A.4 PTEM micrographs of a 5e15 5keV implant annealed at 750C. Each image is
approximately 20tm across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45
m minutes, E) 60 m minutes ............................................ .... .... .... .. ...... .... 45
A.5 PTEM micrographs for a 5e15 10keV implant annealed at 750C. Each image is
approximately 20tm across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45
m minutes, E) 60 m minutes ............................................ .... .... .... .. ...... .... 46
Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science
EVOLUTION OF DEFECTS IN AMORPHIZED SILICON
By
Adrian Ewan Cameron
August 2006
Chair: Mark E. Law
Major Department: Electrical and Computer Engineering
In order to maintain the current trend of laterally scaling CMOS transistors for
better performance and higher transistor density, vertical dimensions must also be scaled
to minimize short channel effects. One way to achieve shallow vertical junctions is
through pre-amorphizing implants (PAI) at low energy to reduce ion channeling during
implantation of the dopant species. These PAI steps create end-of-range (EOR) damage
just below the amorphous/crystalline interface. Understanding how this EOR damage
evolves is important to process modeling and to future technologies. As the PAI energy
is reduced, the damage region is placed closer to the surface. The objective of this study
is to explore how several aspects of the surface affect the evolution of the EOR damage.
These aspects include proximity to the surface through lowered implant energy, reaction
rates of interstitials at the surface, and an electrical field set up at the surface.
The first experiment in this thesis investigates the EOR damage evolution for
several low-energy Ge+ PAls. Silicon wafers were implanted with Ge+ with doses of
5e14 cm-2 at 10keV, 2e15 cm-2 at 5 and 10keV, and 5e15 cm-2 at 5 and 10keV. Anneals
were performed at 750C for 5, 15, 30, 45 and 60 minutes. Plan-view transmission
electron microscopy (PTEM) was used to determine that at all conditions, small, unstable
dislocation loops were formed in the EOR region. Implant dose and energy seemed to
have no effect on trends regarding the dissolution time of the defects. The results were in
general agreement with previous work. From the PTEM analysis, decay time constants
were extracted for modeling purposes.
In the second experiment in this thesis, a model of {311} evolution was used for
FLOOPS simulations. The recombination rate of interstitials at the surface was
controlled using the variable "ksurf' for implant energies of 40, 80, and 160keV at a dose
of lel5 cm-2. Changing the "ksurf' variable had little effect on the dissolution of
{311 }'s, with a sharp drop around "ksurf' = le-6 cm/s which then levels off for
increasing values.
An additional part of the second experiment involved adding modifications to the
above model. This model uses an electrical field set up by the silicon/oxide interface to
explain both pile-up and junction broadening of boron. The key variable for these
simulations is the "pin" value, which controls the magnitude of the field at the surface.
The effect of this field on {311} dissolution was investigated for the 40keV implant
condition. The results show that the effect does not show a trend, but rather no real effect
on the decay rate. This is not surprising since the modifications were developed to
influence dopant ions and not silicon interstitials.
CHAPTER 1
INTRODUCTION
1.1 Background and Motivation
The integrated circuit (IC) has been a part of the growing worldwide technology
industry since its invention in 1959. The invention is credited to Jack Kilby of Texas
Instruments and Robert Noyce of Fairchild Semiconductor [1]. Since its inception, the
integrated circuit has grown in complexity from several parts to several hundred million.
The reason for this growth is the evolution of the complementary metal-oxide
semiconductor transistor, or CMOS. The trend in complexity has followed Moore's Law,
which predicts that the number of transistors on an integrated circuit will double
approximately every year [2]. Through technological innovation, that law has been
anticipated and hurdles overcome so that the prediction has been surprisingly accurate.
There are other more tangible benefits to transistor scaling as well. As the
minimum feature size decreases, the cost per transistor shrinks as does the cost per
function for a given area. In addition, smaller components require less power to operate
and produce less heat, which improves reliability. There are physical limitations which
work to counteract these benefits, such as the escalating cost of research and development
to overcome obstacles like junction leakage, lithographic limitations, and short-channel
effects.
The bench mark for overcoming technological hurdles and establishing new
technologies as cutting edge is the International Technology Roadmap for
Semiconductors (ITRS). The latest version of this map was completed in 2005, and
predicts the needs of the industry for the near and long-term future in all aspects of
production, from doping and size requirements to lithography, packaging, metrology, and
factory integration for both logic devices and memories, both volatile and non-volatile.
The ITRS also predicts when new technologies should be ready for production and if
manufacturing solutions are known or unknown for future requirements. Several of the
key features for the next several years can be found in Table 1.1.
The convention for labeling a technology node is usually to refer to the minimum
feature size, which is normally the gate length of a transistor. Some conventions refer to
the physical gate length while others refer to the printed gate length. Regardless of which
convention is used, the junction depth for the source and drain areas are on the same
order of magnitude. This work focuses on issues pertaining to ultra-shallow junctions,
one of the front-end processes (FEP) in semiconductor production. The need for ultra-
shallow junctions arises from several issues. First, the ITRS maintains a sheet resistance
requirement for the contact area of the source and drain. As the junction depth decreases,
scaled with gate length, the resistivity increases since a deeper junction can incorporate
more active carriers and hence lower resistivity. Therefore it is necessary to find ways of
implanting more carriers into the shallow junctions and activate them during the
annealing process, which is described later. Second, shallower junctions improve the
short-channel effects of small gate length transistors. Figure 1.1 illustrates two transistors
with equal gate lengths, but one has shallow junctions. The depletion region of the
shallow junction has less effect on the channel, thereby reducing the effective channel
length and the short-channel effects.
Table 1.1 ITRS values for the next several technology nodes for key parameters of
interest. MPU is a logic, high-performance, high-production chip.
Year
DRAM /2 pitch (nm)
MPU physical gate length (nm)
Junction depth Xj (nm)
S/D extension (nm)
Extension lateral abruptness
(nm/decade)
MPU Functions per chip
(Mtransistors)
Transistor density, logic
(Mtransistors/cm2)
Transistor density, SRAM
(Mtransistors/cm2)
Equivalent Oxide Thickness (EOT)
(nm)
Vdd (V)
Number of mask levels, MPU
Source: [3]
2006
70
28
30.8
9
3.5
193
122
646
1.84
1.1
33
2007
65
25
27.5
7.5
2.8
286
154
827
1.84
1.1
33
2009
50
20
22
7
2.2
386
245
1348
1.03
1.0
35
2011 2013
40 32
16 13
17.6 n/a
5.8 n/a
1.8 n/a
773 1546
389 617
2187 3532
0.75 n/a
Gate
la High
(A)
Gate
f, Low
(B)
Figure 1.1 Cross section of a CMOS transistor. (A) Transistor with deep junctions.
Depletion regions of source and drain will encroach on channel, shortening
effective channel length. (B) Transistor with shallow junctions. Smaller
depletion regions lengthen the effective channel and reduce short-channel
effects. Courtesy of Paul Rackary of Intel.
1.2 Ion Implantation
Ion implantation is the current dominant technology in control of forming
source/drain areas as well as threshold shift implants and source/drain extensions. The
dopant ion is accelerated and focused on the wafer using electric fields. The dose of
atoms is controlled by longer implant times or a higher beam current. The energy and
mass of the atoms control the projected range, Rp, which is the peak of the dopant profile
after implantation. The dopant profile follows a Gaussian statistical distribution [1]
described by the equation:
C(x) = Cp exp( -(x-Rp)2 / 2ARp2) 1.1
where Cp is the peak concentration predicted by the dose and the straggle, or ARp. X is
measured into the substrate with x=0 the surface of the wafer. Often, implantation is
done through a masking oxide for better control of the projected range and the
concentration peak, which is usually desired to be very near the surface.
1.2.1 Ion Stopping
As the ion is implanted into the lattice, it must have a force act on it to stop. The
two mechanisms for ion stoppage are nuclear stopping and electronic stopping. If the ion
is not stopped sufficiently near the surface, it can tunnel deep into the substrate,
deepening the junction depth. Figure 1.2 shows examples of tunneling, nuclear stopping,
and electronic stopping.
For nuclear stopping, the ion must collide with an atom in the lattice. The resulting
collision can displace the lattice atom and usually will if it is a primary collision. The
collision can result in a secondary damage cascade from both the dopant ion and
displaced lattice atom. Both atoms can travel deeper into the bulk, or the implanted ion
can actually backscatter toward the surface. Nuclear stopping causes damage to the
lattice, which will be discussed in the next section.
There are two types of electronic stopping: local and non-local. Non-local
electronic stopping refers to the drag an ion experiences in a dielectric medium. The
illustration for this can be seen in Figure 1.2 (C). An analogy is a particle moving
through a viscous medium [1]. Local electronic stopping involves collisions of electrons
when the implanted ion is close enough to a lattice atom such that the electron
wavefunctions overlap [1], causing a momentum transfer. This event is illustrated in
Figure 1.2 (D). The dominant mechanism for ion stoppage is nuclear stopping for low-
energy implants, and this also has the greatest effect on trajectory.
Target
Recoil
Incident
Ion
** ** 0 Scauered
A) B)
Dielectric Medium Target
I/on
+
Rewarding 8-field
C) D)
Figure 1.2 Examples of behavior on implanted ions. A) Tunneling when the ion is not
stopped. B) Nuclear stopping, which displaces a lattice atom and can cause
secondary damage. C) Non-local electronic stopping of electrical drag on an
ion in a dielectric medium. D) Local electronic stopping involving collisions
of electrons. All figures from Plummer et al. [1].
1.2.2 Amorphization and Implant Damage
One way to limit the depth of the implant profile is through a pre-amorphizing
implant, or PAI, which eliminates the possibility of ion channeling. This implant is
performed with a non-dopant atom, usually Si+ or Ge+ such that the electrical
characteristics are unchanged, or a co-implanted species such as BF2+ where fluorine is
the amorphizing ion and boron is the dopant. If the dose and energy are sufficiently high
enough, the implant will destroy the lattice structure and an amorphous layer will now be
the top layer of the substrate. Beneath the amorphous layer a highly damaged layer with
a supersaturation ofinterstitials will exist. The damage in this area is classified as Type-
II damage by Jones and is referred to as end-of-range, or EOR damage [4, 5]. In contrast,
Type-I damage occurs for non-amorphizing implants close to the concentration peak at
the projected range.
As a result of the nuclear stopping described above, lattice atoms are displaced
from their sites in the crystal structure. This creates an interstitial and a vacancy in the
lattice, described as a Frenkel pair [1, 6]. New interstitials can also have secondary
collisions with lattice atoms, creating more Frenkel pairs. Most of the Frenkel pairs will
recombine very quickly during the annealing process after implantation. Interstitials,
however, remain in excess in proportion to the implanted dose. This is referred to as the
"+1" model [7]. These interstitials have no corresponding vacancy and can form clusters
and nucleate into larger, more stable defects, since they must either diffuse to the surface
or deeper into the bulk.
If the implant conditions are of sufficient energy and dose, amorphization occurs.
This event can be considered as a critical-point phenomenon where the onset of
amorphization leads to cooperative behavior of the defects which greatly accelerates the
transition away from a crystalline lattice [8]. When this is the case, the "+1" model is no
longer very accurate, since the amorphous region consists totally of interstitials with no
long-range order and the EOR damage consists of a supersaturation of interstitial point
defects created from implanted ions and recoiled atoms from the amorphous region. This
"recoil" model by Jones [9] predicts a reduction in EOR density with increasing dose.
Robertson et al. [5] found that the total number of interstitials in the EOR region was
constant with a changing dose rate for an amorphizing Si+ implant with dose of lel 5cm2.
Other research [9, 10, 11] has shown that the number of interstitials in the EOR region is
a function of implant beam energy. Other conditions such as implant temperature and
species also have an impact on EOR formation, but no single condition has shown a one-
to-one correspondence to EOR density [11].
1.3 Damage Annealing
After the implantation process, the wafer is heated to high temperatures, to repair
damage done to the substrate. During this time, the crystal lattice is regrown, a process
referred to as solid-phase epitaxy, or SPE. Frenkel pairs will begin to be annihilated at
relatively low temperatures around 400C [1]. After they recombine, an excess of
interstitials still remain, in accordance with the "+1" model. These interstitials are not
reincorporated into the lattice because the dopant ions take their place and are then
electrically active.
1.3.1 Solid-Phase Epitaxy
The process of recrystalizing the amorphized silicon substrate during annealing is
called solid-phase epitaxy (SPE). It is a process of layer-by-layer regrowth from the
amorphous/crystalline interface back to the surface. The rate of regrowth is fast, and can
be up to 50 nm/min for <100> oriented silicon at 600C [1]. As recrystallization occurs,
the introduced dopant atoms are incorporated into substitutional lattice sites and become
electrically active. The rest of the regrown crystal is mostly defect free, however, a
region of large damage just beneath the original amorphous/crystalline interface can
exist. This is the EOR damage region.
1.3.2 End-Of-Range Defect Evolution
The interstitials in the EOR damage can evolve into several defect types depending
on the implant and the annealing conditions. One such type is the {311} defect, a rod-
like structure that inhabits the {311} plane and grows in the <110> direction. As Frenkel
pairs are annihilated very quickly, the remaining interstitials will bond to form small
clusters. These clusters can form {311} defects if the implant energy is high enough, or
small dislocation loops. King et al. [12], King [13], and Gutierrez [14] have shown that
5keV implant energy is not high enough to nucleate {311 }'s with Ge+ and that in many
cases 10keV may not be enough. If {311 }'s do form, they can eventually dissolve into
Frank loops and eventually perfect dislocation loops. Eaglesham et al. [15] have
proposed that the dissolution of the {311} defects correlated the anomaly of transient-
enhanced diffusion which depends on interstitials to drastically increase dopant
diffusivity for those species which exhibit an interstitialcy-driven diffusion process such
as boron. Additionally, Li and Jones [16] have shown that {311} defects are the source
of interstitials for dislocation loops.
During annealing the dislocation loop behavior can be described by the Ostwald
ripening theory. This theory states that the large dislocation loops grow at the expense of
the smaller ones, which is a more stable configuration [17]. Similar behavior for {311 }'s
has been observed by Stolk et al. [18]. An evolution tree for the case of Si+ implantation
can be seen in Figure 1.3. This figure shows the observations from several experiments
[15, 16, 18, 19] that the defects undergo four stages of evolution: nucleation, growth,
coarsening, and dissolution.
Si+ Ion Implantation
Amiorphizing Non-Amorphizumg
Si +
End-of-range Projected range
Excess Si Interstitials
Self-interstitial Clusrers
{311} Formation
Dissolution Conservative Congruent
(TED) Unfaulhing Dissolution and
(Loop Formation) Unfaulting
JTE D)
Loop Ripening Loops act Stable Loops
and Dissolution as traps (Leakage current)
Interstitial ntti
Release Interstitial
Release
(TED) Capture
Figure 1.3 Evolutionary path for Si+ self-implantation in the EOR damage region by
Jones [20].
1.3.3 Transient Enhanced Diffusion
Transient enhanced diffusion (TED) is an anomalous process by which the excess
of interstitials created during ion implantation greatly enhanced dopant diffusivity for
very short time scales. It is important to understand this process so that simulation tools
such as FLOOPS (FLorida Object Oriented Process Simulator) [21] can be accurate in
their predictions of dopant diffusion.
The source of the interstitials in TED is thought to come from dissolution of the
{311} defects for the non-amorphous implant case [15, 18, 22]. For the amorphous case,
dislocation loops are also thought to play a role in TED [4, 19]. The effect of species,
dose, implant energy, and annealing temperature on TED has been studied extensively.
Saleh et al. [23] found that TED was dependent on implant energy for le14 cm2 Si+
implants; Eaglesham et al. [24] came to the same conclusion. This supports findings by
Lim et al. [25] that surface etching results in TED reduction, which demonstrates that the
surface plays a role in annealing implant damage. However, during an anneal after an
amorphous implant, the surface is less important since the amorphous layer acts as a
diffusion barrier to interstitials in the EOR layer [26].
1.4 Scope and Approach of this Study
The work in this study is divided into two major parts. The first part deals with
expanding the experiment first started by Gutierrez [14] in exploring the interstitial
evolution for low-energy Ge+ amorphizing implants in Chapter 3. Implants of Ge+ at
conditions of 5el4cm2 at 10keV, 2el5cm-2 at 5 and 10keV, and 5el5cm-2 at 5 and 10keV
were made into Si wafers. Plan-view TEM is used to observe the defect evolution
through a series of anneals at 750C for 5-60 minutes. The results will be helpful in
understanding the EOR kinetic behavior which will lead to improved modeling in process
simulators.
The second part deals with simulations using FLOOPS and the effect of the surface
on {311} dissoluon 1 doluon in Chapter 4. Two sets of simulations were performed for this
work. The first set deals with increasing the surface recombination rate for interstitials to
observe how the surface affects the dissolution rate of {311 }'s. A model by Law and
Jones [27] is the basis for these simulations. The second set of simulations uses
12
modifications to that model by Seebauer et al. [28, 29, 30, 31, 32] which induces an
electrical field at the silicon surface. The effect of the magnitude of this field is
investigated on the {311} dissolution rate. Finally, further possibilities for
experimentation are discussed in Chapter 5.
CHAPTER 2
EXPERIMENTAL AND DATA EXTRACTION PROCEDURES
This chapter contains an overview of the methods for sample preparation and data
extraction techniques for the dose and energy dependence experiment.
2.1 Overview
Implants were performed by Core Systems, Inc. into Czochralski-grown (100)
wafers. Ge+ was implanted at room temperature at a 7 tilt to reduce channeling. Samples
were annealed in a nitrogen ambient at 750 C for 5-60 minutes using a quartz tube
furnace. A 30-second push-pull technique was used to minimize thermal stresses.
Implant damage was viewed using a JEOL 200CX transmission electron microscope
(TEM). Defect counts were performed using scans of negatives created by the TEM
using Adobe Photoshop 7.
2.2 TEM and Sample Preparation
Transmission electron microscopy is the primary way of directly viewing damage
from an implant for this experiment. For viewing the damaged specimens from the top-
down, plan-view (PTEM) is used. PTEM images allows for defects to be visible in the
g220 weak-beam dark-field (WBDF) condition with a g*3g diffraction pattern if the dot
product of the reciprocal lattice vector and the cross product of the Burgers vector and
dislocation line direction are not equal to zero [13].
PTEM samples must be made in order for the microscope to image effectively.
They are prepared in the following fashion:
1. A 3mm disc is cut from the annealed sample using an ultrasonic disc cutter
from Gatan, Inc. The cutter uses a silicon carbide (SiC) abrasive powder
and water. The sample is held in place by mounting it to a glass slide with
crystal bond. The glass slide is then held to the disc cutter stage using
double-sided tape. Acetone is used to remove the crystal bond from the
sample after cutting.
2. The disc is then thinned by hand using a lapping fixture. The sample is
mounted face-down (i.e. the implanted side down) to a metal stage using
crystal bond. The sample is then thinned with figure-eight motions to
-100tm determined by finger touch and visual inspection. A 15[tm slurry
of aluminum oxide (A1203) and water is used for abrasion on a glass plate.
Acetone is again used to clean crystal bond off the sample.
3. Specimens are then mounted face-down to a Teflon stage using hot wax,
leaving only a small portion of the backside uncovered. The sample is then
further thinned using an acid etch of 25% hydrofluoric acid (HF) and 75%
nitric acid (HNO3). The sample is etched until a small bright spot is visible
through the entire sample surrounded by a reddish area.
4. The etched samples are carefully removed from the Teflon stage and soaked
in heptane overnight or until all wax has been removed from the sample.
2.3 PTEM Analysis and Data Extraction
The images generated from the PTEM can be seen in Appendix A. The defect
densities are simply the count of defects in the observed area. Negatives are scanned into
a .bmp file using an Epson Perfection 3490 Photo scanner at 300dpi. Using Adobe
Photoshop, a 4cm x 4cm grid, or larger for lower defect densities, is laid over the image.
The image is zoomed to an appropriate level for easy viewing, and the grid overlay
maintains its scale. The defects are then counted within a grid square and divided by the
area to determine the defect density. The negatives are enlarged by a scale of 50,000x by
the TEM, so an appropriate factor of 50kx2 for area enlargement is included in the defect
counts. The results are averaged over at least 5 squares on the negatives for each implant
and anneal condition. There is an intrinsic +/- 20% error in this method. For the longer
anneals, as fewer defects are counted, the error goes up as the number of samples are
reduced and less data is available. This source of error could dramatically change the
endpoints and the slope of the fitted curve if the curve is fit to the error range instead of
the data point. For example, in counting the 2e15, 5keV implant at 60 minutes, the
number of defects per square was found to be anywhere from zero to twelve, but only
four different areas could be counted due to the size of the squares, which was four times
as large as the areas used for the five minute images. So, for this example, the defect
density of 2.2e9 defects/cm2 was found by counting an average of 5.5 defects in an area
of2.5e-9 cm2 (6.25 cm2 on the viewed image with the magnification).
Data extraction consists of using Microsoft Excel to fit an exponential curve of the
form y = A ex, where x is -t/'. In this equation, t is the anneal time and T is rate of decay.
Other methods are also used to explore the effects of certain variables on T. For example,
the prefactor A is averaged for all implants and then the data forced to fit a curve with
this new term. In addition, the effect of the 20% error was explored by changing the
values of the 5 and 60 minute anneals to both +20% and -20% of the observed value.
The changes are then fit with an exponential curve to see the change in the decay rate.
The entire data set is also graphed and fit to a curve to find the 'average' value of the
decay rate, and to determine if dose, energy, or both have an effect on the decay rate of
defects. Comparisons are also made to previous work by Gutierrez [14].
2.4 Procedures for Simulation Experiments
For the work done using simulations, FLOOPS (FLorida Object Oriented Process
Simulator) was used along with a defect evolution model by Law and Jones [27]. In the
first experiment, the surface reaction rate which controls interstitial recombination was
shifted. The resulting effect on {311} defect dissolution was investigated for a Si+
implant into a Silicon substrate for 40, 80, and 160 keV energies. The value was changed
from le-11 to le-2 cm/s.
16
For the second simulation experiment, code developed by Seebauer was
incorporated into the model [29]. This code affects the surface potential using a modified
Poisson equation, setting up an electric field pointing into the bulk. The code added into
FLOOPS for these simulations can be found in Appendix B. The effects of the electric
field on {311} dissolution was investigated.
CHAPTER 3
DOSE AND ENERGY DEPENDENCE EXPERIMENT
This chapter discusses the results of the investigation of defect dissolution
dependence on the dose and energy of the pre-amorphizing implant.
3.1 Overview
The purpose of this experiment was to further investigate the energy and dose
studies previously done by Gutierrez [14]. Implants were chosen to compliment the lel5
cm-2 implants at 5 and 10keV and the 5keV implants at 5e14 cm-2 and 3e15 cm-2 which
-2
Gutierrez studied. Implants in this experiment were performed at 10keV for 5e14 cm2,
2e15 cm-2, and 5e15 cm-2, and at 5keV for 2e15 cm-2 and 5e15 cm-2. Table 3.1 lists the
implants performed in this work and the relevant implants performed by Gutierrez.
Gutierrez has previously reported that these low energy implants follow a specific
evolutionary pathway that results in small, unstable dislocation loops [14]. These loops
dissolve quickly after approximately 60 minutes with an anneal temperature of 750 C
[14]. Data in this chapter will be shown to be in agreement with previous work.
3.2 Results for 750C Anneals
The data for the defect counts from each implant condition can be viewed in figures
3.1-3.5. These figures plot the defect density (in #/cm2) against time on a log-linear
scale. Data for each figure can be found in Appendix C. In addition, the PTEM images
for each annealed implant can be seen in Appendix A, images A. 1 through A.5. The
images show that the defect types formed are small interstitial clusters and dislocation
loops. No {311} defects were observed at any time point. The evolution of the
dislocation loops followed an Ostwald-ripening mechanism but did not coarsen greatly.
As the graphs show, the defects that are formed in these low-energy implants are
not stable. The average decay rate was approximately 20 minutes. From this average,
and by visual inspection of the PTEM images, it can be concluded that the small
dislocation loops formed are almost completely dissolved by the 60 minute time point for
all implant conditions. Table 3.2 lists the decay rate and R2 for each implant taken from
the exponential curve fit to the data.
From the table below, the data shows a strong fit for all but one of the curves,
5el5cm-2 with 5keV energy. Similarly, only one implant, 2el5cm-2 with 10keV energy,
is not within one standard deviation of the average. As mentioned before, the amount of
error goes up with fewer defects since the amount of statistical data is less. This could
improve the R2 value if the data is fit with larger error bars on the 60-minute data points.
3.3 Discussion and Analysis
Further statistical analysis was performed on the data to determine the trends.
Figure 3.6 shows in graphical form the decay rates of the five implants together. From
this figure it can be seen that no trend exists either by dose or by energy of the implant.
There are 5keV implants with decay rates larger than the 10keV implants, as well as a
smaller dose implant (2el5 cm-2) with a larger decay rate than that of the largest dose
implants. One would assume that any trend, if present, would indicate that higher energy
and higher dose would lead to more damage and longer dissolution time.
The data set as a whole was also graphed and fit to a curve. This graph can be seen
in Figure 3.7. The decay rate from this curve was found to be 19.12 minutes with an R2
value of 0.778. Comparing this value with a curve fit to an average value at each time
point we get a decay rate of 20.79 minutes but an R2 value of 0.9913.
In comparison to previous work by Gutierrez, the same trend is noticeable in each
data set with the exception of one 5e14 5keV implant by Gutierrez which exhibits a
spontaneous combustion beginning around the 45-minute time point and then rapidly
dissolving by 60 minutes. Figure 3.8 shows both data sets together on the same graph up
to the 60 minute anneals. It should be noted that Gutierrez's original data was not
available, so it was extracted from the graphs available in [14]. Also of note is that
Gutierrez performed sub-5 minute anneals using an RTA furnace. That data is included
in Figure 3.7.
In his thesis, Gutierrez also concluded that dose does not have a significant
qualitative or quantitative effect on defect evolution at low energy [14]. The data
presented here supports and affirms that conclusion. Gutierrez does state that there is a
heavy dependence on energy for defect behavior [14]. However, there are two regimes
for the dependence, and 5-10keV energies exhibit the same behavior, whereas 30+keV
energies form different defect morphologies. From the PTEM micrographs in Appendix
A and in [14], it is shown that {311 }'s do not form in the low-energy regime; only small,
unstable dislocation loops. Previous work has suggested a pathway for the defect
evolution for these low energy Germanium implants, as in Figure 3.9.
3.4 Summary
This chapter has presented the data obtained through the defect counts performed
on the anneals of amorphizing Ge+ implants into silicon wafers. The data shows no trend
in defect dissolution time in line with increasing dose or energy. The lack of trends is in
agreement with earlier experiments by Gutierrez [14]. In addition, only small point
defects and unstable dislocation loops were observed.
5e14 10keV
1.00E+11
CM4
E
2 1.00E+10
o
4-
1.OOE+09
0 10 20 30 40 50 60 70
time (min)
Figure 3.1 Defect density dissolution and curve fit for 5e14 10keV implant. The curve
equation is listed on the graph.
2e15 10keV
0 10 20 30 40
time (min)
50 60 70
Figure 3.2 Defect density curve for 2e15 10keV implant. The curve equation is listed on
the graph.
1.00E+11
E 1.00E+10
1.00E+09
2e15 5keV
1.00E+11
CMI
E 1.00E+10
1.00E+09
Defect Density
Expon. (Defect Density)
y = 7E+10e-t/157m'n
0 10 20 30 40 50 60 7
time (min)
Figure 3.3 Decay curve for 2e15 5keV implant. The curve equation is listed on the
graph.
5e15 5keV
1.00E+11
Defect Density
S- Expon. (Defect Density)
y Y=7E+10e-t/22 12min
E 1.00E+10
1.00E+09
0 10 20 30 40 50 60 70
Time (min)
Figure 3.4 Dissolution curve for 5e15 5keV implant. The curve equation is on the graph.
Note that this curve has the smallest R2 value (.7456) of the five implants.
5e1510keV
* Defect Density
-Expon. (Defect Density)
0 10 20 30 40 50 60 70
Time (min)
Figure 3.5 Dissolution curve for 5e15
graph.
10keV implant. The curve equation is listed on the
Table 3.1 List of implants done in this work and relevant previous work by Gutierrez. A
starred (*) condition indicates work done by Gutierrez
Implant Dose (cm-2) Implant Energy (keV)
5e14* 5*
5e14 10
le15* 5*
lel5 10*
2e15 5
2e15 10
3e15* 5*
5e15 5
5e15 10
1.00E+12
S1.00E+11
E
U
O 1.00E+10
1.00E+09
Table 3.2 Decay rates and R2 values (a measure of how well the curve fits the data) for
each implant.
Implant Decay Rate (min) R2
5e14 @ 10keV 15.43 .9706
2e15 @ 5keV 15.7 .938
2e15 @ 10keV 28.99 .9587
5e15 @ 5keV 22.12 .7454
5e15 @ 10keV 18.8 .9028
Average 20.21 5.61 min (std dev)
decay rate (min)
implant
Figure 3.6 Decay rates for each implant condition. Note that there is no apparent trend in
dose or energy.
*decay rate (min)
*2e15 @10keV
5e15 @ 5keV
5e14 @10keV
4 2e15 @ 5keV 5e15 @10keV
Data for All Implants
1.OOE+12
1.OOE+11
1.00E+10
1.00E+09
Density
-Expon. (Density)
y = 9E+10e-t/19 12mln
R2 = 0.7779
0 10 20 30 40 50 60 7
Time
Figure 3.7 Graph of data set for all implants together. Curve fit equation and R2 value is
on the graph. Note that a fit of the average value at each anneal time yields
about the same decay rate but an R2 value of 0.9913.
Data Comparison
1 00E+12
1 00E+11
1 00E+10
1 00E+09
1 00E+08
1 00E+07
0 10 20 30 40 50 60 70
time (min)
Figure 3.8 Comparison of data from this work and previous work by Gutierrez [14]. The
data sets follow similar trends with the exception of the 5e14 5keV implant by
Gutierrez. The reader is referred to Table 3.1 for which implants were
performed for this work.
-le15 5keV
-*-- 1e15 10keV
-- e15 1 OkeV
--5e14 5keV
-3e15 5keV
--5e14 10keV
--2e15 10keV
-'- 2e15 5keV
--5e15 5keV
--5e15 10keV
izing
Ge +
Exce Si.
mug
Itkon
U.
Lop act
as trips
Interatlifl
I
Stable Loops
(Leknge current)
Intrstitial
Release
(TED)
Figure 3.9 Germanium implant defect evolution tree [14]. This is an alternate path to the
high energy implants which form stable loops and {311 }'s. The highlighted
grey path is the observed path both here and by Gutierrez.
Amnrp
End-of-i
I
Nam-Amnmphizin
Projeted rane
Loop Rip
and DJinso
.Oe+. Ian Impla.tai (5-10 keV)
terstitials
CHAPTER 4
EFFECTS OF THE SURFACE ON SIMULATED END-OF-RANGE DAMAGE
4.1 Overview
This chapter details experiments made using FLOOPS to investigate the effects of
the free Silicon surface on end-of-range damage, specifically {311} defects. In the first
experiment, the model by Law and Jones [27] was used to simulate damage from
multiple energy implants and a subsequent 750C anneal. For the second set of
simulations, a model by Seebauer et al. [28, 29 30, 31, 32] was incorporated into the Law
and Jones model to create an electric field on the free surface and explore the effects on
{311} evolution, if any. Code for the Seebauer model can be found in Appendix B.
4.2 Surface Reaction Rate Effects on {311}'s
This first simulation experiment explores the effects of the value of the variable
"ksurf' on {311} evolution. The variable "ksurf' is a measure of how quickly silicon
interstitials and di-interstitials recombine at the surface. It is important to know this
effect, since during an annealing step, when {311 }'s begin to dissolve, they release
interstitials which contribute to TED [15, 33]. The interstitials eventually recombine
back into the lattice at the surface or interact with a vacancy to fill a lattice site. The
default value of "ksurf' is
47t*2.7e-8*0.138 exp(-1.37eV/kT)*
{0.51e14 exp(2.63eV/kT)/[1.0e15 + 0.51 exp(2.63eV/kT)} 4.1
which is 47n multiplied by the lattice spacing which makes up a capture radius for the
defects, default interstitial diffusivity, and kink-site density, and where k is Boltzmann's
constant and T is temperature. The kink-site density is limited by the denominator inside
the braces { }. It represents a limit to the number of capture sites available at the surface
and the energy required to reincorporate an interstitial. The default value for "ksurf' is
set at 6e-19 cm/s for interstitials flowing to a silicon/silicon dioxide interface. This value
is greatly increased for this experiment to observe its effects.
The physics behind the "ksurf' variable can be thought of as a Deal-Grove type
kinetic model with relation to the surface which is similar to the linear-parabolic model of
silicon oxidation. Using this model, the "ksurf' variable can be thought of as controlling
the limiting process in {311} dissolution just as oxide thickness is the limiting step in
oxide growth [1]. In other words, when "ksurf' is very large, the dissolution rate is
limited by the source of the interstitial, i.e. the defect population. In this regime, the
release of interstitials from the defects is the limiting step in defect dissolution, since they
will immediately diffuse to the surface and recombine. For very deep damage layers,
dissolution also depends on the diffusion length to the surface, which could be a
competing factor to interstitial release for the limiting step. This is comparable to the
linear oxidation regime in which surface reaction is the limiting step. When "ksurf' is
small, the limiting factor for interstitial recombination at the surface is the diffusion
length and the recombination rate, meaning that interstitials will not necessarily be able to
recombine as soon as they reach the surface. In this case, however, the interstitials are
likely diffusing more into the bulk than toward the surface, which would be an even
greater limiting step. For this reason, the decay rates for the different energies are very
close. This behavior is comparable to the parabolic oxidation regime where diffusion to
the silicon/oxide interface limits oxide growth. It is, therefore, comparable to change
"ksurf' to vary the distance to the surface, which is thought to control the dissolution rate
of {311} defects [15, 25, 34].
The model addresses {311 evolution and sub-micron interstitial clusters
(SMIC's) which influence TED [4, 15, 23, 27, 33]. The model is based on experimental
data by Law and Jones, and the observations that {311 defects dissolve at a nearly
constant rate (2.3nm/min at 770C) due to the constant end-size of the defect, and that the
population decays proportionally to the interstitial loss rate and inversely to the size of
the defect. In addition, the defect size is not dependent on energy. The dissolution rate is
a function of the interstitial release rate rather than interstitial diffusion to the surface
[27].
The model specifically solves for the number of trapped interstitials in the defects
and the total number of defects, referred to as C311 and D311, respectively. The defects
begin nucleation during the implant, and are simulated using UT-Marlowe and the kinetic
accumulation damage model. The defects begin as small {311 }'s or SMIC's, and then
either grow in the case of {311 }'s or dissolve to the surface for SMIC's. The capture and
release of interstitials by {311 }'s happens only at the end of the defect and is therefore
proportional to the number of defects in the population, D311, hence the nearly constant
dissolution rate. Moreover, this means that the dissolution rate is also dependent on
defect size for a given number of trapped interstitials, C311, since a larger defect
population has fewer defects and therefore fewer ends at which interstitials can be
released. The following equations model the described behavior.
dC311/dt = D311(CI C311Eq) / T311 4.2
dD311/dt = [-D311*C311 Eq/ 311 ]* D311/C311 4.3
dCsMic/dt = CsMIc(CI CSMIC Eq)/ TSMIC 4.4
The above equations use energetic proposed by Cowern [35], and the SMIC's have a
dissolution energy of 3.1eV and the total dissolution energy for the {311}'s is 3.77eV.
The final term in equation 4.3 is the inverse of the average size which accounts for the
observation of the smaller defect populations dissolving faster. For comparisons to
experimental data the reader is referred to [27] and the data included in [23].
The model was used for simulations of 40, 80, and 160keV Si+ implants into silicon
and a subsequent anneal of 135 minutes at 750C. Of interest is the value for T311 which
is the decay rate constant.
The data trends can be seen in Figure 4.1. From this graph, a slight decrease in
dissolution time can be observed when "ksurf' is increased to le-6 cm/s. The data can be
found in Table 4.1. At this point, all the implants undergo a rapid decrease in dissolution
times. Simulations were also performed for "ksurf' with values of le-20 and le10 for
several of the implants. That data is not included in the figure to improve the scale, and
because the values are very close in value to the value at the presented endpoints.
4.3 Effects of a Surface Field on {311}'s
This set of simulations uses a modified version of the model found in section 4.2.
The defect kinetics for the {311 and SMIC type defects remains unchanged. What is
added is a new effect of band-bending at the surface that is a result of the silicon/oxide
interface [28, 29, 30, 31, 32]. Figure 4.2 shows how the band-bending functions in p-
type silicon. The band-bending is attributed to defects created at the interface which lead
to bond rupture [28]. The resulting degree of band-bending is about 0.5eV at a maximum
[28, 29]. The band-bending persisted for all annealing times and temperatures performed
by Seebauer at al [29]. The band-bending is used to explain the pile-up of electrically
active boron within Inm of the interface as well as deepening of the junction depth
because the near-interface electric field repels charged interstitials. For more detail on
the behavior of boron in this model, the reader is referred to work in [28, 29, 30, 31, 32].
Of interest in this model are two important aspects. The first is the changes to the
surface modeling using new terms to determine a surface annihilation probability for
interstitials. The second is a new form of Poisson's equation with new boundary
conditions to set up the near-surface band-bending.
For the surface modeling, a new fraction controls the ability of the surface to act
as either a reflector or sink. The fractionfis then incorporated into a parameter S = 1-f
which is an annihilation probability [29]. The nature of the surface is then controlled by
the following equation.
-Dj dCj,x-o/ dx = Dj (S*Cj, xAx)/ Ax = kr Cj, x Ax 4.5
where Ax represents a point in the bulk and Cj is the concentration of the dopant species.
For this equation, a value off= 1 (S = 0) corresponds to a perfect reflector andf= 0 (S =
1) corresponds to a perfect sink. S was modeled as a constant to be fit to experimental
data [29]. The conclusions of Seebauer et al. was that experiments with band-bending
present exhibit a much lower annihilation probability than experiments at flat band [29].
New boundary conditions for Poisson's equation represent an approximation that
the interface Fermi energy is located 0.5eV above the Ev level of the silicon side of the
interface. The approximation is made for computational simplification [29]. The new
boundary conditions are detailed below in the following equations.
'(x = 0,t) = 's 4.6
'(x = 0,t) = Ev (T)/ q + (0.5eV )/ q 4.7
Both equations are presented by Seebauer et al. in [29]. Two regimes were observed: the
first in which band-bending increases to 0.56eV between 300C to 500C, and the second
in which band-bending decreases to zero above roughly 750C. A temperature ramp was
performed to see the effects of the low-temperature regime, but temperature was never
increased past 750C for simulations performed in this work. The variable of interest is
the 'pin' value, which sets the potential in electron volts at the surface. The default value
of this variable is 0.2eV.
The results of the simulations can be seen below in Figures 4.3 and 4.4. Figure
4.3 is a graphical representation of the potential produced by the Seebauer modifications.
A very low energy B implant was used as the electrically active species to produce this
curve. For figure 4.4, the 40keV implant condition was used from the previous section
with a "ksurf" value of le-6 cm/s. As can be seen, the pin value has no trend in its effect
on the dissolution rate of the {311} defects. All values fall within two standard
deviations of the average value of 67.6 minutes. This result is not surprising, since the
modifications are intended to influence electrically active dopants, not silicon interstitials
released from {311 }'s. This is not much different than the value for the simulations
without the new Poisson equation and boundary conditions, which was a value of 64.03
minutes.
4.4 Summary
This chapter has presented several surface effects on the {311} defect population. The
varying of the "ksurf' variable, which controls the recombination rate of interstitials and
di-interstitials at the surface, was varied for implants of 40, 80, and 160keV implants at a
-2
dose of le15 cm-2. There was little change in the 40, 80, and 160keV implants until a
"ksurf' value of le-6 cm/s, when a sharp drop occurred but leveled out for larger values.
For the second set of simulations, a near-surface electrical field was introduced
and the pinned potential value at the surface varied for the 40keV implant condition with
a "ksurf' value of le-6 cm/s. The {311} dissolution time had no apparent influence from
the surface field or a changing pin value at the surface.
Ksurf vs Tau
--40 keV
-4-80 keV
S1 AI 160 kev
_I A
1 00E-11 1 00E-10 1 00E-09 1 00E-08 1 00E-07 1 00E-06 1 00E-05 1 00E-04 1 00E-03 1 00E-02 1 00E-01 1 00E+00
ksurf value (cmns)
Figure 4.1 Effect of changing "ksurf' for each implant energy on the dissolution time of
{311} defects.
Table 4.1 Values for Figure 4.1. Values are in minutes
ksurf (cm/s) 40 keV 80 keV 160 keV
le-20 104.14 125.2 n/a
le-11 112.82 140.71 206.55
le-10 109.82 138 208.34
le-8 101.67 132.07 209.6
le-6 64.03 118.28 206.94
le-5 29.42 94.84 162.38
le-2 27.45 77.19 164.35
lelO 28 67.17 n/a
S102 Silicon
Ec
Vs~O.5 eV
-4 SCR .,-
Figure 4.2 Schematic of band bending energy diagram for p-type silicon showing a
narrow space-charge region and its influence on charged particles [29].
Potential
0-
-0 01 02 03 04 5
-0 02
-0 04
-Potential
S-0 06
-0 08--
-01
-0 12
Depth (microns)
Figure 4.3 Potential curve created from a low energy B implant into silicon.
Dissolution Time vs Pin Value
0.1 0.2 0.3 0.4 0.5
Surface Pin (eV)
Figure 4.4 Effect of surface pinning value on the dissolution rate of {311 }'s created by a
lel5 cm-2, 40keV Si+ implant into silicon. There is no apparent trend in the
effect of the surface pin on the dissolution time.
-*--tau vs pin value
CHAPTER 5
CONCLUSIONS AND FUTURE WORK
5.1 Overview
The purpose of this work is twofold: to further explore the effects of the surface on
{311} defect evolution, and to flesh out previous work by Gutierrez [14] regarding the
defect evolution of low-energy amorphizing Ge+ implant into silicon. The exploration of
{311} defect evolution is important because {311 }'s are the major contributing source of
interstitials to TED [1, 4, 15, 23, 33, 36]. By understanding the evolution more
accurately, modeling of the process flow becomes more exact and therefore more useful.
Investigation of the defect evolution resulting from a Ge+ PAI is important since Ge+ is
becoming a popular species for amorphization since it achieves amorphization of the
substrate at lower doses and energies than silicon self-implantation. Understanding the
morphology and evolutionary behavior of these defects is a key step in modeling them.
5.2 Dose and Energy Dependence Experiment
-2
Silicon wafers were implanted with 5keV and 10keV Ge+ at doses of 5e14 cm2,
2e15 cm-2, and 5e15 cm-2. They were subsequently annealed at 750C for 5-60 minutes,
and the defect densities were counted using PTEM micrographs, which can be seen in
Appendix A along with the counting data. All observed defects were small interstitial
clusters and small dislocation loops, both of which were unstable at the anneal
temperature. The defect dissolution was fit to an exponential decay curve for each
implant condition as well as for the data set as a whole. There was no observed
dependence or trend with regards to energy or dose. All decay constants were within two
standard deviations of the average decay constant of 20.21 minutes. The defects were
almost completely dissolved by 60 minutes. The data is in general agreement with
previous work by Gutierrez [14] and the comparison of curves can be found in Figure
3.8. One aspect of note, however, was that the spontaneous combustion observed by
-2
Gutierrez for the 5keV, 5e15 cm-2 implant condition was not observed for similar
conditions in this work.
5.3 Simulated Effects of the Surface on {311} Evolution
Simulations were performed using FLOOPS and model of {311} evolution by Law
and Jones [27] based on experimental data by Saleh et al. [23]. For a detailed explanation
of the model, please refer to Chapter 4. The value of the variable "ksurf' which
represents a surface reaction rate was varied to see the effect on {311} dissolution from
le-10 cm/s to le-2 cm/s. This was done as an alternative to changing the distance to the
surface since {311} dissolution is thought to depend on the distance of the damage layer
to the surface [25]. The simulations were performed on implants of le15 cm-2 Si+ into
silicon with energies of 40, 80, and 160 keV. All implants showed little effect until
"ksurf' was raised to le-6 cm/s, when a steep drop was observed until le-2 cm/s where
the values leveled off.
Additional simulations were performed using the same model but with
modifications by Seebauer et al. [29] which uses an electrical field at the surface to
explain both dopant pile-up and junction broadening of boron implants. The simulations
were performed on the 40keV Si+ implant by setting "ksurf' to le-6 cm/s and changing
the pin value which controls the fixed value of the electrochemical potential at the
silicon/oxide interface. The simulations showed no trend or dependence on the effect of
the pin value in {311} dissolution. All values were consistent with minor variations and
very close to the value obtained in the simulations without the modifications by Seebauer
et al. This is not surprising since the modifications were developed to effect charged ion
species and not silicon interstitials.
5.4 Future Work
Several experiments can be performed in order to make both parts of this work
more conclusive. For the energy and dose dependence study, an attempt to recreate the
-2
conditions of Gutierrez's 5e14 cm-2 5keV implant and the observed spontaneous
combustion around 30 minutes is needed to prove if that condition is anomalous or if a
new regime for defect evolution starts with that condition. Additionally, annealing of the
implant conditions at 825C would provide more data to compare to work by Gutierrez
[14] and King [13].
For the simulation part of this work, some minor additions could be added to
increase the amount of data available for analysis. The simulations with "ksurf" and with
the pin value could be re-run at a lower temperature, to see if the band-bending has more
effect and to compare at other values of"ksurf'. In addition, the simulations with the
electric field could be run for other energies, but it is unlikely that these simulations
would show any trend or influence on the {311} evolution.
APPENDIX A
PTEM IMAGES AND DATA
Figure A.1 PTEM micrographs of a 5e14 1OkeV implant and 750C anneal. Each image
is approximately 20tm across. A) 5 minutes, B) 15 minutes C) 30 minutes D)
45 minutes, E) 60 minutes.
Figure A.2 PTEM micrographs for a 2e15 5keV implant annealed at 750C. Each image
is approximately 20tm across. A) 5 minutes, B) 15 minutes C) 30 minutes,
D) 45 minutes, E) 60 minutes.
Figure A.3 PTEM micrographs for a 2el5 10keV implant and 750C anneal. Each image
is approximately 20tm across. A) 5 minutes, B) 15 minutes, C) 30 minutes,
D) 45 minutes, E) 60 minutes.
Figure A.4 PTEM micrographs of a 5e15 5keV implant annealed at 750C. Each image
is approximately 20tm across. A) 5 minutes, B) 15 minutes, C) 30 minutes,
D) 45 minutes, E) 60 minutes.
q~
2k
-i
t'~
Figure A.5 PTEM micrographs for a 5e15 10keV implant annealed at 750C. Each image
is approximately 20gm across. A) 5 minutes, B) 15 minutes, C) 30 minutes,
D) 45 minutes, E) 60 minutes.
time 5e14
(min) 10keV
5 6.89E+10
15 3.43E+10
30 2.14E+10
45 4.12E+09
60 2.14E+09
2e15
10keV
7.57E+10
4.53E+10
2.43E+10
1.81E+10
1.05E+10
2e15 5keV
5.49E+10
3.80E+10
6.53E+09
3.10E+09
2.20E+09
5e15 5keV
4.51E+10
3.21E+10
2.59E+10
2.20E+10
2.40E+09
5e15
10keV
1.36E+11
5.93E+10
1.42E+10
1.05E+10
7.40E+09
data
average
7.61E+10
4.18E+10
1.85E+10
1.16E+10
4.93E+09
Table A.1 Data set used for graphing figures 3.1-3.8.
APPENDIX B
FLOOPS MODIFICATIONS BY SEEBAUER ET AL.
Note that the real portion of interest is the end of the code which sets the boundary
conditions and the changes to the Poisson Equation.
License Agreement
Copyright 1998-2003 The Board of Trustees of the University of Illinois
All rights reserved.
Developed by: Braatz/Seebauer Research Groups
University of Illinois
http://brahms.scs.uiuc.edu
Permission hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to
deal with the Software without restriction, including without limitation the
rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
sell copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimers.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimers in the
documentation and/or other materials provided with the distribution.
3. The names of Richard Braatz, the Braatz Research Group, the
Multiscale Systems Research Laboratory, Edmund G. Seebauer, the
Seebauer Research Group, the University of Illinois, or the names of its
contributors may not be used to endorse or promote products derived
from this Software without specific prior written permission.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY
OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND
NONINFRINGEMENT. IN NO EVENT SHALL THE CONTRIBUTORS
OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
DEALINGS IN THE SOFTWARE.
proc SurfConc {Sol} {
set y [lindex [lindex [print.ld name=$Sol] 1] 1]
return y
}
proc TEDspike {EBi El Eko Eki Edis clEa2 clEa3 clEa4 clEa5 Emix Btrap Strap Ebb
rate T fudge Name} {
# Initializing
init inf=grid3.str
sel z=1.0 name=f2 store
sel z=1.0 name=f3 store
sel z=1.0 name=f4 store
sel z=1.0 name=f5 store
sel z=1.0 name=BsBi store
sel z=1.0 name=BsI store
sel z=1.0 name=BsBiI store
sel z=1.0 name=BsI2 store
sel z=1.0 name=BsBiI2 store
sel z=1.0 name=BsI3 store
sel z=1.0 name=BsBi2I store
sel z=1.0 name=BsBi2I2 store
sel z=1.0 name=BsBiI3 store
sel z=1.0 name=BsBi3I store
sel z=1.0 name=BsI4 store
# Choosing Poisson Eqn and its boundary condition
pdbSetBoolean Silicon Potential TEDmodel 1
pdbSetBoolean Silicon Potential Pin 0
# define the species to be simulated
solution name=MyBi solve !damp !negative add
solution name=MyBs solve !damp !negative add
solution name=MyI solve !damp !negative add
# define all the parameters diffusivityy, rate of reaction, etc)
# Common parameters (note: Ea is binding energy)
set tempK [pdbDelayDouble tempK]
term name=kb add Silicon eqn = "8.617383e-05"
term name=pi add Silicon eqn = "3.14159e0"
term name=captr add Silicon eqn= "2.73e-8"
term name=alpha add Silicon eqn = "kb*$tempK"
term name=Eg add Silicon eqn = "(1.17e0-(4.73e-
4 *$tempK* $tempK)/($tempK+635.0e0)) "
term name=ni add Silicon eqn= "4.84e5*($tempK/1.5)*exp(-
Eg/(2.0eO*kb*$tempK))"
term name=nu add Silicon eqn = "6.1e12"
# Energy levels
term name=Ei add Silicon eqn
term name=Ev add Silicon eqn
term name=Ec add Silicon eqn
term name=EF add Silicon eqn
"-Potential"
"-Eg/2.0eO-Potential"
"Eg/2.0eO-Potential"
:"0.0"
# Asumme equilibrium electron and hole concentration
term name=Myn add Silicon eqn = "ni*exp((EF-Ei)/(kb*$tempK))"
term name=Myp add Silicon eqn = "ni*exp((Ei-EF)/(kb*$tempK))"
# Trap energies
term name=ESi add Silicon eqn
term name=EBi add Silicon eqn
# population of charged species
# +2 Si interstitial
term name=thlp2 add Silicon eqn
# Neutral Si intersitial
term name=thInl add Silicon eqn:
# +1 Boron interstitial
term name=thBip add Silicon eqn
# -1 Boron interstitial
term name=thBin add Silicon eqn
# Diffusivity
term name=diffBi add Silicon eqn
term name=diffl add Silicon eqn =
"((Eg/1.170e0)*$Strap)+Ev"
"((Eg/1.170e0)*$Btrap)+Ev"
= "1/(1+0.5eO*exp((EF-ESi)/(kb*$tempK)))"
= "1/(1+2e0*exp((ESi-EF)/(kb*$tempK)))"
= "1/(1+exp((EF-EBi)/(kb*$tempK)))"
= "1/(l+exp((EBi-EF)/(kb*$tempK)))"
= "1.Oe-3*exp(-$EBi/(kb*$tempK))"
"1.0e-3*exp(-$EI/(kb*$tempK))"
# Necessary terms to make diffusion equations readable by Floops
# For +/- Boron interstitial
# term name=Bil add Silicon eqn
grad(Potential*thBin*MyBi)"
# term name=Bi2 add Silicon eqn
# term name=Bi3 add Silicon eqn
grad(thBin*MyBi))"
# For +/0 Boron intersitial
term name=Bil add Silicon eqn
term name=Bi2 add Silicon eqn
term name=Bi3 add Silicon eqn
# For 2+/0 Si interstitial
term name=I1 add Silicon eqn =
term name=I2 add Silicon eqn =
term name=I3 add Silicon eqn =
# define the diffusion equations
= "grad(Potential*thBip*MyBi)-
= "(thBip-thBin)*MyBi*grad(Potential)"
= "Potential*(grad(thBip*MyBi)-
= "grad(Potential*thBip*MyBi)"
= "(thBip)*MyBi*grad(Potential)"
= "Potential*(grad(thBip*MyBi))"
"2.0eO*grad(thlp2*Potential*MyI)"
"(2.0eO*thlp2*MyI)*grad(Potential)"
"Potential*grad(2e0*thlp2*MyI)"
pdbSetString Silicon MyBi Equation "ddt(MyBi)-
diffBi*(grad(MyBi)+0.5e0/alpha*(Bi +Bi2-Bi3))"
pdbSetString Silicon MyBs Equation "ddt(MyBs)"
pdbSetString Silicon Myl Equation "ddt(MyI)-diffl*(grad(MyI)+0.5e0/alpha*(I1+I2-
13))"
#BsI intermediate
solution name=BsI solve !damp !negative add
term name=Kassoc add Silicon eqn = "4*pi*captr*(diffl)"
term name=Kko add Silicon eqn = "nu*exp(-$Eko/(kb*$tempK))"
term name=Kdis add Silicon eqn = "6.1el2*exp(-$Edis/(kb*$tempK))"
term name=Kki add Silicon eqn = "nu*exp(-$Eki/(kb*$tempK))"
term name=Rkl add Silicon eqn = "Kassoc*MyI*MyBs-Kdis*BsI"
term name=Rk2 add Silicon eqn = "Kki*MyBi-Kko*BsI"
pdbSetString Silicon BsI Equation "ddt(BsI)-Rkl-Rk2"
set Bieqn [pdbGetString Silicon MyBi Equation]
set Ieqn [pdbGetString Silicon Myl Equation]
set Bseqn [pdbGetString Silicon MyBs Equation]
pdbSetString Silicon Myl Equation "$Ieqn+Rkl"
pdbSetString Silicon MyBi Equation "$Bieqn+Rk2"
pdbSetString Silicon MyBs Equation "$Bseqn+Rkl"
# Cluster Evolution
term name=Ea2 add Silicon eqn
term name=Ea3 add Silicon eqn
term name=Ea4 add Silicon eqn
term name=Ea5 add Silicon eqn
#Interstitial Clusters
solution name=f2 solve !damp
solution name=f3 solve !damp
solution name=f4 solve !damp
solution name=f5 solve !damp
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
!negative add
!negative add
!negative add
!negative add
=KI add Silicon eqn = "4*pi*captr*diffl"
=Kflb add Silicon eqn = "nu*exp(-Ea2/(kb*$tempK))"
=Kf2b add Silicon eqn = "nu*exp(-Ea3/(kb*$tempK))"
=Kf3b add Silicon eqn = "nu*exp(-Ea4/(kb*$tempK))"
=Kf4b add Silicon eqn = "nu*exp(-Ea5/(kb*$tempK))"
=R1 add Silicon eqn = "2*KI*MyI*MyI-Kflb*f2"
=R2 add Silicon eqn = "KI*MyI*f2-Kf2b*f3"
=R3 add Silicon eqn = "KI*MyI*f3-Kf3b*f4"
=R4 add Silicon eqn = "KI*MyI*f4-Kf4b*f5"
pdbSetString Silicon f2 Equation "ddt(f2)-R1+R2"
pdbSetString Silicon f Equation "ddt(f3)-R2+R3"
pdbSetString Silicon f4 Equation "ddt(f4)-R3+R4"
pdbSetString Silicon f5 Equation "ddt(f5)-R4"
set Ieqn [pdbGetString Silicon Myl Equation]
pdbSetString Silicon Myl Equation "$Ieqn+2*R1+R2+R3+R4"
# Boron Cluster
solution name=BsBi solve !damp !negative add
term name=KBi add Silicon eqn = "4*pi*captr*diffBi"
term name=KBlb add Silicon eqn = "nu*exp(-$Ebb/(kb*$tempK))"
term name=RB1 add Silicon eqn = "KBi*MyBi*MyBs-KB b*BsBi"
pdbSetString Silicon BsBi Equation "ddt(BsBi)-RB "
set Bieqn [pdbGetString Silicon MyBi Equation]
set Bseqn [pdbGetString Silicon MyBs Equation]
pdbSetString Silicon MyBi Equation "$Bieqn+RB "
pdbSetString Silicon MyBs Equation "$Bseqn+RB 1"
# Mixed Boron Interstitial Cluster
sel z=1.0 name=BsBiI store
sel z=1.0 name=BsI2 store
sel z=1.0 name=BsBiI2 store
sel z=1.0 name=BsI3 store
"$clEa2"
"$clEa3"
"$clEa4"
"$clEa5"
sel z=1.0 name=BsBi2I store
sel z=1.0 name=BsBi2I2 store
sel z=1.0 name=BsBiI3 store
sel z=1.0 name=BsBi3I store
sel z=1.0 name=BsI4 store
solution name=BsBiI solve !damp !negative add
solution name=BsI2 solve !damp !negative add
solution name=BsBiI2 solve !damp !negative add
solution name=BsI3 solve !damp !negative add
solution name=BsBi2I solve !damp !negative add
solution name=BsBi2I2 solve !damp !negative add
solution name=BsBiI3 solve !damp !negative add
solution name=BsBi3I solve !damp !negative add
solution name=BsI4 solve !damp !negative add
=Km3 add Silicon eqn
=Km4 add Silicon eqn
=Km5 add Silicon eqn
=G1 add Silicon eqn =
=G2 add Silicon eqn =
=G3 add Silicon eqn =
=G4 add Silicon eqn =
=G5 add Silicon eqn =
=G6 add Silicon eqn =
=G7 add Silicon eqn =
=G8 add Silicon eqn =
=G9 add Silicon eqn =
=G10 add Silicon eqn z
=G11 add Silicon eqn z
=G12 add Silicon eqn z
=G13 add Silicon eqn =
= "nu*exp(-Ea3/(kb*$tempK))"
= "nu*exp(-Ea4/(kb*$tempK))"
= "nu*exp(-$Emix/(kb*$tempK))"
"KI*MyI*BsBi-Km3*BsBiI"
"KBi*MyBi*BsI-Km3*BsBiI"
"KI*MyI*BsI-Km3 *BsI2"
"KBi*MyBi*BsI2-Km4*BsBiI2"
"KI*MyI*BsBiI-Km4*BsBiI2"
"KI*MyI*BsI2-Km4*BsI3"
"KBi*MyBi*BsBiI-Km4*BsBi2I"
"KBi*MyBi*BsBi2I-Km5*BsBi3I"
"KI*MyI*BsBi2I-Km5*BsBi2I2"
= "KBi*MyBi*BsBiI2-Km5*BsBi2I2"
= "KI*MyI*BsBiI2-Km5*BsBiI3"
= "KBi*MyBi*BsI3-Km5*BsBiI3"
= "KI*MyI*BsI3-Km5*BsI4"
pdbSetString Silicon BsBil Equation "ddt(BsBiI)-G1-G2+G5+G7"
pdbSetString Silicon BsI2 Equation "ddt(BsI2)-G3+G4+G6"
pdbSetString Silicon BsBiI2 Equation "ddt(BsBiI2)-G4-G5+G10+G11"
pdbSetString Silicon BsI3 Equation "ddt(BsI3)-G6+G12+G13"
pdbSetString Silicon BsBi2I Equation "ddt(BsBi2I)-G7+G8+G9"
pdbSetString Silicon BsBi2I2 Equation "ddt(BsBi2I2)-G9-G10"
pdbSetString Silicon BsBiI3 Equation "ddt(BsBiI3)-G1 l-G12"
pdbSetString Silicon BsBi3I Equation "ddt(BsBi3I)-G8"
pdbSetString Silicon BsI4 Equation "ddt(BsI4)-G13"
set Bieqn [pdbGetString Silicon MyBi Equation]
set Ieqn [pdbGetString Silicon Myl Equation]
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
term name=
set BsBieqn [pdbGetString Silicon BsBi Equation]
set Bsleqn [pdbGetString Silicon BsI Equation]
pdbSetString Silicon MyBi Equation "$Bieqn+G2+G4+G7+G8+G10+G12"
pdbSetString Silicon Myl Equation "$Ieqn+G1+G3+G5+G6+G9+G11 +G13"
pdbSetString Silicon BsBi Equation "$BsBieqn+Gl"
pdbSetString Silicon BsI Equation "$BsIeqn+G2+G3"
#Boundary Conditions
if { [pdbGetBoolean Silicon Potential Pin]} {
pdbSetBoolean Gas_Silicon Potential Fixed_Silicon 1
pdbSetString GasSilicon Potential Equation_Silicon "le20*(Potential_Silicon-
0.2+((1.17e0-(4.73e-4*$tempK*$tempK)/($tempK+635.0e0))/4))"
}
pdbSetString Gas_Silicon Myl Equation_Silicon "(-1.0e-3*exp(-$EI/(8.617383e-
05* $tempK))* $fudge*MyI_Silicon)/5e-9"
pdbSetString Gas_Silicon MyBi Equation_Silicon "(-1.0e-3*exp(-$EBi/(8.617383e-
05*$tempK))*$fudge*MyBi_Silicon)/5e-9"
# Annealing profile
tempramp clear
tempramp name=
tempramp name=
tempramp name=
tempramp name=
tempramp name=
tempramp name=
press=0.0
tempramp name=
tempramp name=
tempramp name=
flatly trate=0.0 time=0.3333 temp=168 press=0.0
-upl trate=135 time=(437-168)/(60.0*135) temp=168 press=0.0
-up2 trate=7.6 time=(492-437)/(60.0*7.6) temp=437 press=0.0
-up3 trate=22 time=(660-492)/(60.0*22) temp=492 press=0.0
-flat2 trate=0.0 time=0.1667 temp=660 press=0.0
-rampup trate=$rate time=($T-660)/(60.0*$rate) temp=660
-downl trate=-64 time=($T-810)/(60.0*64) temp=$T press=0.0
down2 trate=-35 time=(810-600)/(60.0*35) temp=810 press=0.0
down3 trate=-14 time=(600-450)/(60.0* 14) temp=600 press=0.0
foreach step flatlyl upl up2 up3 flat2 rampup down down} {
puts ""
puts ""
puts "!!!!!Doing $step !!!!!"
puts ""
puts ""
diffuse name=$step adapt init= le-10
}
struct outf=$Name
}
#TEDspike {EBi El Eko Eki Edis clEa2 clEa3 clEa4 clEa5 Emix Btrap Strap Ebb rate T
fudge Name}
TEDspike 0.359 0.720 0.408 0.460 0.575
1.790 150 1050 le0 up+_0_2+_0sl
TEDspike 0.359 0.720 0.408 0.460 0.575
1.790 150 1050 le-1 up+_0_2+_0s0.1
TEDspike 0.359 0.720 0.408 0.460 0.575
1.790 150 1050 le-2up+_0_2+_0s0.01
TEDspike 0.359 0.720 0.408 0.460 0.575
1.790 150 1050 le-3 up+_0_2+_0sle-3
TEDspike 0.359 0.720 0.408 0.460 0.575
1.790 150 1050 le-4up+_0_2+_0sle-4
TEDspike 0.359 0.720 0.408 0.460 0.575
1.400 2.192 3.055 3.700 3.500 0.330 0.120
1.400 2.192 3.055 3.700 3.500 0.330 0.120
1.400 2.192 3.055 3.700 3.500 0.330 0.120
1.400 2.192 3.055 3.700 3.500 0.330 0.120
1.400 2.192 3.055 3.700 3.500 0.330 0.120
1.400 2.192 3.055 3.700 3.500 0.330 0.120
1.790 150 1050 le-6 up+_0_2+_0sle-6proc PotentialEqns { Mat Sol } {
set pdbMat [pdbName $Mat]
set Vti {[simGetDouble Diffuse Vti]}
set terms [term list]
if searchrh $terms Charge] == -1} {
term name = Charge add eqn = 0.0 $Mat
}
set Poiss 0
if { [pdblsAvailable $pdbMat $Sol Poisson]} {
if { [pdbGetBoolean $pdbMat $Sol Poisson]} {set Poiss 1}
}
set ni [pdbDelayDouble $pdbMat $Sol ni]
if {! $Poiss} {
set neq "0.5*(Charge+sqrt(Charge*Charge+4*$ni*$ni))/$ni"
term name = Noni add eqn= "exp( Potential*$Vti)" $Mat
term name = Poni add eqn = "exp( -Potential*$Vti)" $Mat
set eq "Potential $Vti log($neq)"
pdbSetString $pdbMat $Sol Equation $eq
} else {
#set a solution variable
set sols [solution list]
if { [search $sols Potential] ==-1} {
solution add name = Potential solve damp negative
}
term name = Noni add eqn
term name = Poni add eqn
: "exp( Potential*$Vti)" $Mat
"exp( -Potential*$Vti)" $Mat
set eps "([pdbDelayDouble $pdbMat $Sol Permittivity] 8.854e-14 / 1.602e-19)"
if {[pdbGetBoolean $pdbMat $Sol TEDmodel]} {
puts "! !!! Using TED Poisson model by Jung and Seebauer!!!!!"
# Our modification
term name=Pos add $Mat eqn = "Myp+thBip*MyBi+2*thlp2*MyI"
# For +/0 boron interstitial
term name=Neg add $Mat eqn = "Myn+MyBs"
# For +/- boron interstitial
# term name=Neg add $Mat eqn = "Myn+MyBs+thBin*MyBi"
set eq "($eps*grad(Potential)+(Pos-Neg))"
} else {
puts "! !!! Using Floops Poisson equation!!!!!"
set eq "($eps grad(Potential) + $ni (Poni Noni) + Charge)"
}
pdbSetString $pdbMat $Sol Equation $eq
}
}
proc Potentiallnit { Mat Sol } {
term name = Charge add eqn = 0.0 $Mat
}
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BIOGRAPHICAL SKETCH
The author was born in Nashville, TN, in 1981. After graduating from
Montgomery Bell Academy in 1999, he attended the University of Florida, where he
earned a B.S. in computer engineering in 2004. He continued his studies at UF in the
graduate school of the Electrical and Computer Engineering department and received his
M.S. in 2006.
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EVOLUTION OF DEFECTS IN AMORPHIZED SILICON By ADRIAN EWAN CAMERON A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006
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Copyright 2006 By Adrian Ewan Cameron
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To Mom, Dad, Evins, and Bill.
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iv ACKNOWLEDGMENTS The author would like to thank his pare nts for their unwavering support throughout his academic career. He would also like to thank his advisor, Dr. Mark Law, for his direction and guidance as well as Dr. Kevin Jones for his work on TEM and his insight and knowledge of this area. The author w ould also like to thank the SWAMP group for their help, especially Renata, Ljubo, Russ, Danny, Michelle, Diane, Erik, Serge, and everyone else who has helped prepare samples, answer questions, take TEM pictures, and teach the author how to use lab equipment. Thanks are also extended to Dr. Scott Thompson for serving on the thesis defense committee. The author would like to thank Zoe for her help and for proofreading. A huge thank you goes to Teresa for keeping the SWAMP group moving and organized so well.
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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES.........................................................................................................viii ABSTRACT....................................................................................................................... ..x CHAPTER 1 INTRODUCTION............................................................................................................1 1.1 Background and Motivation...................................................................................1 1.2 Ion Implantation......................................................................................................4 1.2.1 Ion Stopping.................................................................................................5 1.2.2 Amorphization and Implant Damage...........................................................6 1.3 Damage Annealing.................................................................................................8 1.3.1 Solid-Phase Epitaxy......................................................................................8 1.3.2 End-Of-Range Defect Evolution..................................................................9 1.3.3 Transient Enhanced Diffusion....................................................................10 1.4 Scope and Approach of this Study........................................................................11 2 EXPERIMENTAL AND DATA EXTRACTION PROCEDURES...............................13 2.1 Overview...............................................................................................................13 2.2 TEM and Sample Preparation...............................................................................13 2.3 PTEM Analysis and Data Extraction....................................................................14 2.4 Procedures for Simulation Experiments...............................................................15 3 DOSE AND ENERGY DEPENDENCE EXPERIMENT..............................................17 3.1 Overview...............................................................................................................17 3.2 Results for 750 C Anneals....................................................................................17 3.3 Discussion and Analysis.......................................................................................18 3.4 Summary...............................................................................................................19 4 EFFECTS OF THE SURFACE ON SI MULATED END-OF-RANGE DAMAGE......29
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vi 4.1 Overview...............................................................................................................29 4.2 Surface Reaction Rate Effects on {311}s...........................................................29 4.3 Effects of a Surface Field on {311}s...................................................................32 4.4 Summary...............................................................................................................34 5 CONCLUSIONS AND FUTURE WORK.....................................................................39 5.1 Overview...............................................................................................................39 5.2 Dose and Energy Dependence Experiment..........................................................39 5.3 Simulated Effects of the Surface on {311} Evolution..........................................40 5.4 Future Work..........................................................................................................41 APPENDIX A PTEM IMAGES AND DATA.......................................................................................42 B FLOOPS MODIFICATIONS BY SEEBAUER ET AL................................................47 LIST OF REFERENCES...................................................................................................56 BIOGRAPHICAL SKETCH.............................................................................................59
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vii LIST OF TABLES Table page 1.1 ITRS values for the next several technol ogy nodes for key parameters of interest. MPU is a logic, high-performance, high-production chip.........................................3 3.1 List of implants done in this work a nd relevant previous work by Gutierrez. A starred (*) condition indicat es work done by Gutierrez...........................................24 3.2 Decay rates and R2 values (a measure of how well the curve fits the data) for each implant......................................................................................................................25 4.1 Values for Figure 4.1. Values are in minutes...............................................................35 A.1 Data set used for graphing figures 3.1-3.8..................................................................46
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viii LIST OF FIGURES Figure page 1.1 Cross section of a CMOS transistor. (A) Tr ansistor with deep junctions. Depletion regions of source and drain will encr oach on channel, shortening effective channel length. (B) Transist or with shallow junctions. Smaller depletion regions lengthen the effective channel and reduce short-channel effects. Courtesy of Paul Rackary of Intel..................................................................................................4 1.2 Examples of behavior on implanted i ons. A) Tunneling when the ion is not stopped. B) Nuclear stoppi ng, which displaces a lattice atom and can cause secondary damage. C) Non-local electronic stopping of electrica l drag on an ion in a dielectric medium. D) Local elec tronic stopping invol ving collisions of electrons. All figures fr om Plummer et al..................................................................6 1.3 Evolutionary path for Si+ self-implantation in the EOR damage region by Jones.....10 3.1 Defect density dissolution and curve fit for 5e14 10keV implant. The curve equation is listed on the graph..................................................................................20 3.2 Defect density curve for 2e15 10keV implan t. The curve equation is listed on the graph.........................................................................................................................21 3.3 Decay curve for 2e15 5keV implant. The curve equation is listed on the graph........22 3.4 Dissolution curve for 5e15 5keV implant. The curve equation is on the graph. Note that this curve has the smallest R2 value (.7456) of the five implants.............23 3.5 Dissolution curve for 5e15 10keV implant. The curve equation is listed on the graph.........................................................................................................................24 3.6 Decay rates for each implant condition. No te that there is no apparent trend in dose or energy..........................................................................................................25 Figure 3.7 Graph of data set for all implan ts together. Curve fit equation and R2 value is on the graph. Note that a fit of the av erage value at each anneal time yields about the same decay rate but an R2 value of 0.9913...............................................26 3.8 Comparison of data from this work and pr evious work by Gutierrez. The data sets follow similar trends with the exception of the 5e14 5keV implant by Gutierrez.
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ix The reader is referred to Table 3.1 for wh ich implants were performed for this work..........................................................................................................................27 3.9 Germanium implant defect evolution tree. This is an alternate path to the high energy implants which form stable l oops and {311}s. The highlighted grey path is the observed path both here and by Gutierrez..............................................28 4.1 Effect of changing ksurf for each im plant energy on the dissolution time of {311} defects............................................................................................................35 4.2 Schematic of band bending energy diagra m for p-type silicon showing a narrow space-charge region and its infl uence on charged particles.....................................36 4.3 Potential curve created from a low energy B implant into silicon..............................37 4.4 Effect of surface pinning value on the dissolution rate of {311}s created by a 1e15 cm-2, 40keV Si+ implant into silicon. There is no apparent trend in the effect of the surface pin on the dissolution time.....................................................................38 A.1 PTEM micrographs of a 5e14 10keV implant and 750 C anneal. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes C) 30 minutes D) 45 minutes, E) 60 minutes.............................................................................................42 A.2 PTEM micrographs for a 2e 15 5keV implant annealed at 750 C. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes C) 30 minutes, D) 45 minutes, E) 60 minutes.............................................................................................43 A.3 PTEM micrographs for a 2e15 10keV implant and 750 C anneal. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45 minutes, E) 60 minutes.............................................................................................44 A.4 PTEM micrographs of a 5e 15 5keV implant annealed at 750 C. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45 minutes, E) 60 minutes.............................................................................................45 A.5 PTEM micrographs for a 5e15 10keV implant annealed at 750 C. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45 minutes, E) 60 minutes.............................................................................................46
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x Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science EVOLUTION OF DEFECTS IN AMORPHIZED SILICON By Adrian Ewan Cameron August 2006 Chair: Mark E. Law Major Department: Electrical and Computer Engineering In order to maintain the current trend of laterally scaling CMOS transistors for better performance and higher tran sistor density, verti cal dimensions must also be scaled to minimize short channel effects. One way to achieve shallow vertical junctions is through pre-amorphizing implants (PAI) at lo w energy to reduce ion channeling during implantation of the dopant species. These PAI steps create end-of -range (EOR) damage just below the amorphous/crystalline interf ace. Understanding how this EOR damage evolves is important to process modeling and to future technologies. As the PAI energy is reduced, the damage region is placed closer to the surface. The objective of this study is to explore how several aspects of the surf ace affect the evolution of the EOR damage. These aspects include proximity to the surface through lowered implant energy, reaction rates of interstitials at th e surface, and an electrical field set up at the surface. The first experiment in this thesis investigates the EOR damage evolution for several low-energy Ge+ PAIs. Silicon wafers were implanted with Ge+ with doses of
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xi 5e14 cm-2 at 10keV, 2e15 cm-2 at 5 and 10keV, and 5e15 cm-2 at 5 and 10keV. Anneals were performed at 750 C for 5, 15, 30, 45 and 60 minutes Plan-view transmission electron microscopy (PTEM) was used to determ ine that at all conditions, small, unstable dislocation loops were formed in the EOR region. Implant dose and energy seemed to have no effect on trends regard ing the dissolution time of the defects. The results were in general agreement with previous work. Fr om the PTEM analysis, decay time constants were extracted for modeling purposes. In the second experiment in this thes is, a model of {311} evolution was used for FLOOPS simulations. The recombination rate of interstitials at the surface was controlled using the variable ksurf for im plant energies of 40, 80, and 160keV at a dose of 1e15 cm-2. Changing the ksurf variable ha d little effect on the dissolution of {311}s, with a sharp drop around ksurf = 1e-6 cm/s which then levels off for increasing values. An additional part of the second experiment involved adding modifications to the above model. This model uses an electrical field set up by the silic on/oxide interface to explain both pile-up and j unction broadening of boron. The key variable for these simulations is the pin value, which controls the magnitude of the field at the surface. The effect of this field on {311} dissolu tion was investigated for the 40keV implant condition. The results show that the effect doe s not show a trend, but rather no real effect on the decay rate. This is not surprising since the modifications were developed to influence dopant ions and not silicon interstitials.
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1 CHAPTER 1 INTRODUCTION 1.1 Background and Motivation The integrated circuit (IC) has been a part of the growi ng worldwide technology industry since its invention in 1959. The invent ion is credited to Jack Kilby of Texas Instruments and Robert Noyce of Fairchild Semiconductor [1 ]. Since its inception, the integrated circuit has grown in complexity fr om several parts to several hundred million. The reason for this growth is the evol ution of the complementary metal-oxide semiconductor transistor, or CMOS. The tre nd in complexity has followed Moores Law, which predicts that the number of transi stors on an integrated circuit will double approximately every year [2]. Through technological innovation, that law has been anticipated and hurdles overcome so that the prediction has been surprisingly accurate. There are other more tangible benefits to transistor scaling as well. As the minimum feature size decreases, the cost per transistor shrinks as does the cost per function for a given area. In addition, sma ller components require less power to operate and produce less heat, which improves reliabili ty. There are physical limitations which work to counteract these benefits, such as th e escalating cost of re search and development to overcome obstacles like junction leakage, lithographic limitations, and short-channel effects. The bench mark for overcoming technol ogical hurdles and establishing new technologies as cutting edge is th e International T echnology Roadmap for Semiconductors (ITRS). The latest versi on of this map was completed in 2005, and
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2 predicts the needs of the industry for the near and longterm future in all aspects of production, from doping and size requirements to lithography, packaging, metrology, and factory integration for both logic devices a nd memories, both volatile and non-volatile. The ITRS also predicts when new technol ogies should be ready for production and if manufacturing solutions are known or unknown for future requirements. Several of the key features for the next several years can be found in Table 1.1. The convention for labeling a technology node is usually to refer to the minimum feature size, which is normally the gate length of a transistor. Some conventions refer to the physical gate length while others refer to the printed gate length. Regardless of which convention is used, the junction depth for th e source and drain areas are on the same order of magnitude. This work focuses on i ssues pertaining to u ltra-shallow junctions, one of the front-end processes (FEP) in se miconductor production. The need for ultrashallow junctions arises from several issues. First, the ITRS maintains a sheet resistance requirement for the contact area of the source and drain. As the junc tion depth decreases, scaled with gate length, the resistivity incr eases since a deeper junction can incorporate more active carriers and hence lower resistivity. Therefore it is necessary to find ways of implanting more carriers into the shallo w junctions and activate them during the annealing process, which is described late r. Second, shallower junctions improve the short-channel effects of small gate length tran sistors. Figure 1.1 illustrates two transistors with equal gate lengths, but one has shallo w junctions. The depletion region of the shallow junction has less effect on the cha nnel, thereby reducing the effective channel length and the short-channel effects.
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3 Table 1.1 ITRS values for the next severa l technology nodes for key parameters of interest. MPU is a logic, highperformance, high-production chip. Year 2006 2007 2009 2011 2013 DRAM pitch (nm) 70 65 50 40 32 MPU physical gate length (nm) 28 25 20 16 13 Junction depth Xj (nm) 30.8 27.5 22 17.6 n/a S/D extension (nm) 9 7.5 7 5.8 n/a Extension lateral abruptness (nm/decade) 3.5 2.8 2.2 1.8 n/a MPU Functions per chip (Mtransistors) 193 286 386 773 1546 Transistor density, logic (Mtransistors/cm2) 122 154 245 389 617 Transistor density, SRAM (Mtransistors/cm2) 646 827 1348 2187 3532 Equivalent Oxide Thickness (EOT) (nm) 1.84 1.84 1.03 0.75 n/a Vdd (V) 1.1 1.1 1.0 1.0 0.9 Number of mask levels, MPU 33 33 35 35 37 Source: [3]
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4 (A) (B) Figure 1.1 Cross section of a CM OS transistor. (A) Transist or with deep junctions. Depletion regions of source and drain will encroach on channel, shortening effective channel length. (B) Transistor with shallow junctions. Smaller depletion regions lengthen the effective channel and reduce short-channel effects. Courtesy of Pa ul Rackary of Intel. 1.2 Ion Implantation Ion implantation is the current domin ant technology in control of forming source/drain areas as well as threshold shif t implants and source/drain extensions. The dopant ion is accelerated and focused on the wa fer using electric fields. The dose of atoms is controlled by longer implant times or a higher beam current. The energy and
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5 mass of the atoms control the projected range, RP, which is the peak of the dopant profile after implantation. The dopant profile follows a Gaussian statistical distribution [1] described by the equation: C(x) = CP exp( -(x-RP)2 / 2 RP 2 ) 1.1 where CP is the peak concentration predic ted by the dose and the straggle, or RP. X is measured into the substrate with x=0 the su rface of the wafer. Often, implantation is done through a masking oxide for better control of the projected range and the concentration peak, which is usually desi red to be very near the surface. 1.2.1 Ion Stopping As the ion is implanted into the lattice, it must have a force act on it to stop. The two mechanisms for ion stoppage are nuclear st opping and electronic stopping. If the ion is not stopped sufficiently near the surface, it can tunnel deep in to the substrate, deepening the junction depth. Figure 1.2 s hows examples of tunneling, nuclear stopping, and electronic stopping. For nuclear stopping, the ion must collide with an atom in the lattice. The resulting collision can displace the lattice atom and usua lly will if it is a primary collision. The collision can result in a secondary da mage cascade from both the dopant ion and displaced lattice atom. Both atoms can travel deeper into the bulk, or the implanted ion can actually backscatter towa rd the surface. Nuclear stopping causes damage to the lattice, which will be discussed in the next section. There are two types of electronic sto pping: local and non-local. Non-local electronic stopping refers to the drag an ion experiences in a dielectric medium. The illustration for this can be seen in Figure 1.2 (C). An analogy is a particle moving through a viscous medium [1]. Local electron ic stopping involves collisions of electrons
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6 when the implanted ion is close enough to a lattice atom such that the electron wavefunctions overlap [1], causing a momentum transfer. This event is illustrated in Figure 1.2 (D). The dominant mechanism fo r ion stoppage is nuclear stopping for lowenergy implants, and this also has the greatest effect on trajectory. A) B) C) D) Figure 1.2 Examples of behavior on implante d ions. A) Tunneling when the ion is not stopped. B) Nuclear stoppi ng, which displaces a latt ice atom and can cause secondary damage. C) Non-local electron ic stopping of elect rical drag on an ion in a dielectric medium. D) Local electronic stopping i nvolving collisions of electrons. All figures fr om Plummer et al. [1]. 1.2.2 Amorphization and Implant Damage One way to limit the depth of the impl ant profile is through a pre-amorphizing implant, or PAI, which eliminates the possi bility of ion channeling. This implant is performed with a non-dopant atom, usually Si+ or Ge+ such that the electrical characteristics are unchanged, or a co-implanted species such as BF2 + where fluorine is
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7 the amorphizing ion and boron is the dopant. If the dose and energy are sufficiently high enough, the implant will destroy the lattice stru cture and an amorphous layer will now be the top layer of the substrate. Beneath th e amorphous layer a highly damaged layer with a supersaturation of interstitials will exist. Th e damage in this area is classified as TypeII damage by Jones and is referred to as endof-range, or EOR damage [4, 5]. In contrast, Type-I damage occurs for non-amorphizing implan ts close to the concentration peak at the projected range. As a result of the nuclear stopping descri bed above, lattice atoms are displaced from their sites in the crystal structure. Th is creates an interstitia l and a vacancy in the lattice, described as a Frenkel pair [1, 6]. New interstitials can also have secondary collisions with lattice atoms, creating more Fr enkel pairs. Most of the Frenkel pairs will recombine very quickly during the annealing proce ss after implantati on. Interstitials, however, remain in excess in pr oportion to the implan ted dose. This is referred to as the +1 model [7]. These interstitials have no corresponding vacancy and can form clusters and nucleate into larger, more st able defects, since they must either diffuse to the surface or deeper into the bulk. If the implant conditions are of sufficien t energy and dose, am orphization occurs. This event can be considered as a crit ical-point phenomenon where the onset of amorphization leads to cooperative behavior of the defects which greatly accelerates the transition away from a crystalline lattice [8]. When this is the case, the +1 model is no longer very accurate, since the amorphous region consists totally of interstitials with no long-range order and the EOR damage consists of a supersaturation of interstitial point defects created from implanted ions and recoiled atoms from the amorphous region. This
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8 recoil model by Jones [9] predicts a reducti on in EOR density with increasing dose. Robertson et al. [5] found that the total num ber of interstitials in the EOR region was constant with a changing dose rate for an amorphizing Si+ implant with dose of 1e15cm-2. Other research [9, 10, 11] has s hown that the number of inters titials in the EOR region is a function of implant beam energy. Other c onditions such as implant temperature and species also have an impact on EOR forma tion, but no single condition has shown a oneto-one correspondence to EOR density [11]. 1.3 Damage Annealing After the implantation process, the wafer is heated to high temperatures, to repair damage done to the substrate. During this time, the crystal lattice is regrown, a process referred to as solid-phase epitaxy, or SPE. Fr enkel pairs will begin to be annihilated at relatively low temperatures around 400 C [1]. After they recombine, an excess of interstitials still remain, in accordance with the +1 model. These interstitials are not reincorporated into the lattice because the dopant ions take their place and are then electrically active. 1.3.1 Solid-Phase Epitaxy The process of recrystalizing the amorphi zed silicon substrate during annealing is called solid-phase epitaxy (SPE). It is a process of layer-by-layer regrowth from the amorphous/crystalline interface back to the surface. The rate of regrowth is fast, and can be up to 50 nm/min for <100> oriented silicon at 600 C [1]. As recrystallization occurs, the introduced dopant atoms are in corporated into substitution al lattice sites and become electrically active. The rest of the regrown crystal is mo stly defect free, however, a region of large damage just beneath the original amorphous/cryst alline interface can exist. This is the EOR damage region.
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9 1.3.2 End-Of-Range Defect Evolution The interstitials in the EOR damage can e volve into several de fect types depending on the implant and the anneali ng conditions. One such type is the {311} defect, a rodlike structure that inhabits the {311} plane and grows in the <110> direction. As Frenkel pairs are annihilated very quickly, the rema ining interstitials w ill bond to form small clusters. These clusters can form {311} de fects if the implant energy is high enough, or small dislocation loops. King et al. [12], King [13], and Gutierrez [14] have shown that 5keV implant energy is not high enough to nucleate {311}s with Ge+ and that in many cases 10keV may not be enough. If {311}s do fo rm, they can eventu ally dissolve into Frank loops and eventually perfect disloca tion loops. Eaglesham et al. [15] have proposed that the dissolution of the {311} def ects correlated the anomaly of transientenhanced diffusion which depends on inters titials to drastically increase dopant diffusivity for those species which exhibit an interstitialcy-driven di ffusion process such as boron. Additionally, Li and Jones [16] ha ve shown that {311} defects are the source of interstitials for dislocation loops. During annealing the dislocation loop be havior can be described by the Ostwald ripening theory. This theory states that the large dislocation loops gr ow at the expense of the smaller ones, which is a more stable conf iguration [17]. Similar behavior for {311}s has been observed by Stolk et al. [18]. An evolution tree for the case of Si+ implantation can be seen in Figure 1.3. This figure show s the observations from several experiments [15, 16, 18, 19] that the defect s undergo four stages of e volution: nucleation, growth, coarsening, and dissolution.
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10 Figure 1.3 Evolutionary path for Si+ self-implantation in the EOR damage region by Jones [20]. 1.3.3 Transient Enhanced Diffusion Transient enhanced diffusion (TED) is an anomalous process by which the excess of interstitials created duri ng ion implantation greatly enhanced dopant diffusivity for very short time scales. It is important to understand this process so that simulation tools such as FLOOPS (FLorida Object Oriented Process Simulator) [21] can be accurate in their predictions of dopant diffusion.
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11 The source of the interstitial s in TED is thought to come from dissolution of the {311} defects for the non-amorphous implant ca se [15, 18, 22]. For the amorphous case, dislocation loops are also thought to play a role in TED [4, 19 ]. The effect of species, dose, implant energy, and annealing temperat ure on TED has been st udied extensively. Saleh et al. [23] found that TED was de pendent on implant energy for 1e14 cm2 Si+ implants; Eaglesham et al. [24] came to th e same conclusion. This supports findings by Lim et al. [25] that surface etching results in TED reduction, which demonstrates that the surface plays a role in annealing implant dama ge. However, during an anneal after an amorphous implant, the surface is less important since the amorphous layer acts as a diffusion barrier to interstitials in the EOR layer [26]. 1.4 Scope and Approach of this Study The work in this study is divided into two major parts. The first part deals with expanding the experiment first started by Gu tierrez [14] in exploring the interstitial evolution for low-energy Ge+ amorphizing implants in Chapter 3. Implants of Ge+ at conditions of 5e14cm-2 at 10keV, 2e15cm-2 at 5 and 10keV, and 5e15cm-2 at 5 and 10keV were made into Si wafers. Plan-view TEM is used to observe the defect evolution through a series of anneals at 750 C for 5-60 minutes. The results will be helpful in understanding the EOR kinetic behavior which will lead to improved modeling in process simulators. The second part deals with simulations us ing FLOOPS and the effect of the surface on {311} dissolution in Chapter 4. Two sets of simulations were performed for this work. The first set deals with increasing the surface recombination rate for interstitials to observe how the surface affects the dissolu tion rate of {311}s. A model by Law and Jones [27] is the basis for these simulati ons. The second set of simulations uses
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12 modifications to that model by Seebauer et al. [28, 29, 30, 31, 32] which induces an electrical field at the silic on surface. The effect of the magnitude of this field is investigated on the {311} di ssolution rate. Finally, further possibilities for experimentation are discussed in Chapter 5.
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13 CHAPTER 2 EXPERIMENTAL AND DATA EX TRACTION PROCEDURES This chapter contains an overview of the methods for sample preparation and data extraction techniques for the dose and energy dependence experiment. 2.1 Overview Implants were performed by Core System s, Inc. into Czochralski-grown (100) wafers. Ge+ was implanted at room temperature at a 7 tilt to reduce ch anneling. Samples were annealed in a nitrogen ambient at 750 C for 5-60 minutes using a quartz tube furnace. A 30-second push-pull technique wa s used to minimize thermal stresses. Implant damage was viewed using a JEOL 200CX transmission electron microscope (TEM). Defect counts were performed us ing scans of negatives created by the TEM using Adobe Photoshop 7. 2.2 TEM and Sample Preparation Transmission electron microscopy is the pr imary way of directly viewing damage from an implant for this experiment. For viewing the damaged specimens from the topdown, plan-view (PTEM) is used. PTEM images allows for defects to be visible in the g220 weak-beam dark-field (W BDF) condition with a g3g diffraction pattern if the dot product of the reciprocal lattice vector and the cross product of th e Burgers vector and dislocation line direction ar e not equal to zero [13]. PTEM samples must be made in order for the microscope to image effectively. They are prepared in the following fashion:
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14 1. A 3mm disc is cut from the annealed sa mple using an ultrasonic disc cutter from Gatan, Inc. The cutter uses a silicon carbide (SiC) abrasive powder and water. The sample is held in pl ace by mounting it to a glass slide with crystal bond. The glass s lide is then held to th e disc cutter stage using double-sided tape. Acetone is used to remove the crystal bond from the sample after cutting. 2. The disc is then thinned by hand usin g a lapping fixture. The sample is mounted face-down (i.e. the implanted side down) to a metal stage using crystal bond. The sample is then th inned with figure-eight motions to ~100 m determined by finger touch and visual inspection. A 15 m slurry of aluminum oxide (Al2O3) and water is used for abrasion on a glass plate. Acetone is again used to cl ean crystal bond off the sample. 3. Specimens are then mounted face-down to a Teflon stage using hot wax, leaving only a small portion of the back side uncovered. The sample is then further thinned using an acid etch of 25% hydrofluoric acid (HF) and 75% nitric acid (HNO3). The sample is etched until a small bright spot is visible through the entire sample surrounded by a reddish area. 4. The etched samples are carefully removed from the Teflon stage and soaked in heptane overnight or until all wax ha s been removed from the sample. 2.3 PTEM Analysis and Data Extraction The images generated from the PTEM can be seen in Appendix A. The defect densities are simply the count of defects in th e observed area. Negatives are scanned into a .bmp file using an Epson Perfection 3490 Photo scanner at 300dpi. Using Adobe Photoshop, a 4cm x 4cm grid, or larger for lower defect densities, is la id over the image. The image is zoomed to an appropriate leve l for easy viewing, and the grid overlay maintains its scale. The defects are then c ounted within a grid s quare and divided by the area to determine the defect density. The negatives are enlarged by a scale of 50,000x by the TEM, so an appropriate factor of 50kx2 for area enlargement is included in the defect counts. The results are averaged over at l east 5 squares on the negatives for each implant and anneal condition. There is an intrinsic +/20% error in this method. For the longer anneals, as fewer defects are counted, the error goes up as the number of samples are reduced and less data is available. This s ource of error could dr amatically change the endpoints and the slope of the fitted curve if th e curve is fit to the error range instead of
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15 the data point. For example, in counti ng the 2e15, 5keV implant at 60 minutes, the number of defects per square was found to be anywhere from zero to twelve, but only four different areas could be counted due to the size of the squares, which was four times as large as the areas used for the five minute images. So, for this example, the defect density of 2.2e9 defects/cm2 was found by counting an averag e of 5.5 defects in an area of 2.5e-9 cm2 (6.25 cm2 on the viewed image with the magnification). Data extraction consists of using Microsoft Excel to fit an exponential curve of the form y = A ex, where x is t/ In this equation, t is the anneal time and is rate of decay. Other methods are also used to explor e the effects of cer tain variables on For example, the prefactor A is averaged for all implants and then the data forced to fit a curve with this new term. In addition, the effect of the 20% error was explored by changing the values of the 5 and 60 minute anneals to both +20% and -20% of the observed value. The changes are then fit with an exponential curve to see the change in the decay rate. The entire data set is also graphed and fit to a curve to find the average value of the decay rate, and to determine if dose, energy, or both have an effect on the decay rate of defects. Comparisons are also made to previous work by Gutierrez [14]. 2.4 Procedures for Simulation Experiments For the work done using simulations, FLOOP S (FLorida Object Oriented Process Simulator) was used along with a defect evolution model by Law and Jones [27]. In the first experiment, the surface reaction rate whic h controls interstitial recombination was shifted. The resulting effect on {311} def ect dissolution was investigated for a Si+ implant into a Silicon substr ate for 40, 80, and 160 keV energies. The value was changed from 1e-11 to 1e-2 cm/s.
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16 For the second simulation experiment code developed by Seebauer was incorporated into the model [29] This code affects the surf ace potential using a modified Poisson equation, setting up an electric field pointing into the bulk. The code added into FLOOPS for these simulations can be found in Appendix B. The effects of the electric field on {311} dissolution was investigated.
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17 CHAPTER 3 DOSE AND ENERGY DEPENDENCE EXPERIMENT This chapter discusses the results of the investigation of defect dissolution dependence on the dose and energy of the pre-amorphizing implant. 3.1 Overview The purpose of this experiment was to further investigate the energy and dose studies previously done by Gutierrez [14]. Im plants were chosen to compliment the 1e15 cm-2 implants at 5 and 10keV a nd the 5keV implants at 5e14 cm-2 and 3e15 cm-2 which Gutierrez studied. Implants in this expe riment were performed at 10keV for 5e14 cm-2, 2e15 cm-2, and 5e15 cm-2, and at 5keV for 2e15 cm-2 and 5e15 cm-2. Table 3.1 lists the implants performed in this work and the re levant implants performed by Gutierrez. Gutierrez has previously reported that th ese low energy implants follow a specific evolutionary pathway that results in small, unstable dislocation loops [14]. These loops dissolve quickly after approxi mately 60 minutes with an anneal temperature of 750 C [14]. Data in this chapter will be shown to be in agreement with previous work. 3.2 Results for 750 C Anneals The data for the defect counts from each implant condition can be viewed in figures 3.1-3.5. These figures plot th e defect density (in #/cm2) against time on a log-linear scale. Data for each figure can be found in Appendix C. In addition, the PTEM images for each annealed implant can be seen in Appendix A, images A.1 through A.5. The images show that the defect types formed ar e small interstitial clusters and dislocation
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18 loops. No {311} defects were observed at any time point. The evolution of the dislocation loops followed an Ostwald-ripeni ng mechanism but did not coarsen greatly. As the graphs show, the defects that are formed in these low-energy implants are not stable. The average decay rate was appr oximately 20 minutes. From this average, and by visual inspection of the PTEM imag es, it can be concluded that the small dislocation loops formed are almost comple tely dissolved by the 60 minute time point for all implant conditions. Table 3.2 lists the decay rate and R2 for each implant taken from the exponential curve fit to the data. From the table below, the data shows a strong fit for all but one of the curves, 5e15cm-2 with 5keV energy. Similarly, only one implant, 2e15cm-2 with 10keV energy, is not within one standard deviation of the average. As mentioned before, the amount of error goes up with fewer defects since the amount of statistical data is less. This could improve the R2 value if the data is fit with larger error bars on the 60-minute data points. 3.3 Discussion and Analysis Further statistical analysis was performe d on the data to determine the trends. Figure 3.6 shows in graphical form the decay ra tes of the five implants together. From this figure it can be seen that no trend exists either by dose or by en ergy of the implant. There are 5keV implants with decay rates larger than th e 10keV implants, as well as a smaller dose implant (2e15 cm-2) with a larger decay rate th an that of the largest dose implants. One would assume that any trend, if present, would indicate that higher energy and higher dose would lead to more damage and longer dissolution time. The data set as a whole was also graphed and fit to a curve. This graph can be seen in Figure 3.7. The decay rate from this curve was found to be 19.12 minutes with an R2
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19 value of 0.778. Comparing this value with a curve fit to an average value at each time point we get a decay rate of 20.79 minutes but an R2 value of 0.9913. In comparison to previous work by Gutierrez, the same trend is noticeable in each data set with the exception of one 5e14 5keV implant by Gutierrez which exhibits a spontaneous combustion beginning around the 45-minute time point and then rapidly dissolving by 60 minutes. Figure 3.8 shows bot h data sets together on the same graph up to the 60 minute anneals. It should be not ed that Gutierrezs or iginal data was not available, so it was extracted from the graphs available in [14]. Also of note is that Gutierrez performed sub-5 minute anneals using an RTA furnace. That data is included in Figure 3.7. In his thesis, Gutierrez also concluded that dose does not have a significant qualitative or quantitative eff ect on defect evolution at low energy [14]. The data presented here supports and affirms that conc lusion. Gutierrez does st ate that there is a heavy dependence on energy for defect behavior [14]. However, there are two regimes for the dependence, and 5-10keV energies e xhibit the same behavior, whereas 30+keV energies form different defect morphologies From the PTEM micrographs in Appendix A and in [14], it is shown that {311}s do not form in the low-energy regime; only small, unstable dislocation loops. Previous work has suggested a pathway for the defect evolution for these low energy Germanium implants, as in Figure 3.9. 3.4 Summary This chapter has presented the data obta ined through the defect counts performed on the anneals of amorphizing Ge+ implants into silicon wafers The data shows no trend in defect dissolution time in line with increa sing dose or energy. The lack of trends is in
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20 agreement with earlier experiments by Gutierr ez [14]. In addition, only small point defects and unstable dislo cation loops were observed. 5e14 10keV y = 1E+11e-t/15.43min1.00E+09 1.00E+10 1.00E+11 010203040506070 time (min)Defects/cm^2 density Expon. (density) Figure 3.1 Defect density dissolution and curv e fit for 5e14 10keV implant. The curve equation is listed on the graph.
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21 2e15 10keV y = 8E+10e-t/28.99min1.00E+09 1.00E+10 1.00E+11 010203040506070 time (min)#/cm^2 Defect Density Expon. (Defect Density) Figure 3.2 Defect density curve for 2e15 10keV im plant. The curve equation is listed on the graph.
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22 2e15 5keV y = 7E+10e-t/15.7min1.00E+09 1.00E+10 1.00E+11 010203040506070 time (min)#/cm^2 Defect Density Expon. (Defect Density) Figure 3.3 Decay curve for 2e15 5keV implant. The curve equation is listed on the graph.
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23 5e15 5keV y = 7E+10e-t/22.12min1.00E+09 1.00E+10 1.00E+11 010203040506070 Time (min)3/cm^2 Defect Density Expon. (Defect Density) Figure 3.4 Dissolution curve for 5e15 5keV implan t. The curve equation is on the graph. Note that this curve has the smallest R2 value (.7456) of the five implants.
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24 5e15 10keV y = 1E+11e-t/18.8min1.00E+09 1.00E+10 1.00E+11 1.00E+12 010203040506070 Time (min)Density (#/cm^2) Defect Density Expon. (Defect Density) Figure 3.5 Dissolution curve for 5e15 10keV implan t. The curve equation is listed on the graph. Table 3.1 List of implants done in this work and relevant previous work by Gutierrez. A starred (*) condition indicat es work done by Gutierrez Implant Dose (cm-2) Implant Energy (keV) 5e14* 5* 5e14 10 1e15* 5* 1e15 10* 2e15 5 2e15 10 3e15* 5* 5e15 5 5e15 10
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25 Table 3.2 Decay rates and R2 values (a measure of how we ll the curve fits the data) for each implant. Implant Decay Rate (min) R2 5e14 @ 10keV 15.43 .9706 2e15 @ 5keV 15.7 .938 2e15 @ 10keV 28.99 .9587 5e15 @ 5keV 22.12 .7454 5e15 @ 10keV 18.8 .9028 Average 20.21 5.61 min (std dev) decay rate (min) 2e15 @ 5keV 2e15 @ 10keV 5e15 @ 5keV 5e15 @ 10keV 5e14 @ 10keV 0 5 10 15 20 25 30 35 0123456 implantmin decay rate (min) Figure 3.6 Decay rates for each implant condition. Note that there is no apparent trend in dose or energy.
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26 Data for All Implants y = 9E+10e-t/19.12minR2 = 0.7779 1.00E+09 1.00E+10 1.00E+11 1.00E+12 010203040506070 TimeDensity Density Expon. (Density) Figure 3.7 Graph of data set for all implan ts together. Curve fit equation and R2 value is on the graph. Note that a fit of the av erage value at each anneal time yields about the same decay rate but an R2 value of 0.9913.
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27 Data Comparison1.00E+07 1.00E+08 1.00E+09 1.00E+10 1.00E+11 1.00E+12 010203040506070 time (min)Defect Density (#/cm^2) 1e15 5keV 1e15 10keV 5e14 5keV 3e15 5keV 5e14 10keV 2e15 10keV 2e15 5keV 5e15 5keV 5e15 10keV Figure 3.8 Comparison of data from this work and previous work by Gutierrez [14]. The data sets follow similar trends with the exception of the 5e14 5keV implant by Gutierrez. The reader is referred to Table 3.1 for which implants were performed for this work.
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28 Figure 3.9 Germanium implant defect evolution tree [14]. This is an al ternate path to the high energy implants which form stable loops and {311}s. The highlighted grey path is the observed pa th both here and by Gutierrez.
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29 CHAPTER 4 EFFECTS OF THE SURFACE ON SI MULATED END-OF-RANGE DAMAGE 4.1 Overview This chapter details experiments made us ing FLOOPS to investigate the effects of the free Silicon surface on end-of-range damage specifically {311} defects. In the first experiment, the model by Law and Jones [27] was used to simulate damage from multiple energy implants and a subsequent 750 C anneal. For the second set of simulations, a model by Seebauer et al. [28, 29 30, 31, 32] was incorporated into the Law and Jones model to create an electric fiel d on the free surface and e xplore the effects on {311} evolution, if any. Code for the Seeb auer model can be found in Appendix B. 4.2 Surface Reaction Rate Effects on {311}s This first simulation experiment explores the effects of the va lue of the variable ksurf on {311} evolution. The variable ksu rf is a measure of how quickly silicon interstitials and di-int erstitials recombine at the surface. It is important to know this effect, since during an ann ealing step, when {311}s begin to dissolve, they release interstitials which contribute to TED [15, 33]. The intersti tials eventually recombine back into the lattice at the su rface or interact with a vacancy to fill a lattice site. The default value of ksurf is 4 *2.7e-8*0.138 exp(-1.37eV/kT)* {0.51e14 exp(2.63eV/kT)/[1.0e15 + 0.51 exp(2.63eV/kT)} 4.1 which is 4 multiplied by the lattice spacing which makes up a capture radius for the defects, default interstitial diffusivity, a nd kink-site density, and where k is Boltzmanns
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30 constant and T is temperature. The kink-site density is limited by the denominator inside the braces {}. It represents a limit to the number of capture sites av ailable at the surface and the energy required to reincorporate an inte rstitial. The default value for ksurf is set at 6e-19 cm/s for interstitials flowing to a silicon/silicon dioxide in terface. This value is greatly increased for this expe riment to observe its effects. The physics behind the ksurf variable can be thought of as a Deal-Grove type kinetic model with relation to the surface which is similar to the linear-parabolic model of silicon oxidation. Using this model, the ksurf variable can be thought of as controlling the limiting process in {311} dissolution just as oxide thickness is the limiting step in oxide growth [1]. In other words, when k surf is very large, the dissolution rate is limited by the source of the interstitial, i.e. the defect population. In this regime, the release of intersti tials from the defects is the limiting step in def ect dissolution, since they will immediately diffuse to the surface and recombine. For very deep damage layers, dissolution also depends on the diffusion le ngth to the surface, which could be a competing factor to interstitial release for th e limiting step. This is comparable to the linear oxidation regime in which surface reacti on is the limiting step. When ksurf is small, the limiting factor for interstitial recombination at the surface is the diffusion length and the recombination rate, meaning that interstitials will not necessarily be able to recombine as soon as they reach the surface. In this case, however, the interstitials are likely diffusing more into the bulk than towa rd the surface, which would be an even greater limiting step. For this reason, the d ecay rates for the differe nt energies are very close. This behavior is co mparable to the parabolic oxidation regime where diffusion to the silicon/oxide interface limits oxide growth. It is, therefore, comparable to change
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31 ksurf to vary the distance to the surface, wh ich is thought to control the dissolution rate of {311} defects [15, 25, 34]. The model addresses {311} evolution a nd sub-micron interstitial clusters (SMICs) which influence TED [4, 15, 23, 27, 33] The model is based on experimental data by Law and Jones, and the observations that {311} defects dissolve at a nearly constant rate (2.3nm/min at 770 C) due to the constant end-si ze of the defect, and that the population decays proportionally to the interstiti al loss rate and inversely to the size of the defect. In addition, the defect size is not dependent on energy. The dissolution rate is a function of the interstitial release rate rath er than interstitial diffusion to the surface [27]. The model specifically solves for the number of trapped interstitials in the defects and the total number of de fects, referred to as C311 and D311, respectively. The defects begin nucleation during the implant, and are simulated using UT-Marlowe and the kinetic accumulation damage model. The defects begin as small {311}s or SMICs, and then either grow in the case of {311}s or dissolve to the surface for SMICs. The capture and release of intersti tials by {311}s happens only at the e nd of the defect and is therefore proportional to the number of defects in the population, D311, hence the nearly constant dissolution rate. Moreover, th is means that the dissolution rate is also dependent on defect size for a given number of trapped interstitials, C311, since a larger defect population has fewer defects and therefore fe wer ends at which interstitials can be released. The following equations model the described behavior. dC311/dt = D311(CI C311 Eq) / 311 4.2 dD311/dt = [-D311*C311 Eq/ 311 ]* D311/C311 4.3
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32 dCSMIC/dt = CSMIC(CI CSMIC Eq)/ SMIC 4.4 The above equations use energetics proposed by Cowern [35], and the SMICs have a dissolution energy of 3.1eV and the total di ssolution energy for the {311}s is 3.77eV. The final term in equation 4.3 is the inverse of the averag e size which accounts for the observation of the smaller defect populations dissolving faster. For comparisons to experimental data the reader is referred to [27] and the data included in [23]. The model was used for simulations of 40, 80, and 160keV Si+ implants into silicon and a subsequent anneal of 135 minutes at 750 C Of interest is the value for 311 which is the decay rate constant. The data trends can be seen in Figure 4.1. From this graph, a slight decrease in dissolution time can be observed when ksurf is increased to 1e-6 cm/s. The data can be found in Table 4.1. At this point, all the impl ants undergo a rapid decrease in dissolution times. Simulations were also performed for ksurf with values of 1e-20 and 1e10 for several of the implants. That data is not included in the fi gure to improve the scale, and because the values are very close in value to the value at the presented endpoints. 4.3 Effects of a Surface Field on {311}s This set of simulations uses a modified version of the model found in section 4.2. The defect kinetics for the {311} and SMIC t ype defects remains unchanged. What is added is a new effect of band-bending at the surface that is a result of the silicon/oxide interface [28, 29, 30, 31, 32]. Figure 4.2 show s how the band-bending functions in ptype silicon. The band-bending is attributed to defects created at th e interface which lead to bond rupture [28]. The resulting degree of band-bending is about 0.5eV at a maximum [28, 29]. The band-bending persisted for all annealing times and temperatures performed by Seebauer at al [29]. The band-bending is used to explain the pile-up of electrically
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33 active boron within 1nm of th e interface as well as deepening of the junction depth because the near-interface elec tric field repels charged interstitials. For more detail on the behavior of boron in this model, the read er is referred to work in [28, 29, 30, 31, 32]. Of interest in this model are two important aspects. The first is the changes to the surface modeling using new terms to determine a surface annihilation probability for interstitials. The second is a new form of Poissons equation with new boundary conditions to set up the n ear-surface band-bending. For the surface modeling, a new fraction f controls the ability of the surface to act as either a reflector or sink. The fraction f is then incorporated into a parameter S = 1f which is an annihilation probability [29]. The nature of the surface is then controlled by the following equation. -Dj dCj,x=0/ dx = Dj (S*Cj, x= x)/ x = kr Cj, x= x 4.5 where x represents a point in the bulk and Cj is the concentration of the dopant species. For this equation, a value of f = 1 (S = 0) corresponds to a perfect reflector and f = 0 (S = 1) corresponds to a perfect sink. S was modele d as a constant to be fit to experimental data [29]. The conclusions of Seebauer et al. was that experi ments with band-bending present exhibit a much lower annihilation proba bility than experiment s at flat band [29]. New boundary conditions for Poissons equa tion represent an approximation that the interface Fermi energy is located 0.5eV above the Ev level of the silicon side of the interface. The approximation is made for co mputational simplification [29]. The new boundary conditions are detailed be low in the following equations. (x = 0,t) = s 4.6 (x = 0,t) = Ev (T)/ q + (0.5eV )/ q 4.7
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34 Both equations are presented by Seebauer et al in [29]. Two regimes were observed: the first in which band-bending increases to 0.56eV between 300 C to 500 C, and the second in which band-bending decrea ses to zero above roughly 750 C. A temperature ramp was performed to see the effects of the low-temperature regime but temperature was never increased past 750 C for simulations performed in this wo rk. The variable of interest is the pin value, which sets the potential in electron volts at the surface. The default value of this variable is 0.2eV. The results of the simulations can be seen below in Figures 4.3 and 4.4. Figure 4.3 is a graphical representation of the potenti al produced by the Seebauer modifications. A very low energy B implant was used as the electrically active species to produce this curve. For figure 4.4, the 40keV implant condi tion was used from the previous section with a ksurf value of 1e-6 cm/s. As can be seen, the pin value has no trend in its effect on the dissolution rate of the {311} defects. All values fall within two standard deviations of the average valu e of 67.6 minutes. This resu lt is not surprising, since the modifications are intended to in fluence electrically active dop ants, not silicon interstitials released from {311}s. This is not much di fferent than the value for the simulations without the new Poisson equation and bounda ry conditions, which was a value of 64.03 minutes. 4.4 Summary This chapter has presented several surface effects on the {311} defect population. The varying of the ksurf variable, which controls the recombination rate of interstitials and di-interstitials at the surface, was varied for implants of 40, 80, and 160keV implants at a dose of 1e15 cm-2. There was little change in th e 40, 80, and 160keV implants until a ksurf value of 1e-6 cm/s, when a sharp drop occurred but leveled out for larger values.
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35 For the second set of simulations, a nea r-surface electrical field was introduced and the pinned potential value at the surface varied for the 40keV implant condition with a ksurf value of 1e-6 cm/s. The {311} di ssolution time had no apparent influence from the surface field or a changi ng pin value at the surface. Ksurf vs Tau1 10 100 1000 1.00E-111.00E-101.00E-091.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+00 ksurf value (cm/s)Tau (min) 40 keV 80 keV 160 kev Figure 4.1 Effect of changing ksurf for each implant energy on the dissolution time of {311} defects. Table 4.1 Values for Figure 4.1. Values are in minutes ksurf (cm/s) 40 keV 80 keV 160 keV 1e-20 104.14 125.2 n/a 1e-11 112.82 140.71 206.55 1e-10 109.82 138 208.34
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36 1e-8 101.67 132.07 209.6 1e-6 64.03 118.28 206.94 1e-5 29.42 94.84 162.38 1e-2 27.45 77.19 164.35 1e10 28 67.17 n/a Figure 4.2 Schematic of band bending ener gy diagram for p-type silicon showing a narrow space-charge region and its in fluence on charged particles [29].
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37 Potential -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 00.10.20.30.40.50.6 Depth (microns)eV Potential Figure 4.3 Potential curve created fro m a low energy B implant into silicon.
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38 Dissolution Time vs Pin Value 66 66.5 67 67.5 68 68.5 69 69.5 70 70.5 71 00.10.20.30.40.50.6 Surface Pin (eV)311 dissolution (min) tau vs pin value Figure 4.4 Effect of surface pinning value on th e dissolution rate of {311}s created by a 1e15 cm-2, 40keV Si+ implant into silicon. There is no apparent trend in the effect of the surface pin on the dissolution time.
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39 CHAPTER 5 CONCLUSIONS AND FUTURE WORK 5.1 Overview The purpose of this work is twofold: to fu rther explore the eff ects of the surface on {311} defect evolution, and to flesh out previous work by Gutierrez [14] regarding the defect evolution of low-energy amorphizing Ge+ implant into silicon. The exploration of {311} defect evolution is important because {31 1}s are the major contributing source of interstitials to TED [1, 4, 15, 23, 33, 36]. By underst anding the evolution more accurately, modeling of the proc ess flow becomes more exact and therefore more useful. Investigation of the defect evolution resulting from a Ge+ PAI is important since Ge+ is becoming a popular species for amorphizati on since it achieves amorphization of the substrate at lower doses and energies than silicon self-implantati on. Understanding the morphology and evolutionary behavior of thes e defects is a key st ep in modeling them. 5.2 Dose and Energy Dependence Experiment Silicon wafers were implanted with 5keV and 10keV Ge+ at doses of 5e14 cm-2, 2e15 cm-2, and 5e15 cm-2. They were subsequently annealed at 750 C for 5-60 minutes, and the defect densities were counted usi ng PTEM micrographs, which can be seen in Appendix A along with the counting data. All observed defects were small interstitial clusters and small dislocation loops, both of which were unstable at the anneal temperature. The defect dissolution was fit to an exponential decay curve for each implant condition as well as for the data set as a whole. There was no observed dependence or trend with regards to energy or dose. All decay constants were within two
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40 standard deviations of the average decay constant of 20.21 minutes. The defects were almost completely dissolved by 60 minutes. The data is in general agreement with previous work by Gutierrez [14] and the comparison of curves can be found in Figure 3.8. One aspect of note, however, was that the spontaneous combustion observed by Gutierrez for the 5keV, 5e15 cm-2 implant condition was not observed for similar conditions in this work. 5.3 Simulated Effects of the Surface on {311} Evolution Simulations were performed using FL OOPS and model of {311} evolution by Law and Jones [27] based on experimental data by Sa leh et al. [23]. For a detailed explanation of the model, please refer to Chapter 4. The value of the variable ksurf which represents a surface react ion rate was varied to see the effect on {311} dissolution from 1e-10 cm/s to 1e-2 cm/s. This was done as an alternative to changing the distance to the surface since {311} dissolution is thought to depend on the distance of the damage layer to the surface [25]. Th e simulations were performed on implants of 1e15 cm-2 Si+ into silicon with energies of 40, 80, and 160 keV. All implants showed little effect until ksurf was raised to 1e-6 cm/s, when a steep drop was observed until 1e-2 cm/s where the values leveled off. Additional simulations were performe d using the same model but with modifications by Seebauer et al. [29] which us es an electrical fiel d at the surface to explain both dopant pile-up and junction broa dening of boron implants. The simulations were performed on the 40keV Si+ implant by setting ksurf to 1e-6 cm/s and changing the pin value which controls the fixed value of the electrochemical potential at the silicon/oxide interface. The simulations showed no trend or dependence on the effect of the pin value in {311} dissolution. All values were consistent with minor variations and
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41 very close to the value obtain ed in the simulations without the modifications by Seebauer et al. This is not surprising since the modifications were de veloped to effect charged ion species and not silicon interstitials. 5.4 Future Work Several experiments can be performed in order to make both pa rts of this work more conclusive. For the energy and dose de pendence study, an attempt to recreate the conditions of Gutierrezs 5e14 cm-2 5keV implant and the observed spontaneous combustion around 30 minutes is needed to prove if that condition is anomalous or if a new regime for defect evolution starts with that condition. Additionally, annealing of the implant conditions at 825 C would provide more data to compare to work by Gutierrez [14] and King [13]. For the simulation part of this work, so me minor additions could be added to increase the amount of data available for anal ysis. The simulations with ksurf and with the pin value could be re-run at a lower temp erature, to see if th e band-bending has more effect and to compare at othe r values of ksurf. In a ddition, the simulations with the electric field could be run for other energi es, but it is unlikely that these simulations would show any trend or infl uence on the {311} evolution.
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42 APPENDIX A PTEM IMAGES AND DATA A B C D E Figure A.1 PTEM micrographs of a 5e14 10keV implant and 750 C anneal. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes C) 30 minutes D) 45 minutes, E) 60 minutes.
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43 A B C D E Figure A.2 PTEM micrographs for a 2e15 5keV implant annealed at 750 C. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes C) 30 minutes, D) 45 minutes, E) 60 minutes.
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44 A B C D E Figure A.3 PTEM micrographs for a 2e15 10keV implant and 750 C anneal. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45 minutes, E) 60 minutes.
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45 A B C D E Figure A.4 PTEM micrographs of a 5e15 5keV implant annealed at 750 C. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45 minutes, E) 60 minutes.
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46 A B C D E Figure A.5 PTEM micrographs for a 5e15 10keV implant annealed at 750 C. Each image is approximately 20 m across. A) 5 minutes, B) 15 minutes, C) 30 minutes, D) 45 minutes, E) 60 minutes. time (min) 5e14 10keV 2e15 10keV 2e15 5keV 5e15 5keV 5e15 10keV data average 5 6.89E+10 7.57E+105.49E+104 .51E+101.36E+11 7.61E+10 15 3.43E+10 4.53E+103.80E+103 .21E+105.93E+10 4.18E+10 30 2.14E+10 2.43E+106.53E+092 .59E+101.42E+10 1.85E+10 45 4.12E+09 1.81E+103.10E+092 .20E+101.05E+10 1.16E+10 60 2.14E+09 1.05E+102.20E+092 .40E+097.40E+09 4.93E+09 Table A.1 Data set used for graphing figures 3.1-3.8.
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47 APPENDIX B FLOOPS MODIFICATIONS BY SEEBAUER ET AL. Note that the real portion of interest is the end of th e code which sets the boundary conditions and the changes to the Poisson Equation. License Agreement Copyright 1998-2003 The Board of Trus tees of the University of Illinois All rights reserved. Developed by: Braatz/Seebauer Research Groups University of Illinois http://brahms.scs.uiuc.edu Permission hereby granted, free of char ge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal with the Software without restriction, including without limitation the rights to use, copy, modi fy, merge, publish, distribute, sublicense, and/or sell copies of the Softwa re, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: 1. Redistributions of source code must retain the above copyright notice, this list of conditions a nd the following disclaimers. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions a nd the following disclaimers in the documentation and/or other material s provided with the distribution. 3. The names of Richard Braatz, the Braatz Research Group, the Multiscale Systems Research Labo ratory, Edmund G. Seebauer, the Seebauer Research Group, the University of Illinois, or the names of its contributors may not be used to e ndorse or promote products derived from this Software without speci fic prior written permission.
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48 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EV ENT SHALL THE CONTRIBUTORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. proc SurfConc {Sol} { set y [lindex [lindex [print.1d name=$Sol] 1] 1] return y } proc TEDspike {EBi EI Eko Eki Edis clEa 2 clEa3 clEa4 clEa5 Emix Btrap Strap Ebb rate T fudge Name} { # Initializing init inf=grid3.str sel z=1.0 name=f2 store sel z=1.0 name=f3 store sel z=1.0 name=f4 store sel z=1.0 name=f5 store sel z=1.0 name=BsBi store sel z=1.0 name=BsI store sel z=1.0 name=BsBiI store sel z=1.0 name=BsI2 store sel z=1.0 name=BsBiI2 store sel z=1.0 name=BsI3 store sel z=1.0 name=BsBi2I store sel z=1.0 name=BsBi2I2 store sel z=1.0 name=BsBiI3 store sel z=1.0 name=BsBi3I store sel z=1.0 name=BsI4 store # Choosing Poisson Eqn and its boundary condition pdbSetBoolean Silicon Potential TEDmodel 1 pdbSetBoolean Silicon Potential Pin 0 # define the species to be simulated
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49 solution name=MyBi solve !damp !negative add solution name=MyBs solve !damp !negative add solution name=MyI solve !damp !negative add # define all the parameters (di ffusivity, rate of reaction, etc) # Common parameters (note: Ea is binding energy) set tempK [pdbDelayDouble tempK] term name=kb add Silicon eqn = "8.617383e-05" term name=pi add Silicon eqn = "3.14159e0" term name=captr add Silicon eqn = "2.73e-8" term name=alpha add Silicon eqn = "kb*$tempK" term name=Eg add Silicon eqn = "(1.17e0-(4.73e4*$tempK*$tempK)/($tempK+635.0e0)) term name=ni add Silicon eqn = "4.84e15*($tempK^1.5)*exp(Eg/(2.0e0*kb*$tempK))" term name=nu add Silicon eqn = "6.1e12" # Energy levels term name=Ei add Silicon eqn = "-Potential" term name=Ev add Silicon eqn = "-Eg/2.0e0-Potential" term name=Ec add Silicon eqn = "Eg/2.0e0-Potential" term name=EF add Silicon eqn = "0.0" # Asumme equilibrium electron and hole concentration term name=Myn add Silicon eqn = "ni*exp((EF-Ei)/(kb*$tempK))" term name=Myp add Silicon eqn = "ni*exp((Ei-EF)/(kb*$tempK))" # Trap energies term name=ESi add Silicon eqn = "((Eg/1.170e0)*$Strap)+Ev" term name=EBi add Silicon eqn = "((Eg/1.170e0)*$Btrap)+Ev" # population of charged species # +2 Si interstitial term name=thIp2 add Silicon eqn = "1/(1+0.5e0*exp((EF-ESi)/(kb*$tempK)))" # Neutral Si intersitial term name=thIn1 add Silic on eqn = "1/(1+2e0*exp((ESi-EF)/(kb*$tempK)))" # +1 Boron interstitial term name=thBip add S ilicon eqn = "1/(1+exp ((EF-EBi)/(kb*$tempK)))" # -1 Boron interstitial term name=thBin add S ilicon eqn = "1/(1+exp ((EBi-EF)/(kb*$tempK)))" # Diffusivity term name=diffBi add S ilicon eqn = "1.0e-3*exp(-$EBi/(kb*$tempK))" term name=diffI add Silicon eqn = "1.0e-3*exp(-$EI/(kb*$tempK))"
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50 # Necessary terms to make diffusion equations readable by Floops # For +/Boron interstitial # term name=Bi1 add Silicon eqn = "grad(Potential*thBip*MyBi)grad(Potential*thBin*MyBi)" # term name=Bi2 add Silicon eqn = "(thBip-thBin)*MyBi*grad(Potential)" # term name=Bi3 add Silicon eqn = "Potential*(grad(thBip*MyBi)grad(thBin*MyBi))" # For +/0 Boron intersitial term name=Bi1 add Silicon eqn = "grad(Potential*thBip*MyBi)" term name=Bi2 add Silic on eqn = "(thBip)*MyBi*grad(Potential)" term name=Bi3 add Silic on eqn = "Potential*(grad(thBip*MyBi))" # For 2+/0 Si interstitial term name=I1 add Silic on eqn = "2.0e0*grad(thIp2*Potential*MyI)" term name=I2 add Silicon eqn = "(2.0e0*thIp2*MyI)*grad(Potential)" term name=I3 add Silic on eqn = "Potential*grad(2e0*thIp2*MyI)" # define the diffusion equations pdbSetString Silicon MyBi Equation "ddt(MyBi)diffBi*(grad(MyBi)+0.5e0/alpha*(Bi1+Bi2-Bi3))" pdbSetString Silicon MyBs Equation "ddt(MyBs)" pdbSetString Silicon MyI Equation "ddt(M yI)-diffI*(grad(MyI)+0.5e0/alpha*(I1+I2I3))" #BsI intermediate solution name=BsI solve !damp !negative add term name=Kassoc add Silicon eqn = "4*pi*captr*(diffI)" term name=Kko add Silicon eqn = "nu*exp(-$Eko/(kb*$tempK))" term name=Kdis add Silicon eqn = "6.1e12*exp(-$Edis/(kb*$tempK))" term name=Kki add Silicon eqn = "nu*exp(-$Eki/(kb*$tempK))" term name=Rk1 add Silicon eqn = "Kassoc*MyI*MyBs-Kdis*BsI" term name=Rk2 add Silicon eqn = "Kki*MyBi-Kko*BsI" pdbSetString Silicon BsI Equation "ddt(BsI)-Rk1-Rk2" set Bieqn [pdbGetString Silicon MyBi Equation] set Ieqn [pdbG etString Silicon MyI Equation] set Bseqn [pdbGetString Silicon MyBs Equation] pdbSetString Silicon MyI Equation "$Ieqn+Rk1" pdbSetString Silicon MyBi Equation "$Bieqn+Rk2" pdbSetString Silicon MyBs Equation "$Bseqn+Rk1" # Cluster Evolution
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51 term name=Ea2 add Silicon eqn = "$clEa2" term name=Ea3 add Silicon eqn = "$clEa3" term name=Ea4 add Silicon eqn = "$clEa4" term name=Ea5 add Silicon eqn = "$clEa5" #Interstitial Clusters solution name=f2 solve !damp !negative add solution name=f3 solve !damp !negative add solution name=f4 solve !damp !negative add solution name=f5 solve !damp !negative add term name=KI add Silicon eqn = "4*pi*captr*diffI" term name=Kf1b add Silicon eqn = "nu*exp(-Ea2/(kb*$tempK))" term name=Kf2b add Silicon eqn = "nu*exp(-Ea3/(kb*$tempK))" term name=Kf3b add Silicon eqn = "nu*exp(-Ea4/(kb*$tempK))" term name=Kf4b add Silicon eqn = "nu*exp(-Ea5/(kb*$tempK))" term name=R1 add Silicon eqn = "2*KI*MyI*MyI-Kf1b*f2" term name=R2 add Silicon eqn = "KI*MyI*f2-Kf2b*f3" term name=R3 add Silicon eqn = "KI*MyI*f3-Kf3b*f4" term name=R4 add Silicon eqn = "KI*MyI*f4-Kf4b*f5" pdbSetString Silicon f2 Equation "ddt(f2)-R1+R2" pdbSetString Silicon f3 Equation "ddt(f3)-R2+R3" pdbSetString Silicon f4 Equation "ddt(f4)-R3+R4" pdbSetString Silicon f5 Equation "ddt(f5)-R4" set Ieqn [pdbG etString Silicon MyI Equation] pdbSetString Silicon MyI Equation "$Ieqn+2*R1+R2+R3+R4" # Boron Cluster solution name=BsBi solve !damp !negative add term name=KBi add Silicon eqn = "4*pi*captr*diffBi" term name=KB1b add S ilicon eqn = "nu*exp(-$Ebb/(kb*$tempK))" term name=RB1 add S ilicon eqn = "KBi*MyBi*MyBs-KB1b*BsBi" pdbSetString Silicon BsBi Equation "ddt(BsBi)-RB1" set Bieqn [pdbGetString Silicon MyBi Equation] set Bseqn [pdbGetString Silicon MyBs Equation] pdbSetString Silicon MyBi Equation "$Bieqn+RB1" pdbSetString Silicon MyBs Equation "$Bseqn+RB1" # Mixed Boron Interstitial Cluster sel z=1.0 name=BsBiI store sel z=1.0 name=BsI2 store sel z=1.0 name=BsBiI2 store sel z=1.0 name=BsI3 store
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52 sel z=1.0 name=BsBi2I store sel z=1.0 name=BsBi2I2 store sel z=1.0 name=BsBiI3 store sel z=1.0 name=BsBi3I store sel z=1.0 name=BsI4 store solution name=BsBiI solve !damp !negative add solution name=BsI2 solve !damp !negative add solution name=BsBiI2 solve !damp !negative add solution name=BsI3 solve !damp !negative add solution name=BsBi2I solve !damp !negative add solution name=BsBi2I2 solve !damp !negative add solution name=BsBiI3 solve !damp !negative add solution name=BsBi3I solve !damp !negative add solution name=BsI4 solve !damp !negative add term name=Km3 add Silicon eqn = "nu*exp(-Ea3/(kb*$tempK))" term name=Km4 add Silicon eqn = "nu*exp(-Ea4/(kb*$tempK))" term name=Km5 add Silicon eqn = "nu*exp(-$Emix/(kb*$tempK))" term name=G1 add S ilicon eqn = "KI*MyI*BsBi-Km3*BsBiI" term name=G2 add S ilicon eqn = "KBi*MyBi*BsI-Km3*BsBiI" term name=G3 add Silicon eqn = "KI*MyI*BsI-Km3*BsI2" term name=G4 add Silic on eqn = "KBi*MyBi*BsI2-Km4*BsBiI2" term name=G5 add S ilicon eqn = "KI*MyI*BsBiI-Km4*BsBiI2" term name=G6 add S ilicon eqn = "KI*MyI*BsI2-Km4*BsI3" term name=G7 add Silic on eqn = "KBi*MyBi*BsBiI-Km4*BsBi2I" term name=G8 add Silic on eqn = "KBi*MyBi*BsBi2I-Km5*BsBi3I" term name=G9 add Silic on eqn = "KI*MyI*BsBi2I-Km5*BsBi2I2" term name=G10 add Silic on eqn = "KBi*MyBi*BsBiI2-Km5*BsBi2I2" term name=G11 add Silic on eqn = "KI*MyI*BsBiI2-Km5*BsBiI3" term name=G12 add Silic on eqn = "KBi*MyBi*BsI3-Km5*BsBiI3" term name=G13 add Silicon eqn = "KI*MyI*BsI3-Km5*BsI4" pdbSetString Silicon BsBiI Equation "ddt(BsBiI)-G1-G2+G5+G7" pdbSetString Silicon BsI2 Equation "ddt(BsI2)-G3+G4+G6" pdbSetString Silicon BsBiI2 Equation "ddt(BsBiI2)-G4-G5+G10+G11" pdbSetString Silicon BsI3 Equation "ddt(BsI3)-G6+G12+G13" pdbSetString Silicon BsBi2I Equation "ddt(BsBi2I)-G7+G8+G9" pdbSetString Silicon BsBi2I2 Equation "ddt(BsBi2I2)-G9-G10" pdbSetString Silicon BsBiI3 Equation "ddt(BsBiI3)-G11-G12" pdbSetString Silicon BsBi3I Equation "ddt(BsBi3I)-G8" pdbSetString Silicon BsI4 Equation "ddt(BsI4)-G13" set Bieqn [pdbGetString Silicon MyBi Equation] set Ieqn [pdbG etString Silicon MyI Equation]
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53 set BsBieqn [pdbGetString Silicon BsBi Equation] set BsIeqn [pdbGetString Silicon BsI Equation] pdbSetString Silicon MyBi Equation "$Bieqn+G2+G4+G7+G8+G10+G12" pdbSetString Silicon MyI Equation "$Ieqn+G1+G3+G5+G6+G9+G11+G13" pdbSetString Silicon BsBi Equation "$BsBieqn+G1" pdbSetString Silicon BsI Equation "$BsIeqn+G2+G3" #Boundary Conditions if {[pdbGetBoolean Silicon Potential Pin]} { pdbSetBoolean Gas_Silicon Potential Fixed_Silicon 1 pdbSetString Gas_Silicon Potential Equa tion_Silicon "1e20*(Potential_Silicon0.2+((1.17e0-(4.73e-4*$tempK*$tempK)/($tempK+635.0e0))/4))" } pdbSetString Gas_Silicon MyI Equation_S ilicon "(-1.0e-3*exp(-$EI/(8.617383e05*$tempK))*$fudge*MyI_Silicon)/5e-9" pdbSetString Gas_Silicon MyBi Equati on_Silicon "(-1.0e-3*exp(-$EBi/(8.617383e05*$tempK))*$fudge*MyBi_Silicon)/5e-9" # Annealing profile temp_ramp clear temp_ramp name=flat1 trate=0.0 time=0.3333 temp=168 press=0.0 temp_ramp name=up1 trate=13 5 time=(437-168)/(60.0*135) temp=168 press=0.0 temp_ramp name=up2 trate=7. 6 time=(492-437)/(60.0*7.6) temp=437 press=0.0 temp_ramp name=up3 trate=22 time=(660-492)/(60.0*22) temp=492 press=0.0 temp_ramp name=flat2 trate=0.0 time=0.1667 temp=660 press=0.0 temp_ramp name=rampup trate=$rate time=($T-660)/(60.0*$rate) temp=660 press=0.0 temp_ramp name=down1 trate= -64 time=($T-810)/(60.0*64) temp=$T press=0.0 temp_ramp name=down2 trate= -35 time=(810-600)/(60.0*35) temp=810 press=0.0 temp_ramp name=down3 trate= -14 time=(600-450)/(60.0*14) temp=600 press=0.0 foreach step {flat1 up1 up2 up3 flat2 rampup down1 down2} { puts "" puts "" puts "!!!!!Doing $step !!!!!" puts "" puts "" diffuse name=$step adapt init=1e-10 } struct outf=$Name } #TEDspike {EBi EI Eko Eki Edis clEa2 clEa 3 clEa4 clEa5 Emix Btrap Strap Ebb rate T fudge Name}
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54 TEDspike 0.359 0.720 0.408 0.460 0.575 1.400 2.192 3.055 3.700 3.500 0.330 0.120 1.790 150 1050 1e0 up+_0_2+_0s1 TEDspike 0.359 0.720 0.408 0.460 0.575 1.400 2.192 3.055 3.700 3.500 0.330 0.120 1.790 150 1050 1e-1 up+_0_2+_0s0.1 TEDspike 0.359 0.720 0.408 0.460 0.575 1.400 2.192 3.055 3.700 3.500 0.330 0.120 1.790 150 1050 1e-2 up+_0_2+_0s0.01 TEDspike 0.359 0.720 0.408 0.460 0.575 1.400 2.192 3.055 3.700 3.500 0.330 0.120 1.790 150 1050 1e-3 up+_0_2+_0s1e-3 TEDspike 0.359 0.720 0.408 0.460 0.575 1.400 2.192 3.055 3.700 3.500 0.330 0.120 1.790 150 1050 1e-4 up+_0_2+_0s1e-4 TEDspike 0.359 0.720 0.408 0.460 0.575 1.400 2.192 3.055 3.700 3.500 0.330 0.120 1.790 150 1050 1e-6 up+_0_2+_0s1e-6proc PotentialEqns { Mat Sol } { set pdbMat [pdbName $Mat] set Vti {[simGetDouble Diffuse Vti]} set terms [term list] if {[lsearch $terms Charge] == -1} { term name = Charge add eqn = 0.0 $Mat } set Poiss 0 if {[pdbIsAvailable $pdbMat $Sol Poisson]} { if {[pdbGetBoolean $pdbMat $Sol Poisson]} {set Poiss 1} } set ni [pdbDela yDouble $pdbMat $Sol ni] if {! $Poiss} { set neq "0.5*(Charge +sqrt(Charge*Charge+4*$ni*$ni))/$ni" term name = Noni add eqn = "exp( Potential*$Vti)" $Mat term name = Poni a dd eqn = "exp( -Potential*$Vti)" $Mat set eq "Potential $Vti log($neq)" pdbSetString $pdbMat $Sol Equation $eq } else { #set a solution variable set sols [solution list] if {[lsearch $sols Potential] == -1} { solution add name = Potential solve damp negative } term name = Noni add eqn = "exp( Potential*$Vti)" $Mat term name = Poni a dd eqn = "exp( -Potential*$Vti)" $Mat
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55 set eps "([pdbDelayDouble $pdbM at $Sol Permittivity] 8.854e-14 / 1.602e-19)" if {[pdbGetBoolean $pdbMat $Sol TEDmodel]} { puts "!!!!!Using TED Poisson model by Jung and Seebauer!!!!!" # Our modification term name=Pos add $Mat eqn = "Myp+thBip*MyBi+2*thIp2*MyI" # For +/0 boron interstitial term name=Neg add $Mat eqn = "Myn+MyBs" # For +/boron interstitial # term name=Neg add $Mat eqn = "Myn+MyBs+thBin*MyBi" set eq "($eps*grad(Potential)+(Pos-Neg))" } else { puts "!!!!!Using Floops Poisson equation!!!!!" set eq "($eps grad(Pot ential) + $ni (Poni Noni) + Charge)" } pdbSetString $pdbMat $Sol Equation $eq } } proc PotentialInit { Mat Sol } { term name = Charge add eqn = 0.0 $Mat }
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56 LIST OF REFERENCES 1. Plummer, J.D., M.D. Deal, P.B. Griffin, Silicon VLSI Technology 2000, Upper Saddle River, NJ: Prentice Hall. 2. Moore, G.E., Electronics. 38 114 (1965). 3. Semiconductor Industry Association, International Technology Roadmap for Semiconductors 2005. San Jose, CA, 2005. 4. Jones, K.S., J. Liu, L. Zhang, V. Krishnamoorthy, R.T. DeHoff, Nuclear Instruments and Methods in Physics Research B. 106 227 (1995). 5. Roberston, L.S., A. Lilak, M.E. Law, K.S. Jones, P.S. Kringhoj, L.M. Rubin, J. Jackson, D.S. Simons, P. Chi, Applied Physics Letters. 71 3105 (1997). 6. Williams, J.S., Materials Science and Engineering A. 253 8 (1998). 7. Giles, M.D., Journal of the Electrochemical Society. 138 1160 (1991). 8. Holland, O.W., S.J. Pennycook, G.L. Albert, Applied Physics Letters. 55 2503 (1989). 9. Jones, K.S., D. Venables, Journal of Applied Phisics. 69 2931 (1991). 10. Laanab, L., C. Bergaud, C. Bonafos, A. Ma rtinez, A. Claverie, Nuclear Instruments and Methods in Physics Research B. 96 236 (1995). 11. Claverie, A., L. Laanab, C. Bonafos, C. Bergaud, A. Martinez, D. Mathiot, Nuclear Instruments and Methods in Physics Research B. 96 202 (1995). 12. King, A.C., A.F. Gutierrez, A.F. Saavedra, K.S. Jones, D.F. Downey, Journal of Applied Physics. 93 2449 (2003). 13. King, A.C., Masters Thesis, University of Florida, 2003. 14. Gutierrez, A.F., Masters Thesis University of Florida, 2001. 15. Eaglesham, D.J., P.A. Stolk, H.-J. Gossmann, J. M. Poate, Applied Physics Letters. 65 2305 (1994).
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57 16. Li, J., K.S. Jones, Applied Physics Letters. 73 3748 (1998). 17. Bonafos, C., D. Mathiot. A. Clav erie, Journal of Applied Physics. 83 3008 (1998). 18. Stolk, P.A., H.-J. Gossmann, D.J. Eaglesham, J.M. Poate, Nuclear Instruments and Methods in Physics Research B. 96 187 (1995). 19. Lampin, E., V. Senez, A. Claver ie, Journal of Applied Physics. 85 8137 (1995). 20. Jones, K.S., Annealing Kinetics of Ion Implanted Damage in Silicon. 2001, Gainesville, FL. 21. Law, M.E., Florida Object Oriented Pr ocess Simulator. Gainesville, FL, 1999. 22. Stolk, P.A., H.-J. Gossmann, D.J. Eaglesha m, D.C. Jacobson, C.S. Rafferty, G.H. Gilmer, M. Jaraiz, J.M. Poate, H.S. Luftman, T.E. Haynes, Journal of Applied Physics. 81 6031 (1997). 23. Saleh, H., M.E. Law, S. Bharatan, K.S. Jones, V. Krishnamoorthy, T. Buyuyklimanli, Applied Physics Letters. 77 112 (2000). 24. Eaglesham, D.J., A. Agarwal, T.E. Haynes, H.-J. Gossman, D.C. Jacobson, J.M. Poate, Nuclear Instruments and Methods in Physics B. 120 1 (1996). 25. Lim, D.R., C.S. Rafferty, F.P. Kl emens, Applied Physics Letters. 67 2302 (1995). 26. Omri, M., C. Bonafos, A. Claverie, A. Nejim, F. Cristiano, D. Alquier, A. Martinez, N.E.B. Cowern, Nuclear Inst ruments and Methods in Physics B. 120 5 (1996). 27. Law, M.E., K.S. Jones, Internationa l Electron Devices Meeting. 511 (2000).5Dev, K., E.G. Seebauer, Surface Science. 550 185 (2004). 28. Dev, K., E.G. Seebauer, Surface Science. 550 185 (2004). 29. Yung, M.Y.L, R. Gunawan, R.D. Braatz, E.G.Seebauer, Journal of Applied Physics. 95 1134 (2004). 30. Dev, K., M.Y.L. Yung, R. Gunawan, R.D. Br aatz, E.G. Seebauer, Physical Review B. 68 (19) (2003). 31. Jung, M.Y.L., C.T.M. Kwok, R.D. Braatz, E.G. Seebauer, Journal of Applied Physics. 97 063520 (2005). 32. Kwok, C.T.M., K. Dev, R.D. Braatz, E.G. Seebauer, Journal of Applied Physics. 98 013524 (2005).
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59 BIOGRAPHICAL SKETCH The author was born in Nashville, TN, in 1981. After graduating from Montgomery Bell Academy in 1999, he attended the University of Florida, where he earned a B.S. in computer engineering in 2004. He continued his studies at UF in the graduate school of the Electri cal and Computer Engineering department and received his M.S. in 2006.
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