ARTICLE IN PRESS
Journal of Crystal Growth 311 (2009) 3195–3203
Contents lists available at ScienceDirect
Journal of Crystal Growth
journal homepage: www.elsevier.com/locate/jcrysgro
Atomistic examinations of the solid-phase epitaxial growth of silicon
B.A. Gillespie , H.N.G. Wadley
Department of Materials Science and Engineering, Wilsdorf Hall, University of Virginia, P.O. Box 400237, Charlottesville, VA 22904, USA
a r t i c l e in fo
abstract
Article history:
Received 3 November 2008
Received in revised form
6 January 2009
Accepted 27 February 2009
Communicated by D.W. Shaw
Available online 17 March 2009
The low-temperature vapor deposition of silicon thin films and the ion implantation of silicon can result
in the formation of amorphous silicon layers on a crystalline silicon substrate. These amorphous layers
can be crystallized by a thermally activated solid-phase epitaxial (SPE) growth process. The
transformations are rapid and initiate at the buried amorphous to crystalline interface within the
film. The initial stages of the transformation are investigated here using a molecular dynamics
simulation approach based upon a recently proposed bond order potential for silicon. The method is
used first to predict an amorphous structure for a rapidly cooled silicon melt. The radial distribution
function of this structure is shown to be similar to that observed experimentally. Molecular dynamics
simulations of its subsequent crystallization indicate that the early stage, rate limiting mechanism
appears to be removal of tetrahedrally coordinated interstitial defects in the nominally crystalline
region just behind the advancing amorphous to crystalline transition front. The activation barriers for
this interstitials migration within the bulk crystal lattice are calculated and are found to be comparable
to the activation energy of the overall solid-phase epitaxial growth process simulated here.
& 2009 Elsevier B.V. All rights reserved.
PACS:
81.15.Np
87.15.ap
61.72.uf
81.10.Jt
61.43.Dq
Keywords:
A1. Computer simulation
A1. Recrystallization
A3. Solid-phase epitaxy
1. Introduction
The synthesis of epitaxial silicon thin films by the lowtemperature condensation of its vapor to form an amorphous
film followed by annealing to create a crystalline structure is
widely utilized during microelectronic device fabrication [1,2].
Amorphous layers can also be formed during ion implantation of
crystalline silicon, and these are also recrystallized by thermal
treatments [3]. This solid-phase epitaxial growth (SPEG) process
proceeds by the thermally induced epitaxial growth of a crystal
seed into the metastable amorphous region [2]. The need to
control point defect populations, dislocation types and densities,
and stacking fault concentrations in films grown by these
processes has stimulated significant interest in the mechanisms
of atomic reassembly at the epitaxial interface.
Thermal annealing experiments indicate the growth rate of the
crystalline phase into an amorphous silicon system obeys Arrhenius
kinetics with single activation energy of 2.7 eV. This is thought to
result from a (unspecified) defect formation energy of 2.4 eV and a
defect migration energy of 0.4 eV [2]. These experimental studies also
indicate that the transformations rates can be rapid. For example, a
2500-Å-thick a-Si film transforms fully to a crystalline structure in
Corresponding author.
E-mail address: [email protected] (B.A. Gillespie).
0022-0248/$ - see front matter & 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.jcrysgro.2009.02.050
2.5 s at a temperature of 725 1C (a growth rate of 0.1 mm/s) [2]. The
SPEG rate can be affected by self-ion bombardment of the films [2].
The ion bombardment of amorphous films results in a lowering of the
activation energy for the SPEG process to 0.18–0.4 eV [4,5]. Bernstein
et al. argue that this low activation energy results from the ion impact
assisted formation of the rate limiting defects. The transformation
from the amorphous to crystalline state of the ion irradiated structure
is then only controlled by the migration of these defects with an
activation energy in the 0.4 eV range [6].
A detailed understanding of the atomistic mechanisms involved in SPEG has been impeded by the difficulties of highresolution imaging of the moving (sometimes very rapidly) buried
interface [7]. Computational modeling has therefore been used to
investigate the SPEG process [6–12]. The use of computational
modeling techniques is restricted by the relatively large number
of atoms (of order 103) that must be used to characterize each
phase [6]. Additionally these systems need to be simulated for an
extended time (41 ns) to observe even the initial movement of
the a–c interface [6]. The use of high fidelity, unbiased parameterfree quantum mechanical calculations such as density functional
theory (DFT), is therefore prohibited [7]. A molecular dynamics
(MD) approach appears the most promising, provided it employs
an interatomic potential that adequately captures the radial and
angular dependences of the interatomic interactions.
A computational study by Motooka et al. employing on the
order of 1000 atoms over a nanosecond timescale and utilizing the
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Tersoff potential [13] found two temperature driven growth
regimes in contrast to the single, experimentally observed
temperature dependency [7]. Their MD results indicated that at
low temperature, SPEG proceeded via a 2-D planar growth
mechanism with an activation energy of 2.6 eV. At higher
temperatures however, {111} facets were formed at the interface
and the activation energy for growth decreased to 1.2 eV.
Bernstein et al. also identified two temperature driven growth
regimes in a study employing an environmentally dependent
interatomic potential (EDIP) [6,14]. However, they report an
activation energy of only 0.470.2 eV at low temperature and an
energy of 2.070.5 eV in the high-temperature regime.
These activation energies are clearly in conflict with the Tersoff
potential predictions. While both studies argue that removal of
lattice defects at the a–c interface is rate limiting, the defect
whose migration controls the transformation rate remained
unclear.
The most recent computational studies of SPEG performed by
Garter and Weber [10–13] have employed both the Tersoff and the
Stillinger–Weber potential [8–12,15,16]. They examined the
morphology of the a–c interface and observed that the interface
is not sharp, but rather extends over a 6–8 atomic monolayer thick
region. They argue that the rearrangement of atomic defects in the
transition region is the limiting atomic mechanism in SPEG. They
also show that the concentration of the defects predicted by the
Tersoff potential is about double that predicted by the Stillinger–Weber approach [16]. It appears that the details of the atomic
reassembly process observed in these studies are affected by the
potential that is used for the simulation.
Here, we use a recently developed bond order potential (BOP)
for silicon and a molecular dynamics simulation method to
examine the initial stages of the amorphous to crystalline
transformation of silicon [17–21]. The BOP is an analytic, manybody interatomic potential derived by coarse graining the
electronic structure within a two-center, tight-binding representation of covalent bonding. This results in an interatomic potential
that explicitly accounts for both the s and p bonding components
of covalent bonding. It also explicitly includes a term to account
for the promotion energy associated with the hybridization of the
atomic orbitals. While the BOP approach to molecular dynamics
simulations is more computationally demanding than many other
potentials, the use of this potential here is motivated by the high
quality of its predictive results for silicon bulk properties (such as
melting temperature and the cohesive energies of a wide range of
structures) and its reasonable estimates for point defect energies
and structures [17].
Computational resource limitations constrain our simulations
with this BOP approach to systems of 1000 atoms and for short
times (1 ns). As a result, the simulation is capable of only
resolving the initial atomic reassembly processes. We note at the
outset that the initial growth rates observed below and in
previous studies of the simulations of the SPEG process in silicon
are several orders of magnitude faster than that observed
experimentally [6–12]. We suspect there exist a SPEG mechanism
that is activated after the initial stage examination is complete.
The discovery of its mechanism awaits much larger timescale MD
simulations.
The atomic scale structure of the amorphous films created
using the BOP have been examined, and are found to contain a
high concentration of both 3 and 5 coordinated atoms. This
indicates that the BOP predicts a highly defected amorphous film
similar to that observed in ion-implanted films. These defects
result in fast diffusion pathways and a correlation is drawn
between removal of interstitial defects at the a–c interface and
rapid epitaxial growth. The BOP-based simulations are then
employed to investigate the activation energy barriers to the
migration of interstitial defects within the bulk. These energy
barriers are observed to be similar to the calculated overall
activation energy for solid-phase epitaxial growth process.
2. Simulation details
A complete description of the development of the bond order
potential can be found in Refs. [17–21]. There are numerous ways
to synthesize amorphous silicon including quenching from the
melt [22], low-temperature vapor deposition [23–25], and ion
bombardment [26,27]. The a-Si films generated by each method
have different atomic scale structures [2]. Amorphous silicon
generated by rapidly cooling the liquid phase results in the
formation of a network of tetrahedrally coordinated atoms with
no long-range order (an ‘‘ideal’’ amorphous film) [22]. Lowtemperature vapor deposited films are amorphous, but also
sometimes contain low-density regions and voids [2]. These are
a consequence of self-shadowing during the deposition process
combined with low atom mobility on the film surface [2]. When
the deposited atoms are unable to significantly migrate across the
surface, the atoms assemble into a random network with no longrange periodicity. Ion implantation causes atoms to be displaced
from their lattice sites by primary and secondary collision
processes [2]. Continuous ion bombardment results in the overlap
of the damage zone of individual impacts eventually leading to a
fully amorphous structure. Amorphous silicon films created by ion
bombardment contain a large concentration of three- and fivefold bonding defects [28].
To prepare a computational amorphous/crystalline (a–c) interface a 23.0375 Å [1 0 1̄] by 43.44 Å [0 1 0] by 23.0375 Å [1 0 1]
volume single crystal was created. This crystal was made up of
1152 atoms distributed in 32 (0 1 0) layers. Periodic boundary
conditions were employed in the [1 0 1̄] and [1 0 1] directions. The
top 24 monolayers were then melted elevating their temperature
to 2000 K for 50 ps (for 25,000 time steps with a time step,
Dt=2 fs), while the bottom 8 monolayers were thermally constrained to 500 K with the lowest two layers rigidly fixed in space.
This resulted in a thin crystalline substrate with a layer of liquid
silicon on top. This system was then quenched to the desired
temperature over a period of 50 ps to create a computational
sample containing a region of crystalline and amorphous material
separated by an amorphous to crystalline interface. This system
was then thermally annealed for 5 ns and the resulting epitaxial
growth rate and rate limiting defect migration energy barriers are
investigated.
The epitaxial growth rate was measured by tracking the rate of
change of the number of crystalline atoms present in the system
by identifying the bonding environment of an atom and that of its
neighbors. In order for an atom to be classified as part of a
crystalline region it was required to maintain, within a tolerance
of 101, the 1091 tetrahedral arrangement of its bonds with its four
nearest neighbors. The increase in the number of atoms that
satisfied this condition gave the epitaxial growth rate in atoms per
unit time interval.
The interstitials present in the crystallized region were also
identified and their diffusion pathways were examined
using molecular statics techniques [29]. Starting from a
given interstitial configuration, the interstitial atom was incrementally moved in the direction of minimum energy along
a path to another interstitial position. After each incremental
movement, the entire system was allowed to relax in energy
around the constrained interstitial atom. This then allowed
the energy along the migration path to be computed and the
energy barrier to interstitial migration within the crystal to be
determined.
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3. The amorphous structure
4. Epitaxial crystallization
The radial distribution function (RDF) for the a-Si film
produced by the rapid solidification simulation is shown in
Fig. 1. The simplest view of amorphous silicon is that of a
continuous random network of tetrahedrally coordinated atoms
[2]. Therefore one would expect that the RDF of an amorphous
structure will display a large slender peak centered near the bulk
silicon equilibrium nearest neighbor distance, followed by
broadened secondary and tertiary peaks. The RDF obtained by
analyzing the quenched structure generally agrees with this
interpretation. The data obtained from the simulation also agree
well with that deduced by experiment [30].
Many of the other interatomic potentials poorly predict the
random tetrahedral network of a-Si, predicting a large number of
3 and 5 coordinated atoms [31]. The inset in Fig. 1 shows the
distribution of atomic coordinations in the amorphous region
predicted by the BOP analysis. The BOP predicts a broad
distribution of atomic coordination’s with a maximum at 4 and
an average of 4.16. While amorphous silicon films are usually
considered a uniform random network of coordination 4 atoms, in
practice the various experimental methods for generating amorphous thin films result in slightly different amorphous states [2].
It should also be noted that the quenching rate plays a significant
role in the a-Si structure. For example, the amorphous film
generated by ion implantation techniques contains many atoms
that are not four-fold coordinated [2]. Spectroscopic studies of
self-implanted a-Si have shown a large concentration of dangling
bonds associated with three-fold coordinated atoms and floating
bonds resulting from five-fold coordinated atoms [28]. The
significant fraction of atoms that do not have four-fold coordination suggest the amorphous region of the BOP simulation is highly
defected. This high concentration of defects suggests that the
(very rapidly cooled) simulated structure is similar to that ion
beam irradiated structures where defects are introduced to the
system by a non-thermal ion collision process.
The quenched computational system was annealed at numerous temperatures between 700 and 950 K and the growth rate of
the a–c interface during the SPEG process was determined. This is
plotted as a function of inverse absolute temperature in Fig. 2. The
growth rate data are reasonably well fitted by an Arrhenius
relation with an activation energy barrier of 0.87 eV. This
activation energy is about twice that experimentally reported
for ion beam irradiated silicon [5]. Earlier simulation studies have
reported a wide range of activation energies [6–12], and it should
be noted that the activation barrier obtained here is comparable to
that observed in simulations employing the Stillinger–Weber
potential and a similar MD cell [12]. Using their environmentally
dependent modeling approach, Bernstein et al. [6] have shown
that the low-temperature activation barrier (0.2 eV) observed in
their simulations corresponds to the migration of defects while
the larger value (2.0 eV) seen at higher temperatures corresponds
to a more complicated process involving defect formation and
diffusion. The a-Si film formed by very rapidly quenching the SiBOP structure contained a large concentration of ‘‘frozen in’’
defects and we suspect this is responsible for our observation of
an activation barrier lying between those of the Bernstein et al.
limits.
To investigate the atomic scale details of the a–c transformation, time resolved atomic structures near the a–c interface for
annealing temperatures of 700 and 900 K are presented in Figs. 3
and 4. They show the advancing amorphous to crystalline front
moving through the amorphous region. It can be seen that the
most recently crystallized region in each time resolved view
consists of a predominantly crystalline lattice containing a high
concentration of interstitial defects. Detailed examination of the
transition region indicates that overlap of the lattice strains of
these interstitial defects eventually gives rise to the continuous
random network of the a-Si layer as one move upwards through
the simulated region.
Fig. 1. Radial distribution function g(r) for a-Si compared to experimental a-Si
data. Inset: the atomic coordination distribution of silicon atoms in the a-Si region
graphed as a percentage of frequency as predicted by simulation.
Fig. 2. Dependence of the SPE growth rate on simulated temperature.
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Fig. 3. Snapshots of the simulated silicon system at T=700 K. The transition region is characterized by a predominantly crystalline lattice with a high concentration of
interstitial defects. These interstitial defects can be seen here and are typically tetrahedrally coordinated. (a) t=0 ps, (b) t=l00 ps, (c) t=200 ps, and (d) t=300 ps.
To investigate the influence of these remnant defects upon the
advance of the a–c interface we have plotted the number of
crystallized atoms in the simulated structure against transformation time for a transformation at 800 K, Fig. 5. It can be seen that
the growth of the crystalline phase is unsteady with sudden
jumps in transformation rate interspersed by periods of
significantly slower transformation. The overall growth rate of
the crystalline phase is therefore limited by the atomistic
rearrangements occurring during these periods of low
crystalline growth. An examination of the atomic structure of
the system before and just after a shift from a slow to fast growth
mode reveals that the velocity jump occurs upon elimination of an
interstitial atom in the crystalline phase just behind the transition
region. This occurred for all of the simulated temperatures. An
example of such a rapid crystallization after the elimination of a
near interface defect can be clearly seen in the time resolved
atomic structures of Fig. 4(c) and (d). This result is in qualitative
agreement with the conclusions of Lu et al. who argued that
removal of defects residing at the a–c interface was the rate
controlling mechanism for SPEG [28].
To characterize the nature of the defects within the partially
crystallized system, we have calculated bond angle distributions
functions, g(y), for each region, Fig. 6. The angular distribution
function for the transition region, Fig. 6(b), shows a broad
peak centered on the tetrahedral bond angle (1091) with a
shoulder extending towards 751. A small secondary peak is
also evident at a bond angle of 501. We note that a [11 0]-split
type interstitial defect has a bond angle of 501, while a
tetrahedral defect has bonds with an angle of 701 [17]. The
average coordination of these interstitials was obtained by
visually identifying 100 interstitial atoms in the various
simulations and determining their coordinations. This resulted
in an average coordination of 4.05 for the transition region
interstitials. The large angular distribution concentrations at 501
and 751 within the transition region indicate the presence of a
high concentration of defects with configurations that include
those bonding angles, such as the [11 0]-split and tetrahedral
interstitial types. Previous calculations have determined the
formation energy of these point defects to be 3.37 and 2.63 eV,
respectively [17].
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Fig. 4. Snapshots of the simulated silicon system at T=900 K. Tetrahedrally coordinated interstitial defects can be seen at the a–c interface. (a) t=0 ps, (b) t=40 ps, (c) t=70 ps,
and (d) t=100 ps.
The diffusion pathways associated with these two interstitials
have been investigated using a molecular statics approach. We
have employed notational shorthand for the point defects as
follows: silicon vacancy (V), tetrahedral interstitial (T), hexagonal
interstitial (H), and the [11 0]-split interstitial (X). The specific
defect migration pathways that have been examined are presented in Figs. 7–10. These are the V-to-C, T-to-X, T-to-H, and T-toC. It is important to remember that these are intended to be
approximations of the motions encountered at the a–c interface.
These combinations were chosen because each involves a single
defect migrating to either another defect location or to a crystal
lattice site. The energy barriers to motion range from 0.49 to
1.88 eV.
For the defect motions examined here, migration of a vacancy
into an adjacent lattice site had the lowest activation energy. Fig. 7
shows the atom motion that occurs as the vacancy is moved. The
formation energy of the silicon vacancy has been previously
predicted by the BOP to be 2.76 eV. The Si-BOP predicts a volume
decrease of 40% for the silicon vacancy as the adjacent atoms
relax inwards. The migration pathway for the silicon vacancy is
simple; an adjacent atom switches places with the vacancy. The
energy barrier to this motion is 0.49 eV. In more detail, the
adjacent atom, labeled 1 in Fig. 7, moves in a [1̄11̄] direction
towards the vacancy site. At the midpoint of this motion, the third
configuration in Fig. 7c, bonds are formed with 3 new atoms.
Atom 1 after this point has 6 atoms to which it is bonded. As the
atom moves closer to the vacancy site, the original three bonds are
subjected to significant strains (and as are the bonds of atoms
bonded to those atoms as well) and shift inwards toward atom 1.
The original three heavily strained bonds finally break when atom
1 occupies the former vacancy site. The non-symmetric nature of
the energy curve in Fig. 7f reflects this atomic mechanism. The
observed drop in energy when those bonds finally break
corresponds to the relaxation of the stored strain energy in the
original bonds.
The second lowest energy migration pathway involves the
switch between a tetrahedral interstitial and a [11 0]-split
interstitial. This calculation has been performed in two
ways. The first, the T-to-X has atoms T and C, as labeled in
Fig. 8, fixed in space and moved incrementally to the minimum
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Fig. 5. A small excerpt in time showing the thermally driven epitaxial growth of
silicon crystal. The dashed lines highlight the change in growth rate, and can be
used to isolate the rate limiting atomic mechanism to the growth. The solid line
indicates the overall growth rate.
energy configuration of the X interstitial. The second method, the
X-to-C, has atom X1, as labeled in Fig. 8, fixed in space and
incrementally moved into its associated lattice site; atom X2 is
allowed to move freely and as a result minimizes into a
tetrahedral site. In both of these methods all other atoms are
allowed to reach their minimum energy configuration at each
increment. Both methods simulate the motion between a T and X
interstitial configuration. The energy barrier to this migration is
0.75–0.97 eV. Fig. 8 shows the high energy configuration for this
atomic motion. Significant lattice distortions occur in the
neighboring atoms. Because of the very small energy barrier to
migration in the X-to-T direction (0.14 eV) it is unlikely that X type
interstitials will have a long lifespan in simulation.
The third defect migration of interest is the migration of an
interstitial from one tetrahedral site to another tetrahedral site. It
should be noted that the midpoint between any two tetrahedral
sites is a hexagonal site. Therefore, by symmetry, the energetic of
the migration can be fully considered by examining the T-to-H
pathway as shown in Fig. 9. The hexagonal interstitial is predicted
by the Si-BOP to be metastable with an energy of formation of
3.85 eV [17]. Any small thermally induced distortion from perfect
symmetry will result in the hexagonally coordinated interstitial
defect transitioning into a tetrahedral site. As a result the energy
barrier to migration from one tetrahedral site to another is
approximately the same as the difference between their formation
energies, 1.10 eV.
The final and highest energy defect migration examined is for a
tetrahedral coordinated atom to directly displace a neighboring
lattice site atom. This atomic motion is labeled T-to-C. The
tetrahedral interstitial atom is incrementally moved towards a
neighboring lattice atom site. This pushes the crystalline atom out
of its lattice site towards a nearby low energy tetrahedral site (not
the same tetrahedral site that is already occupied). The high
energy configuration of this motion is shown in Fig. 10.
Considerable lattice distortion is encountered in this motion due
to the motion requiring the breaking and reforming of 6 strong
atomic bonds. This atomistic mechanism encounters an energy
barrier of 1.88 eV, considerably higher than any of the other
motions examined.
The above analysis indicates several possible pathways
for a tetrahedral interstitial to migrate to a nearby tetrahedral
Fig. 6. Distribution of bond angles in the crystalline region (a), the transition
region (b) and the amorphous region (c).
interstitial site. The tetrahedral interstitial atom could directly
displace an adjacent crystal atom, pushing that atom into a nearby
tetrahedral site. This motion, the T-to-C mechanism, has been
shown to have a very large energy of activation of 1.88 eV. Another
path migrates the tetrahedral interstitial through a hexagonal
interstitial site. This pathway has been found to have an activation
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Fig. 7. Vacancy migration pathway in the bulk silicon lattice. (a) The initial configuration of the vacancy; the relaxation of the crystal lattice in towards the vacancy is
shown. (b)–(d) The transition configurations 2–4, respectively. (e) The final configuration, identical to the initial except the vacancy has moved to an adjacent lattice site. (f)
The energy barriers to vacancy motion.
barrier of 1.1 eV, which is much lower than the T-to-C mechanism
but still higher than the T-to-X pathway. The lowest energy
pathway for tetrahedral interstitial migration is to first overcome
a 0.75–0.97 eV energy barrier to form a X interstitial. This energy
range is obtained from energy differences in migrating the
interstitial atom in both directions. The X interstitial then
overcomes a 0.14 eV barrier to transform back into a T interstitial
in a new tetrahedral site. Because this last motion has the lowest
energy, it is the mechanism that is most likely to occur.
5. Summary
We have studied the solid-phase epitaxial growth of silicon
using the recently developed bond order potential [17]. The solidphase epitaxial process involves the spontaneous, thermally
activated rearrangement of atomic bonds at the amorphous/
crystal interface [2]. For an ion-implanted amorphous surface,
experimental studies have shown that this process results in the
motion of a sharp a–c interface towards the free surface [2]. The
growth rate of the crystalline region (or the velocity of the a–c
interface) can be well modeled by an Arrhenius relation with
activation energy of 2.7 eV [2]. Ion bombardment introduces
defects into the amorphous film which enhance the growth rate
and reduce the activation energy to 0.18–0.4 eV [6]. The rapid
quenching from the liquid phase method used to obtain the
amorphous film used in the present simulations results in a highly
defected amorphous film. As a result the a-Si found in the present
simulations is similar to an unrelaxed amorphous film under ion
bombardment. The BOP predicts activation energy of 0.87 eV for
the SPE process.
Previous atomistic modeling research has shown that defects
play a key role in SPEG [6–12]. The exact nature of that role has
differed depending on which interatomic potential was employed.
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Fig. 8. Interstitial migration pathway for the T-to-X transition. Interstitial atoms are designated by hollow circles and atoms on different planes are differentiated by
differing size. The interstitial atoms move on the smaller circle atom plane. (a) The tetrahedral intersitial configuration. (b) The configuration of the highest energy. (c) The X
intersitial configuration. (d) The energy barrier to intersitial motion.
Fig. 9. Interstitial migration pathway for the T-to-H transition. The interstitial
atoms are represented by hollow circles. Atoms on different planes are of differing
sizes. (a) The tetrahedral intersitial configuration. (b) The hexagonal intersitial
configuration. (c) The energy barrier to interstitial motion.
The BOP also indicated that defect migration is an essential aspect
of the atomistic mechanism that rate limits the SPE process. The
BOP-based simulations clearly indicate that the rapidly advancing
crystalline front is slowed by the need to remove trapped
interstitials at the interface. These interstitials distort the
surrounding crystal lattice and prevent further crystallization
until they are removed. These interstitials have been found to be
four-fold coordinated, indicating that they are predominantly of
the (11 0)-split (X) and tetrahedral (T) type. The bonding
Fig. 10. Interstitial migration pathway for the T-to-C transition. Atoms in different
planes are represented by circles of differing sizes. The interstitials are shown as
open circles, (a) the tetrahedral interstitial. (b) The atomic structure at the energy
peak. (c) The new tetrahedral interstitial was formed by a lattice site atom. (d) The
energy barrier to this motion.
environment of the transition region in which these interstitials
are found is predominantly crystalline. We therefore believe that
the activation energy for the movement of these interstitials
through a crystalline lattice will be comparable to the activation
energy of their movement in the transition region. The X-to-T
transition was found to have an energy barrier between 0.75 and
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0.97 eV. This energy is comparable to the 0.87 eV activation energy
for SPE as predicted by the BOP. This result suggests that the
annihilation of interstitial defects at the a–c interface is the rate
limiting mechanism for solid-phase epitaxial growth.
Acknowledgements
We gratefully acknowledge the support of this work by DARPA
and ONR under ONR Contract no. N00014-03-C-0288. C. Schwartz
and J. Christodoulou were the program managers.
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