Using density functional theory (DFT) calculations and kinetic simulations, we have investigated the influence of boron atoms on self-interstitial clustering in Si. From DFT calculations of neutral interstitial clusters with a single B atom (BsIn, nIn–1 + BsI) becomes substantially weaker than that of an interstitial (BsIn-->BsIn–1 + I) when n>=4. This implies boron can be liberated while leaving an interstitial cluster behind. Our kinetic simulations including the boron liberation explain well experimental observations reported by J. L. Benton et al., J. Appl. Phys. 82, 120 (1997)

Goddard, William A., III

Hwang, Gyeong S.

English

Caltech Authors - Main

APPLIED PHYSICS LETTERS VOLUME 83, NUMBER 5 4 AUGUST 2003Catalytic role of boron atoms in self-interstitial clustering in Si
Gyeong S. Hwanga) and William A. Goddard IIIb)
Materials and Process Simulation Center (139-74), California Institute of Technology, Pasadena,
California 91125
~Received 13 September 2002; accepted 30 May 2003!
Using density functional theory~DFT! calculations and kinetic simulations, we have investigated
the influence of boron atoms on self-interstitial clustering in Si. From DFT calculations of neutral
interstitial clusters with a single B atom~BsIn, n<4!, we find that the binding of B~BsIn→In21
1BsI) becomes substantially weaker than that of an interstitial~BsIn→BsIn211I) whenn>4. This
implies boron can be liberated while leaving an interstitial cluster behind. Our kinetic simulations
including the boron liberation explain well experimental observations reported by J. L. Benton
et al., J. Appl. Phys.82, 120 ~1997!. © 2003 American Institute of Physics.
@DOI: 10.1063/1.1596729#e
st
e
a
n
in
th
nt
m
e
als
th
e,
c
a
d
in
an
v
,
o
d
ia
tia
a
n
ct
le
a-
ve
the
ers
ial
h of
ity-
-
3
g
y.
sing
o a
si-
re
e
e
s
ber
x-
m
y
-ty
maContinued scaling of Si devices below 0.1mm requires
formation of ultrashallow junctions to avoid short-chann
effects.1 Ultralow-energy ion beams are currently mo
widely used to introduce dopants into the Si substrate. G
erally this must be followed by high-temperature therm
annealing to eliminate substrate damage generated by e
getic ion bombardment and to electrically activate the
jected dopants. During the implantation and annealing,
dopant atoms exhibit transient enhanced diffusion~TED!.
This is a particularly serious problem for boron~a major
p-type dopant!, which exhibits large TED. The conseque
doping profile spreading imposes a great difficulty in for
ing ultrashallow pn junctions in deep submicron devic
structures.
It is now well understood that excess Si self-interstiti
generated during implantation are mainly responsible for
B TED. Due to large mobility even at room temperatur2
single interstitials can diffuse and annihilate at the surfa
Therefore, at the onset of annealing most interstitials
likely to remain in the form of clusters. It is widely believe
that, in ultrashallow junction formation byultralow energy
ion implantation, the main sources for free interstitials dur
postimplantation annealing are small interstitial clusters
boron-interstitial complexes3–6 along with extended$311%
defects. The formation of boron-interstitial complexes ha
been extensively studied using first principles calculations7,8
also supported by recent experiments.9 However, little is
known about the role of single B atoms in the growth
small interstitial clusters.
Deep level transient spectroscopy recently provided
rect evidence for the existence of small Si interstit
clusters.10 These results showed that the small intersti
clusters didnot contain large numbers of B atoms even in
B doped layer~where B concentration wasnot high enough
to induce B clustering!. This was surprising because rece
ab initio calculations7,8 suggested that Si interstitials intera
very strongly with substitutional B to form stable BsI, BsI2 ,
a!Present address: Department of Chemical Engineering, The Universi
Texas, Austin, Texas.
b!Author to whom correspondence should be addressed; electronic
wag@wag.caltech.edu1040003-6951/2003/83(5)/1047/3/$20.00
Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject to Al
n-
l
er-
-
e
-
e
e.
re
g
d
e
f
i-
l
l
t
and BsI3 complexes with large thermal stability comparab
to that of small interstitial clusters.7,8
In order to provide a basis for understanding the form
tion of interstitial clusters in the presence of B, we ha
carried out
~i! first-principles quantum mechanics calculations on
structures and energetics of small interstitial clust
with and without a single B atom and
~ii ! kinetic model based simulations on boron-interstit
concentration variations.
These results suggest that B can catalyze the growt
small Si interstitial clusters.
Our first principles calculations are based on dens
functional theory~DFT! within the local spin density ap
proximation ~LSDA!, as implemented in the CPMD V3.
package.11 We used a nonlocal, norm-conservin
pseudopotential12 and a plane-wave cutoff energy of 20 R
Defect systems considered in this study were modeled u
64-atom supercells with a fixed volume corresponding t
Si–Si bond distance of 2.35 Å in pure Si. The atomic po
tions were allowed to relax fully until all residual forces we
smaller than 531024 Hartree/Bohr. The geometries wer
optimized using only onek point ~G! for the Brillouin-zone
integrations.~The geometry optimization is rather insensitiv
to the number ofk point sets.! However, the total energie
were reevaluated using a (23232) mesh ofk points in the
scheme of Monkhorst–Pack.13
We first examined structure and energetics of a num
of interstitial clusters containing only Si (In , n<3) and con-
taining a single boron atom (BIn , n<4). Figure 1 shows the
fully relaxed structure and LSDA energy for all clusters e
amined. To ensure that we would find the global minimu
~instead of a high-energy local minimum state!, we per-
formed ab initio molecular dynamics followed by energ
minimization for many different initial configurations.
The BsI configuration@Fig. 1~a!# has the Si interstitial~I!
next to the B substitutional (Bs) in a tetrahedral site. The
binding energy between I and Bs is calculated to be 1.14 eV
@virtually identical to 1.160.1 eV obtained in a previous lo
cal density approximation~LDA ! calculation#.15
For BsI2 we find the B to be substitutional with two
of
il:7 © 2003 American Institute of Physics
IP license or copyright, see http://apl.aip.org/apl/copyright.jsp
a
n
o
l
ith
.6
n.
m
o
.4
l-
i
he
n
A
e
r
r-
ding
nter-
ter-
re
in-
a
fol-
of
ly
in
ers
nifi-
t
ysi-
er
ys-
or
ms
-
el
en-
f
of
g
d
ial
tial
re.
on-
of
bo-
his
-
ed
ses
of
im-
r-
on
ron
rs.
nl
1048 Appl. Phys. Lett., Vol. 83, No. 5, 4 August 2003 G. S. Hwang and W. A. Goddard IIIinterstitials on each side~dumbbell! in the C1h symmetry
@Fig. 1~b!#. We find the BsI2 cluster to be quite stable with
binding energy of 1.65 eV~the energy required to release a
interstitial from the BsI2 cluster!. This is consistent with a
recent LDA calculation which leads to a binding energy
1.9 eV between (BsI)
1 and I.7–8
We also identified a stable neutral BsI3 structure@Fig.
1~c!# that appears quite different from the BI3
1 configuration
reported recently by Liuet al.7–8 Two Si lattice atoms~close
to the B atom! are significantly displaced from their origina
position, allowing all bonds to be well reconstructed w
appropriate bond lengths. We obtain a binding energy of 1
eV ~energy required to release an interstitial from the BsI3
cluster!.
Inserting an additional Si interstitial into the BsI3 cluster,
leads to a BsI4 cluster that is also quite stable~a binding
energy of 1.59 eV! toward releasing an interstitial. This BsI4
cluster @Fig. 1~d!# can be visualized as an I3 structure@see
Fig. 1~f!# that is distorted by insertion of an interstitial boro
This result suggests that the presence of B atoms
help the Si interstitials grow into compact configurations. F
crystalline Si, the compact tri-interstitial cluster (I3) has a
formation energy;0.2 eV lower than the ring cluster and 0
eV lower than elongated clusters.16
Figure 1 also shows compact I2 and I3 clusters~fully
relaxed structures!. The I2 and I3 formation energies are ca
culated to be 2.63 and 1.99 eV, respectively~in excellent
agreement with the values of 2.5 and 1.9 eV obtained
recent DFT–LDA calculations!.16 We calculate the formation
energy for a Si self-interstitial to be 3.3 eV, very close to t
result of 3.3–3.35 eV from other DFT–LDA calculations.15
We also examined the possibility of boron liberatio
from the B-containing interstitial clusters. Our DFT–LSD
calculations show that the decay of BsI3 into BsI and I2 re-
quires an energy of 2.0 eV, which is larger than the 1.66
FIG. 1. Structure and energetics of boron-interstitial and interstitial o
clusters examined in this study. Boron is indicated by the hatched ball.Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject to Af
6
ay
r
n
V
for BsI3→BsI21I. @The barrier for boron-interstitial pair dif-
fusion ~0.68 eV!17 is also likely to be larger than that fo
interstitial diffusion ~0.15–0.2 eV!.#18 Thus from BsI3 we
calculate that boron (BsI) liberation is less favorable than
interstitial liberation.
However, for BsI4 , the binding energy of boron (BsI4
→BsI1I3) decreases significantly to 1.0 eV while the inte
stitial binding energy (BsI4→I1BsI3) of 1.60 eV remains
nearly unchanged. These results demonstrate that the bin
energy of boron decreases as the number of integrated i
stitials increases. This is consistent with the very weak in
action between boron and extended$311% defects.7 This bind-
ing energy reduction would allow boron to release mo
favorably than an interstitial from BsIn whenn>4.
These results suggest that boron atoms may catalyze
terstitial agglomeration. That is, boron atoms provide
means to capture and integrate interstitials into a cluster,
lowed by the emission of the boron to facilitate formation
additional interstitial clusters. In this study, we consider on
charge neutral clusters, which may lead to some errors
estimating the binding energies of boron-interstitial clust
~as the cluster structures and energies could change sig
cantly at different charge states!.7,8 However, we believe tha
our results give a reasonable description in the overall ph
cal picture, particularly for boron-interstitial clusters und
near intrinsic conditions~as considered herein!. In fact, cur-
rent first principles calculations on various charge-state s
tems are still quite uncertain.7,8,14
This catalytic reaction may provide an explanation f
the experimental observation that a large fraction of B ato
remains electrically active.~In these experiments, the Si im
plant doses were 13109– 531013 cm22 and the doped B
concentration was about 731015 cm23.)
To illustrate this process we carried out kinetic-mod
based simulations in which we started with a boron conc
tration of 731015 cm23 and added interstitials at a rate o
1016 cm23 s for 10 s to achieve a total concentration
1017 cm23. The interstitial diffusivity is approximated usin
0.0013exp(2Em/kBT), whereEm50.2 eV.
18 The calculated
diffusivity of 331027 cm2/s at room temperature is in goo
agreement with an experimental estimate of>1027 cm2/s.19
Figure 2~a! shows the concentrations of boron-interstit
clusters and self-interstitial clusters after 10 s of intersti
implantation into the boron-doped layer at room temperatu
Here, boron clustering can be ignored due to the low B c
centration. Our simulation result shows that about 97%
the injected interstitials are incorporated into pre-existing
ron sites with just 3% remaining as interstitial clusters. T
ratio is a function of the interstitial injection rate and diffu
sivity; that is, a higher fraction of interstitials is aggregat
into boron-interstitial clusters as the injection rate decrea
and/or the diffusivity increases. Although many details
defect dynamics~such as vacancy formation! are ignored in
our simulation, we see that boron can efficiently capture
planted interstitials to form boron-interstitial complexes du
ing implantation. We expect that this interstitial aggregati
will lead to entrenchment of most boron atoms~if the im-
planted interstitial concentration is far greater than the bo
concentration!. Indeed our simulation results show that~vir-
tually! all boron atoms are embedded in interstitial cluste
y
IP license or copyright, see http://apl.aip.org/apl/copyright.jsp
on
e
-
om
itia
in
n
e
-
at
o
u
al
s
o
i
-
ing
ng
nd
g
ns
ha-
ur
nd
r-
ti-
u-
ron
rs,
ro-
tsu
ful
for
ed
I,
n-
ett.
tt.
pl.
m,
la
ory,
and
M.
ng
er,
s.
ia,
Rev.
L.
m.
. J.
ett.
1049Appl. Phys. Lett., Vol. 83, No. 5, 4 August 2003 G. S. Hwang and W. A. Goddard IIIFigure 2 also shows simulated concentrations of bor
interstitial and self-interstitial clusters after 10 min of subs
quent postimplantation annealing at 500 and 700 °C~with
@Fig. 2~c!# and without @Fig. 2~b!# boron liberation from
boron-interstitial complexes!. In these simulations, we as
sume that the energy barriers for interstitial release fr
boron-interstitial and interstitial clusters are comparable@ap-
proximated as the sum ofEm and Eb ; Em50.2 eV
18 and
Eb (nI)52.722.65@nI
1/22(nI21)
1/2# eV,20 wherenI is the
number of interstitial incorporated#. Without boron liberation
about 100% of boron atoms are still embedded in interst
clusters at 500 °C and;30% are at 700 °C.~The fraction of
substitutional boron decreases with the concentration of
jected interstitials.! On the other hand, when we allow boro
to release~once the boron-interstitial cluster size becom
greater than Bs– I4), virtually all boron atoms recover to sub
stitutional locations. Thus, our simulations demonstr
clearly that without boron liberation, a significant amount
boron would still remain as boron-interstitial clusters~under
the conditions considered in this study!.
Now we suspect that the boron-catalyzed reaction o
lined earlier may facilitate the formation of small interstiti
clusters, especially during implantation and/or early stage
post-implantation annealing. As a result, a larger fraction
interstitials would remain in the substrate. Since B-TED
FIG. 2. The concentrations of boron-interstitial (Bs– In) and self-interstitial
(In) clusters.~a! After 10 s of interstitial implantation,~b!–~c! after 10 min
of subsequent postimplantation annealing at 500 and 700 °C@~b! without
and ~c! with boron liberation from boron-interstitial clusters#.Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject to A-
-
l
-
s
e
f
t-
of
f
s
mainly determined by the availability of interstitials, the in
creased concentration of interstitials would influence dop
profile evolution. This suggests the importance of includi
the B-catalyzed process, along with interstitial clustering a
boron-interstitial complex formation/dissolution, in modelin
ultrashallow junction formation.
In summary, based on our first principles calculatio
and kinetic simulations we propose and validate the mec
nism of boron-catalyzed interstitial cluster formation. O
first principles calculations show the reduction of boron a
interstitial interaction with the number of interstitials inco
porated, leading to boron liberation while leaving an inters
tial cluster. A comparison of experiments with kinetic sim
lations supports the boron liberation. The liberated bo
may then induce formation of additional interstitial cluste
i.e., B-catalyzed interstitial cluster formation.
The authors thank the Seiko-Epson Corporation for p
viding financial support and the authors thank Masami
Uehara and Yuzuru Sato of Seiko-Epson for many help
discussions. G.S.H. also thanks the Welch Foundation
their partial financial support. The facilities of the MSC us
in this work are supported by grants from DOE–ASC
ARO/DURIP, ONR/DURIP, ARO/MURI, ONR/MURI,
IBM, NIH, NSF, ChevronTexaco, Beckman Institute, Ge
eral Motors, and Asahi Kasei.
1E. C. Jones and E. Ishida, Mater. Sci. Eng., R.24, ~1998!, and references
cited therein.
2G. D. Watkins, Phys. Rev. B12, 5824~1975!.
3L. H. Zhang, K. S. Jones, P. H. Chi, and D. S. Simons, Appl. Phys. L
67, 2025~1995!.
4A. D. Lilak, S. K. Earles, M. E. Law, and K. S. Jones, Appl. Phys. Le
74, 2038~1999!.
5E. Schroer, V. Privitera, F. Priolo, E. Napolitani, and A. Carnera, Ap
Phys. Lett.74, 3996~1999!.
6G. Mannino, N. E. B. Cowern, F. Roozeboom, and J. G. M. van Berku
Appl. Phys. Lett.76, 855 ~2000!.
7X. Y. Liu, W. Windl, and M. P. Masquelier, Appl. Phys. Lett.77, 2018
~2000!.
8T. J. Lenosky, B. Sadigh, S. K. Theiss, M. J. Caturla, and T. D. de
Rubia, Appl. Phys. Lett.77, 1834~2000!.
9A. Agarwal, H. J. Gossmann, D. J. Eaglesham, S. B. Herner, A. T. Fi
and T. E. Haynes, Appl. Phys. Lett.74, 2331~1999!.
10J. L. Benton, S. Libertino, P. Kringhøj, D. J. Eaglesham, J. M. Poate,
S. Coffa, J. Appl. Phys.82, 120 ~1997!; J. L. Benton, K. Halliburton, S.
Libertino, D. J. Eaglesham, and S. J. Coffa, Appl. Phys. Lett.84, 4749
~1998!.
11J. Hutter, A. Alavi, T. Deutch, M. Bernasconi, S. Goedecker, D. Marx,
Tuckerman, and M. Parrinello, CPMD, MPI fuer Festkoerperforschu
and IBM Zurich Research Laboratory 1995–1999.
12S. Goedecker, M. Teter, and J. Hutter, Phys. Rev. B54, 1703~1996!.
13H. J. Monkhorst and J. D. Pack, Phys. Rev. B13, 5188~1976!.
14W. Windl, M. M. Bunea, R. Stumpf, S. T. Dunham, and M. P. Masqueli
Phys. Rev. Lett.83, 4345~1999!.
15J. Zhu, T. D. de la Rubia, L. H. Yang, C. Maihiot, and G. H. Gilmer, Phy
Rev. B54, 4741~1996!, and references cited therein.
16J. Kim, F. Kirchhoff, J. W. Wilkins, and F. S. Khan, Phys. Rev. Lett.84,
503 ~2000!.
17B. Sadigh, T. J. Lenosky, S. K. Theiss, M.-J. Caturla, T. D. de la Rub
and M. A. Foad, Phys. Rev. Lett.83, 4341~1999!.
18W. K. Leung, R. J. Needs, G. Rajagopal, S. Itoh, and S. Ihara, Phys.
Lett. 83, 2351~1998!.
19E. J. H. Collart, K. Weemers, N. E. B. Cowern, J. Politiek, P. H.
Bancken, J. G. M. von Berkum, and D. J. Gravesteijn, Nucl. Instru
Methods Phys. Res. B139, 98 ~1998!.
20L. Pelaz, G. H. Gilmer, M. Jaraiz, S. B. Herner, H. J. Gossmann, D
Eaglesham, G. Hobler, C. S. Rafferty, and J. Barbolla, Appl. Phys. L
70, 2285~1997!.IP license or copyright, see http://apl.aip.org/apl/copyright.jsp


Catalytic role of boron atoms in self-interstitial clustering in Si

APPLIED PHYSICS LETTERS VOLUME 83, NUMBER 5 4 AUGUST 2003Catalytic role of boron atoms in self-interstitial clustering in Si
Gyeong S. Hwanga) and William A. Goddard IIIb)
Materials and Process Simulation Center (139-74), California Institute of Technology, Pasadena,
California 91125
~Received 13 September 2002; accepted 30 May 2003!
Using density functional theory ~DFT! calculations and kinetic simulations, we have investigated
the influence of boron atoms on self-interstitial clustering in Si. From DFT calculations of neutral
interstitial clusters with a single B atom ~BsIn, n<4!, we find that the binding of B ~BsIn→In21
1BsI) becomes substantially weaker than that of an interstitial ~BsIn→BsIn211I) when n>4. This
implies boron can be liberated while leaving an interstitial cluster behind. Our kinetic simulations
including the boron liberation explain well experimental observations reported by J. L. Benton
et al., J. Appl. Phys. 82, 120 ~1997!. © 2003 American Institute of Physics.
@DOI: 10.1063/1.1596729#Continued scaling of Si devices below 0.1 mm requires
formation of ultrashallow junctions to avoid short-channel
effects.1 Ultralow-energy ion beams are currently most
widely used to introduce dopants into the Si substrate. Gen-
erally this must be followed by high-temperature thermal
annealing to eliminate substrate damage generated by ener-
getic ion bombardment and to electrically activate the in-
jected dopants. During the implantation and annealing, the
dopant atoms exhibit transient enhanced diffusion ~TED!.
This is a particularly serious problem for boron ~a major
p-type dopant!, which exhibits large TED. The consequent
doping profile spreading imposes a great difficulty in form-
ing ultrashallow pn junctions in deep submicron device
structures.
It is now well understood that excess Si self-interstitials
generated during implantation are mainly responsible for the
B TED. Due to large mobility even at room temperature,2
single interstitials can diffuse and annihilate at the surface.
Therefore, at the onset of annealing most interstitials are
likely to remain in the form of clusters. It is widely believed
that, in ultrashallow junction formation by ultralow energy
ion implantation, the main sources for free interstitials during
postimplantation annealing are small interstitial clusters and
boron-interstitial complexes3–6 along with extended $311%
defects. The formation of boron-interstitial complexes have
been extensively studied using first principles calculations,7,8
also supported by recent experiments.9 However, little is
known about the role of single B atoms in the growth of
small interstitial clusters.
Deep level transient spectroscopy recently provided di-
rect evidence for the existence of small Si interstitial
clusters.10 These results showed that the small interstitial
clusters did not contain large numbers of B atoms even in a
B doped layer ~where B concentration was not high enough
to induce B clustering!. This was surprising because recent
ab initio calculations7,8 suggested that Si interstitials interact
very strongly with substitutional B to form stable BsI, BsI2 ,
a!Present address: Department of Chemical Engineering, The University of
Texas, Austin, Texas.
b!Author to whom correspondence should be addressed; electronic mail:
wag@wag.caltech.edu1040003-6951/2003/83(5)/1047/3/$20.00
Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject and BsI3 complexes with large thermal stability comparable
to that of small interstitial clusters.7,8
In order to provide a basis for understanding the forma-
tion of interstitial clusters in the presence of B, we have
carried out
~i! first-principles quantum mechanics calculations on the
structures and energetics of small interstitial clusters
with and without a single B atom and
~ii! kinetic model based simulations on boron-interstitial
concentration variations.
These results suggest that B can catalyze the growth of
small Si interstitial clusters.
Our first principles calculations are based on density-
functional theory ~DFT! within the local spin density ap-
proximation ~LSDA!, as implemented in the CPMD V3.3
package.11 We used a nonlocal, norm-conserving
pseudopotential12 and a plane-wave cutoff energy of 20 Ry.
Defect systems considered in this study were modeled using
64-atom supercells with a fixed volume corresponding to a
Si–Si bond distance of 2.35 Å in pure Si. The atomic posi-
tions were allowed to relax fully until all residual forces were
smaller than 531024 Hartree/Bohr. The geometries were
optimized using only one k point ~G! for the Brillouin-zone
integrations. ~The geometry optimization is rather insensitive
to the number of k point sets.! However, the total energies
were reevaluated using a (23232) mesh of k points in the
scheme of Monkhorst–Pack.13
We first examined structure and energetics of a number
of interstitial clusters containing only Si (In , n<3) and con-
taining a single boron atom (BIn , n<4). Figure 1 shows the
fully relaxed structure and LSDA energy for all clusters ex-
amined. To ensure that we would find the global minimum
~instead of a high-energy local minimum state!, we per-
formed ab initio molecular dynamics followed by energy
minimization for many different initial configurations.
The BsI configuration @Fig. 1~a!# has the Si interstitial ~I!
next to the B substitutional (Bs) in a tetrahedral site. The
binding energy between I and Bs is calculated to be 1.14 eV
@virtually identical to 1.160.1 eV obtained in a previous lo-
cal density approximation ~LDA! calculation#.15
For BsI2 we find the B to be substitutional with two7 © 2003 American Institute of Physics
to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
1048 Appl. Phys. Lett., Vol. 83, No. 5, 4 August 2003 G. S. Hwang and W. A. Goddard IIIinterstitials on each side ~dumbbell! in the C1h symmetry
@Fig. 1~b!#. We find the BsI2 cluster to be quite stable with a
binding energy of 1.65 eV ~the energy required to release an
interstitial from the BsI2 cluster!. This is consistent with a
recent LDA calculation which leads to a binding energy of
1.9 eV between (BsI)1 and I.7–8
We also identified a stable neutral BsI3 structure @Fig.
1~c!# that appears quite different from the BI3
1 configuration
reported recently by Liu et al.7–8 Two Si lattice atoms ~close
to the B atom! are significantly displaced from their original
position, allowing all bonds to be well reconstructed with
appropriate bond lengths. We obtain a binding energy of 1.66
eV ~energy required to release an interstitial from the BsI3
cluster!.
Inserting an additional Si interstitial into the BsI3 cluster,
leads to a BsI4 cluster that is also quite stable ~a binding
energy of 1.59 eV! toward releasing an interstitial. This BsI4
cluster @Fig. 1~d!# can be visualized as an I3 structure @see
Fig. 1~f!# that is distorted by insertion of an interstitial boron.
This result suggests that the presence of B atoms may
help the Si interstitials grow into compact configurations. For
crystalline Si, the compact tri-interstitial cluster (I3) has a
formation energy ;0.2 eV lower than the ring cluster and 0.4
eV lower than elongated clusters.16
Figure 1 also shows compact I2 and I3 clusters ~fully
relaxed structures!. The I2 and I3 formation energies are cal-
culated to be 2.63 and 1.99 eV, respectively ~in excellent
agreement with the values of 2.5 and 1.9 eV obtained in
recent DFT–LDA calculations!.16 We calculate the formation
energy for a Si self-interstitial to be 3.3 eV, very close to the
result of 3.3–3.35 eV from other DFT–LDA calculations.15
We also examined the possibility of boron liberation
from the B-containing interstitial clusters. Our DFT–LSDA
calculations show that the decay of BsI3 into BsI and I2 re-
quires an energy of 2.0 eV, which is larger than the 1.66 eV
FIG. 1. Structure and energetics of boron-interstitial and interstitial only
clusters examined in this study. Boron is indicated by the hatched ball.Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject for BsI3→BsI21I. @The barrier for boron-interstitial pair dif-
fusion ~0.68 eV!17 is also likely to be larger than that for
interstitial diffusion ~0.15–0.2 eV!.#18 Thus from BsI3 we
calculate that boron (BsI) liberation is less favorable than
interstitial liberation.
However, for BsI4 , the binding energy of boron (BsI4
→BsI1I3) decreases significantly to 1.0 eV while the inter-
stitial binding energy (BsI4→I1BsI3) of 1.60 eV remains
nearly unchanged. These results demonstrate that the binding
energy of boron decreases as the number of integrated inter-
stitials increases. This is consistent with the very weak inter-
action between boron and extended $311% defects.7 This bind-
ing energy reduction would allow boron to release more
favorably than an interstitial from BsIn when n>4.
These results suggest that boron atoms may catalyze in-
terstitial agglomeration. That is, boron atoms provide a
means to capture and integrate interstitials into a cluster, fol-
lowed by the emission of the boron to facilitate formation of
additional interstitial clusters. In this study, we consider only
charge neutral clusters, which may lead to some errors in
estimating the binding energies of boron-interstitial clusters
~as the cluster structures and energies could change signifi-
cantly at different charge states!.7,8 However, we believe that
our results give a reasonable description in the overall physi-
cal picture, particularly for boron-interstitial clusters under
near intrinsic conditions ~as considered herein!. In fact, cur-
rent first principles calculations on various charge-state sys-
tems are still quite uncertain.7,8,14
This catalytic reaction may provide an explanation for
the experimental observation that a large fraction of B atoms
remains electrically active. ~In these experiments, the Si im-
plant doses were 13109 – 531013 cm22 and the doped B
concentration was about 731015 cm23.)
To illustrate this process we carried out kinetic-model
based simulations in which we started with a boron concen-
tration of 731015 cm23 and added interstitials at a rate of
1016 cm23 s for 10 s to achieve a total concentration of
1017 cm23. The interstitial diffusivity is approximated using
0.0013exp(2Em /kBT), where Em50.2 eV.18 The calculated
diffusivity of 331027 cm2/s at room temperature is in good
agreement with an experimental estimate of >1027 cm2/s.19
Figure 2~a! shows the concentrations of boron-interstitial
clusters and self-interstitial clusters after 10 s of interstitial
implantation into the boron-doped layer at room temperature.
Here, boron clustering can be ignored due to the low B con-
centration. Our simulation result shows that about 97% of
the injected interstitials are incorporated into pre-existing bo-
ron sites with just 3% remaining as interstitial clusters. This
ratio is a function of the interstitial injection rate and diffu-
sivity; that is, a higher fraction of interstitials is aggregated
into boron-interstitial clusters as the injection rate decreases
and/or the diffusivity increases. Although many details of
defect dynamics ~such as vacancy formation! are ignored in
our simulation, we see that boron can efficiently capture im-
planted interstitials to form boron-interstitial complexes dur-
ing implantation. We expect that this interstitial aggregation
will lead to entrenchment of most boron atoms ~if the im-
planted interstitial concentration is far greater than the boron
concentration!. Indeed our simulation results show that ~vir-
tually! all boron atoms are embedded in interstitial clusters.to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
1049Appl. Phys. Lett., Vol. 83, No. 5, 4 August 2003 G. S. Hwang and W. A. Goddard IIIFigure 2 also shows simulated concentrations of boron-
interstitial and self-interstitial clusters after 10 min of subse-
quent postimplantation annealing at 500 and 700 °C ~with
@Fig. 2~c!# and without @Fig. 2~b!# boron liberation from
boron-interstitial complexes!. In these simulations, we as-
sume that the energy barriers for interstitial release from
boron-interstitial and interstitial clusters are comparable @ap-
proximated as the sum of Em and Eb ; Em50.2 eV18 and
Eb (n I)52.722.65 @n I1/22(n I21)1/2# eV,20 where n I is the
number of interstitial incorporated#. Without boron liberation
about 100% of boron atoms are still embedded in interstitial
clusters at 500 °C and ;30% are at 700 °C. ~The fraction of
substitutional boron decreases with the concentration of in-
jected interstitials.! On the other hand, when we allow boron
to release ~once the boron-interstitial cluster size becomes
greater than Bs – I4), virtually all boron atoms recover to sub-
stitutional locations. Thus, our simulations demonstrate
clearly that without boron liberation, a significant amount of
boron would still remain as boron-interstitial clusters ~under
the conditions considered in this study!.
Now we suspect that the boron-catalyzed reaction out-
lined earlier may facilitate the formation of small interstitial
clusters, especially during implantation and/or early stages of
post-implantation annealing. As a result, a larger fraction of
interstitials would remain in the substrate. Since B-TED is
FIG. 2. The concentrations of boron-interstitial (Bs – In) and self-interstitial
(In) clusters. ~a! After 10 s of interstitial implantation, ~b!–~c! after 10 min
of subsequent postimplantation annealing at 500 and 700 °C @~b! without
and ~c! with boron liberation from boron-interstitial clusters#.Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject mainly determined by the availability of interstitials, the in-
creased concentration of interstitials would influence doping
profile evolution. This suggests the importance of including
the B-catalyzed process, along with interstitial clustering and
boron-interstitial complex formation/dissolution, in modeling
ultrashallow junction formation.
In summary, based on our first principles calculations
and kinetic simulations we propose and validate the mecha-
nism of boron-catalyzed interstitial cluster formation. Our
first principles calculations show the reduction of boron and
interstitial interaction with the number of interstitials incor-
porated, leading to boron liberation while leaving an intersti-
tial cluster. A comparison of experiments with kinetic simu-
lations supports the boron liberation. The liberated boron
may then induce formation of additional interstitial clusters,
i.e., B-catalyzed interstitial cluster formation.
The authors thank the Seiko-Epson Corporation for pro-
viding financial support and the authors thank Masamitsu
Uehara and Yuzuru Sato of Seiko-Epson for many helpful
discussions. G.S.H. also thanks the Welch Foundation for
their partial financial support. The facilities of the MSC used
in this work are supported by grants from DOE–ASCI,
ARO/DURIP, ONR/DURIP, ARO/MURI, ONR/MURI,
IBM, NIH, NSF, ChevronTexaco, Beckman Institute, Gen-
eral Motors, and Asahi Kasei.
1 E. C. Jones and E. Ishida, Mater. Sci. Eng., R. 24, ~1998!, and references
cited therein.
2 G. D. Watkins, Phys. Rev. B 12, 5824 ~1975!.
3 L. H. Zhang, K. S. Jones, P. H. Chi, and D. S. Simons, Appl. Phys. Lett.
67, 2025 ~1995!.
4 A. D. Lilak, S. K. Earles, M. E. Law, and K. S. Jones, Appl. Phys. Lett.
74, 2038 ~1999!.
5 E. Schroer, V. Privitera, F. Priolo, E. Napolitani, and A. Carnera, Appl.
Phys. Lett. 74, 3996 ~1999!.
6 G. Mannino, N. E. B. Cowern, F. Roozeboom, and J. G. M. van Berkum,
Appl. Phys. Lett. 76, 855 ~2000!.
7 X. Y. Liu, W. Windl, and M. P. Masquelier, Appl. Phys. Lett. 77, 2018
~2000!.
8 T. J. Lenosky, B. Sadigh, S. K. Theiss, M. J. Caturla, and T. D. de la
Rubia, Appl. Phys. Lett. 77, 1834 ~2000!.
9 A. Agarwal, H. J. Gossmann, D. J. Eaglesham, S. B. Herner, A. T. Fiory,
and T. E. Haynes, Appl. Phys. Lett. 74, 2331 ~1999!.
10 J. L. Benton, S. Libertino, P. Kringhøj, D. J. Eaglesham, J. M. Poate, and
S. Coffa, J. Appl. Phys. 82, 120 ~1997!; J. L. Benton, K. Halliburton, S.
Libertino, D. J. Eaglesham, and S. J. Coffa, Appl. Phys. Lett. 84, 4749
~1998!.
11 J. Hutter, A. Alavi, T. Deutch, M. Bernasconi, S. Goedecker, D. Marx, M.
Tuckerman, and M. Parrinello, CPMD, MPI fuer Festkoerperforschung
and IBM Zurich Research Laboratory 1995–1999.
12 S. Goedecker, M. Teter, and J. Hutter, Phys. Rev. B 54, 1703 ~1996!.
13 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 ~1976!.
14 W. Windl, M. M. Bunea, R. Stumpf, S. T. Dunham, and M. P. Masquelier,
Phys. Rev. Lett. 83, 4345 ~1999!.
15 J. Zhu, T. D. de la Rubia, L. H. Yang, C. Maihiot, and G. H. Gilmer, Phys.
Rev. B 54, 4741 ~1996!, and references cited therein.
16 J. Kim, F. Kirchhoff, J. W. Wilkins, and F. S. Khan, Phys. Rev. Lett. 84,
503 ~2000!.
17 B. Sadigh, T. J. Lenosky, S. K. Theiss, M.-J. Caturla, T. D. de la Rubia,
and M. A. Foad, Phys. Rev. Lett. 83, 4341 ~1999!.
18 W. K. Leung, R. J. Needs, G. Rajagopal, S. Itoh, and S. Ihara, Phys. Rev.
Lett. 83, 2351 ~1998!.
19 E. J. H. Collart, K. Weemers, N. E. B. Cowern, J. Politiek, P. H. L.
Bancken, J. G. M. von Berkum, and D. J. Gravesteijn, Nucl. Instrum.
Methods Phys. Res. B 139, 98 ~1998!.
20 L. Pelaz, G. H. Gilmer, M. Jaraiz, S. B. Herner, H. J. Gossmann, D. J.
Eaglesham, G. Hobler, C. S. Rafferty, and J. Barbolla, Appl. Phys. Lett.
70, 2285 ~1997!.to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp


https://authors.library.caltech.edu/1866/1/HWAapl03a.pdf

Catalytic role of boron atoms in self-interstitial clustering in Si

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main

Caltech Authors - Main