Ab initio
modeling of boron clustering in silicon
Xiang-Yang Liu
a)
Computational Materials Group, Motorola, Inc., Los Alamos, New Mexico 87545
Wolfgang Windl
Computational Materials Group, Motorola, Inc., Austin, Texas 78721
Michael P. Masquelier
Computational Materials Group, Motorola, Inc., Los Alamos, New Mexico 87545
͑Received 19 June 2000; accepted for publication 7 August 2000͒
We present results of ab initio calculations for the structure and energetics of boron-interstitial
clusters in Si and a respective continuum model for the nucleation, growth, and dissolution of such
clusters. The structure of the clusters and their possible relationship to boron precipitates and
interstitial-cluster formation are discussed. We find that neither the local-density approximation nor
the generalized-gradient approximation to the density-functional theory result in energetics that
predict annealing and activation experiments perfectly well. However, gentle refitting of the
numbers results in a model with good predictive qualities. © 2000 American Institute of Physics.
͓S0003-6951͑00͒04539-3͔
Ion implantation is currently the method of choice for
introducing dopants such as boron into silicon.
1
However,
energetic ions damage the host material and create a super-
saturation of defects in Si, which impair the device perfor-
mance. Annealing following the implant is used to heal the
implant damage, while activating the dopant atoms electri-
cally at the same time. The implant-anneal cycle can cause,
on the one hand, excessive transient enhanced diffusion of
the implanted B, and on the other hand, the formation of B
precipitates which immobilize and deactivate the B atoms
well below the solid solubility limit.
2
From the observation
of the trapping of interstitials ͑Is͒ by these precipitates,
3
it
was concluded that they consist of B–I clusters ͑BICs͒.
A notable body of simulation work in order to model
these effects exists,
4–9
which all are based on the clustering
energetics of the BICs. Two different approaches have been
chosen to determine these energetics: First, an inverse-
modeling fit of the BIC energies to a large set of secondary-
ion mass spectroscopy ͑SIMS͒ measurements.
8
However, fit-
ting a large number of parameters in inverse modeling can be
subject to ambiguities and furthermore does not help to iden-
tify the structure of the clusters. The second approach, ato-
mistic calculations, especially within density-functional
theory ͑DFT͒,
9–13
can in principle overcome these limita-
tions; however, the problems to find global instead of local
minima
14
and the possibly considerable error bars for misco-
ordinated defects
15
also require a cautious use of this ap-
proach. Previously, only one set of BIC reaction barriers
from first-principles
16
for B
n
I
m
(nр4) clusters had been
available, where, the influence of the different charge states
had been neglected. Very recently, revised barriers from a
new study which has been performed in parallel to our work
have been published by the same group,
9
after indications
had been found that the previous numbers could not explain
all experiments: In Ref. 7, several of the cluster energies of
Ref. 16 had to be refitted in order to predict annealing ex-
periments correctly. Also, the predictions of Ref. 4, based on
the cluster energies of Ref. 16, where an ‘‘activation win-
dow’’ for B anneals was predicted, have been shown recently
not to be in agreement with experiment.
17
However, since
Ref. 9, where the very recent reaction barriers are given, still
reports this activation window, our study may help to resolve
this important discrepancy between ab initio modeling and
experiment.
We present in this letter a systematic study of BIC ener-
getics including the influence of charges and a careful struc-
ture minimization within the BIC phase space. We show the
possible structures of the BICs that our calculations suggest
to have the lowest total energy. Also, we discuss the consid-
erable differences between the results within the local-
density approximation ͑LDA͒ and the generalized-gradient
approximation ͑GGA͒. Finally, we compare our results to the
other calculations and to the inverse-modeling results of Ref.
8, and present continuum activation results.
For our calculations, we used the DFT code
VASP
with
ultrasoft pseudopotentials within both LDA and GGA.
18
We
employed a harder variation of the B pseudopotential with a
cutoff energy of 230 eV and 64 atom supercells with a 4
3
Monkhorst–Pack k-point sampling. The procedure to calcu-
late energies for charged systems and the total-energy cor-
rections for occupied defect states are identical to the ones
described in Ref. 12.
We examined a number of BICs B
n
I
m
with n,mр4, as
well as B
12
I
7
, which has been studied theoretically before
without presenting formation energy values,
19
and single B
atoms in ͕311͖ defects. As pointed out before,
14
it is not clear
in advance which final atomic arrangement the different
clusters will assume in the global-minimum structure. In or-
der to decrease the threat of finding a high-energy local in-
stead of the global minimum, we started for each cluster
from many different initial configurations that were structur-
ally relaxed, which, however, does not guarantee that we
really found the energetically most favorable structures. Fur-
ther details will be published elsewhere.
20
Figure 1 summarizes our first-principles results. For all
examined clusters ͑except for B
4
ϭ
and B-͕311͖͒ we show the
a͒
Electronic mail: r40298@email.sps.mot.com
APPLIED PHYSICS LETTERS VOLUME 77, NUMBER 13 25 SEPTEMBER 2000
20180003-6951/2000/77(13)/2018/3/$17.00 © 2000 American Institute of Physics