The role of di-boron diffusion in evolution of B diffusion profiles has been investigated. We find that boron pair (B-s-B-i) diffusion can become as important as boron-interstitial pair (B-s-Si-i) diffusion when both boron concentration and annealing temperature are very high, leading to concentration-dependent B diffusion. Our simulated B diffusion profiles with dramatic shouldering are in excellent agreement with experimental ones reported by Schroer [Appl. Phys. Lett. 74, 3996 (1999)] for high-temperature (approximate to 1200 degrees C) postimplantion annealing of ultralow-energy (approximate to500 eV) implanted high-concentration (>10(19) cm(-3)) boron in silicon

Goddard, William A., III

Hwang, Gyeong S.

English

Caltech Authors - Main

APPLIED PHYSICS LETTERS VOLUME 83, NUMBER 17 27 OCTOBER 2003Shouldering in B diffusion profiles in Si: Role of di-boron diffusion
Gyeong S. Hwanga) and William A. Goddard IIIb)
Materials and Process Simulation Center, Beckman Institute (139-74), California Institute of Technology,
Pasadena, California 91125
~Received 26 March 2002; accepted 17 August 2003!
The role of di-boron diffusion in evolution of B diffusion profiles has been investigated. We find that
boron pair (Bs – Bi) diffusion can become as important as boron-interstitial pair (Bs – Sii) diffusion
when both boron concentration and annealing temperature are very high, leading to
concentration-dependent B diffusion. Our simulated B diffusion profiles with dramatic shouldering
are in excellent agreement with experimental ones reported by Schroer et al. @Appl. Phys. Lett. 74,
3996 ~1999!# for high-temperature ~’1200 °C! postimplantion annealing of ultralow-energy ~’500
eV! implanted high-concentration (.1019 cm23) boron in silicon. © 2003 American Institute of
Physics. @DOI: 10.1063/1.1619219#Boron doping is an essential ingredient in the fabrication
of silicon-based semiconductor devices. As gate dimensions
shrink to nanometer scales ~<100 nm!, it becomes critical to
gain precise control of doping profiles. Consequently, a great
deal of effort is being devoted to understanding and control-
ling transient enhanced diffusion ~TED! of boron during im-
plantation and postimplantation annealing.
While it is understood that a mobile boron-silicon inter-
stitial pair (B–Sii) plays an important role in B TED,1,2 still
little is known about underlying reasons for the enhancement
~or the retardation! of B diffusion at high concentrations of
boron (.1018 cm23) ~or impurities, such as carbon or oxy-
gen!.
We were particularly intrigued by the diffusion profiles
~Fig. 1! determined by Schroer et al.3 using secondary ion
mass spectroscopy ~SIMS!. Their results show clearly a
concentration-dependent behavior; that is, B diffusion is en-
hanced as the B concentration increases. They implanted bo-
ron at energies ;500 eV with a dose of 1015 cm22 into a
p-type, epitaxially grown ~epi! silicon layer on Si~001!.
Then, the substrate was annealed at 1200 °C. The concentra-
tions of oxygen and carbon in the epi-Si layer are typically
less than 1015 cm23. Hence, impurities are likely to play an
insignificant role in determining the doping profiles in these
experiments. In addition, high temperature annealing at
1200 °C results in fast dissolution of B clusters formed at the
very early stages of annealing. Therefore, the density of im-
mobile large boron clusters, if any, is too low to influence
diffusion profile evolution. This suggests that only Si inter-
stitials and mobile B species should be considered in explain-
ing these experiments. In the absence of concentration-
dependent and/or transient effects, single component
diffusion should lead to a Gaussian distribution ~once the
diffusion profile is fully developed!, but the experimental
results3 in Fig. 1 differ substantially from a simple Gaussian.
B TED appears to be enhanced with increasing B concentra-
tion, leading to shouldering in the diffusion profiles. The
a!Present address: Department of Chemical Engineering, University of
Texas, Austin, Texas.
b!Author to whom correspondence should be addressed; electronic mail:
wag@wag.caltech.edu3500003-6951/2003/83(17)/3501/3/$20.00
Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject shouldering behavior is consistent with a previous experi-
mental observation4 that shows B diffusion enhancement at
high B concentration; that is, 10B diffusion increased at the
presence of high concentrations (’1019 cm23) of back-
ground boron 11B. In fact, the concentration-dependent B
diffusion has been explained by the variation of charged de-
fect concentrations under extrinsic conditions ~i.e., Fermi
level shift effect, vide infra!.10
In this letter, we present the influence of di-boron diffu-
sion and other possible factors including Fermi level shift on
evolution of B diffusion profiles.
The kinetic model used here includes only the formation/
dissolution of Bs – Sii and Bs – Bi pairs; that is, Bs
1Sii↔Bs – Sii and Bs1Bs – Sii↔Bs1Bi↔Bs – Bi . This ne-
glects many details in the interactions between B and Si
atoms. But the influence of larger immobile B clusters should
be negligible due to their low concentrations as a result of
fast dissolution at high temperature annealing. When cluster-
ing is insignificant, the equilibrium concentrations of Bs – Sii
and Bs – Bi are mainly determined by the total boron and
interstitial concentrations. Hence, the simplified kinetics
should provide a reasonable description in the overall physi-
cal picture.
Figure 2 shows a comparison between simulated diffu-
sion profiles and SIMS profiles3 ~from Fig. 1!. Our simula-
tions start with the initial ~as implanted! distribution while
FIG. 1. The experimental ~SIMS! profiles ~Ref. 3! for three different anneal-
ing times, t51, 5, and 15 s. Fitting Gaussian functions to the early time
evolutions leads to significant discrepancies for longer time, indicating that
at least two components play a role.1 © 2003 American Institute of Physics
to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
3502 Appl. Phys. Lett., Vol. 83, No. 17, 27 October 2003 G. S. Hwang and W. A. Goddard IIIcontrolling precipitation ~and/or evaporation! at the surface
to match the integrated amount of B in the substrate to be
same as experiments. When both Bs – Sii and Bs – Bi diffu-
sion are included, as shown in Fig. 2, we see that there is
excellent agreement between the simulated and experimental
results. Suppose that only Bs – Sii diffusion is important and
the Fermi level effect is insignificant, then substantial B clus-
tering would lead to capture of mobile Bs – Sii species by a
second B complex to form a stable multiboron cluster. Such
clustering would impede B TED, leading to a ‘‘tailing’’ be-
havior ~i.e., the displacement of diffusion profiles becomes
larger as the B concentration decreases! opposite to what is
observed ~see the inset in Fig. 2!.
In the absence of the Fermi level shift effect, essential to
the success in accurate modeling these experiments was in-
cluding diffusion of the boron dimer (Bs – Bi). Recently,
Hwang and Goddard5 used first principles quantum mechan-
ics ~DFT/GGA! to follow the details of boron dimer diffu-
sion. They found a pathway leading to an energy barrier of
only 1.81 eV for the dimer diffusion. Although far larger
than the activation energy for Bs – Sii diffusion ~;0.68 eV!,1
the larger binding energy for Bs – Bi6,7 leads to a Bs – Bi con-
tribution to diffusion comparable with the Bs – Sii when both
B concentration and annealing temperature are very high.5
Since clustering is insignificant at 1200 °C, the shape of
the diffusion profile is dominated by the ratio of the mean
diffusion length between Bs – Bi and Bs – Sii pairs,
l(Bs – Bi)/l(Bs – Sii).8 Based on literature values of the dif-
fusivities and binding energies
@De~Sii!55 exp~21/kBT ! cm2/s,9
De~Bs – Sii!5131023 exp~20.68/kBT ! cm2/s,3
Eb~Bs – Sii!50.5 eV,7
and Eb(Bs – Bi)51.5 eV#,7 we deduce that the ratio of the
mean diffusion length between Bs – Bi and Bs – Sii pairs is8
l(Bs – Bi)/l(Bs – Sii)’56.46. The results in Fig. 2, used a
value of l(Bs – Bi)/l(Bs – Sii)555, well within the uncer-
tainty. ~Since the density of free Si interstitials does not af-
fect the mean diffusion length, these simulations simply as-
sume the free interstitial concentration of 1014 cm23.)3
The importance of di-boron diffusion is determined
mainly by the total concentration of nonclustered ~free! bo-
FIG. 2. A comparison between the experimental ~SIMS! profiles ~Ref. 3!
and the profiles from simulations. The simulations, which include both
Bs – Bi and Bs – Sii diffusion, are in quantitative agreement with experiment
providing strong support for the role of the B dimer diffusion at high tem-
peratures. The inset shows a comparison between SIMS and simulated pro-
file with Bs – Si diffusion only.Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject ron. We define g as the relative contribution of Bs – Bi and
Bs – Sii to B TED in terms of the equilibrium concentrations
(Ceq) and the diffusivities (De):
g52De~Bs – Bi!Ceq~Bs – Bi)/De~Bs – Sii!Ceq~Bs – Sii).
Here the factor of 2 arises because two boron atoms are
transported in Bs – Bi diffusion. Our kinetic simulation shows
that, as the total boron concentration is increased, the Bs – Bi
concentration increases almost quadratically, but in contrast
the Bs – Sii concentration increases sublinearly at a high B
concentration region (.1018 cm23) due to suppression by
Bs – Bi cluster formation.5 As a result, at 1020 cm23, the
equilibrium concentration of Bs – Bi becomes four orders of
magnitude larger than the Bs – Sii one.5 We calculate that
g’1.4 when CB51020 cm23 ~it increases linearly with CB)
using the diffusivities and the binding energies listed before.
Here, the prefactor of Bs – Bi and Bs – Sii dissociation rates is
estimated based on the Debye frequency (51013 s21).
This study suggests that the Bs – Bi component may be-
come as important as the Bs – Sii component in determining
diffusion profiles when both B concentration and annealing
temperature are very high. For low temperature annealing
~,900 °C!, however, the boron clustering at high concentra-
tions (.1018 cm23) makes di-boron diffusion unimportant.
Next, we discuss the influence of the following factors
on doping profile evolution:
~i! Fermi level shift;
~ii! density distribution of neutral interstitials;
~iii! impurities such as oxygen and carbon; and
~iv! stresses caused by surfaces and extended defects.
Fermi level shift. In p-doped Si, interstitials may charge
positively or remain neutral. Under extrinsic conditions, the
concentration of the charged interstitials is a function of the
Fermi level ~that depends on the dopant concentration!10,11
while the concentration of neutral interstitials remains un-
changed. Therefore, the total interstitial concentration
changes with the boron concentration if a substantial fraction
of interstitials were charged, which may in turn result in a
concentration-dependent behavior10 as boron diffusion is
mainly mediated by interstitials. Thus, an accurate estimation
of the relative density of interstitials at a different charge
state is essential.
The relative populations for positively charged intersti-
tials under intrinsic conditions are determined by the donor
levels, the Fermi level, and the substrate temperature.12,13 For
the first donor level ’Ec21.2 eV,6 the second donor level
’Ec20.4 eV,6 the intrinsic Fermi level ’0.6 eV ~where Ec
is conduction band minimum!, for instance, the estimated
relative concentrations of 0, 11, and 21 charged interstitials
are 1, 7.531023, and 0.038 at 1200 °C, respectively. With
the intrinsic carrier concentration (ni) of ’231019 cm23 at
1200 °C, for p51020 cm23 ~i.e., p/ni55! the relative popu-
lations of 11, 21 charged interstitials increase to 3.75
31022 and 0.95, respectively. This indicates that the total
interstitial concentration may increases substantially in the
extrinsic region.
In addition to the interstitial concentration variation, the
dissociation and diffusion rates of boron-interstitial com-
plexes are likely to be strongly influenced by the Fermi-levelto AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
3503Appl. Phys. Lett., Vol. 83, No. 17, 27 October 2003 G. S. Hwang and W. A. Goddard IIIposition.1,2,6,7 However, the energies of the different charge
states of boron-interstitial pairs and interstitials are poorly
known, thus it is difficult to quantify the Fermi level effect.
Density distribution of neutral interstitials. The intersti-
tials are usually generated by high-energy ion bombardment
and remain in the form of small clusters during implantation.
At the onset of annealing, most of the interstitial clusters
~including interstitial-boron complexes! may exist near the
surface. At the nonequilibrium stage where these clusters
serve as a main source for excess interstitials through disso-
lution, a sizable gradient in the interstitial density may de-
velop along the depth. However, high temperature annealing
~’1200 °C! results in rapid dissolution of the clusters. Ac-
cording to a recent measurement,9 $311% defects decay expo-
nentially with annealing temperature; the characteristic de-
cay time ranges from ;40 s at 815 °C to ;4 h at 670 °C.
Extrapolating to 1200 °C leads to a decay time of ,1023 s.
Given that smaller clusters dissolve much faster than the ex-
tended $311% complexes, this estimate suggests that most of
interstitial clusters formed during implantation and/or the
early stages of annealing evaporate within 1023 s at 1200 °C.
If so then the diffusion profile evolution will be barely influ-
enced by the interstitial density gradient.
Even if the dissolution rate is far slower than 1023 s, the
resulting density gradient of interstitials will be insignificant
in a short length scale ~,100 nm! due to their high mobility
@De(Si)’1.531023 cm2/s at 1200 °C#.14 In the end, the
free interstitials may be equilibrated with interstitial-
containing clusters. Once the equilibrium is established, the
number of free interstitials decreases with the density of
traps ~such as interstitial clusters and boron-interstitial com-
plexes!. Thus, the observed shouldering phenomenon for B is
quite unlikely to involve density gradient of free Si intersti-
tials.
Impurities. Interactions with oxygen and carbon
may affect the boron diffusion by forming BiCs ~interstitial
boron-substitutional carbon! or/and BiOi ~interstitial
boron-interstitial oxygen! complexes.15 However, the con-
centrations of oxygen and carbon in the epi-Si layer are typi-
cally less than 1015 cm23. Hence, we believe that such im-
purities play an insignificant role in determining doping
profiles in the high B concentration regime
(.1017 cm23).
Stresses. Stresses have been proposed as a factor that
may influence boron diffusion, albeit there is a controversy
over whether they enhance or retard B diffusion.16 Very large
stresses are usually built up in the silicon area near the edge
of thin gate layers due to lattice mismatch. In addition, ex-
tended defects such as dislocation loops may create a stress
field around them. However, the Schroer experiments3 in-
volve a planar free surface, which imposes only a small
stress on the substrate. Thus, the induced stresses cannot be
important. At high temperatures ~.1000 °C!, extended de-Downloaded 21 Dec 2005 to 131.215.225.171. Redistribution subject fects ~if any! would be dissolved too fast to have significant
influence.17
In summary, we show di-boron diffusion can be impor-
tant and lead to shouldering in B diffusion profiles for high
temperature ~’1200 °C! annealing with high B concentra-
tions (.1019 cm23). This study suggests that di-boron dif-
fusion and Fermi-level shift would result in a similar
concentration-dependent behavior of B diffusion, but their
relative contributions are hard to be quantified as the relevant
energetics is still poorly known.
The authors thank Masamitsu Uehara and Yuzuru Sato of
Seiko-Epson Corporation for many helpful discussions. They
thank Seiko-Epson Corporation for providing financial sup-
port. G.S.H. also thanks the Welch Foundation for their par-
tial financial support. The facilities of the MSC are also sup-
ported by grants from DOE-ASCI, ARO/DURIP, NSF ~CHE!
ARO/MURI, NIH, Chevron-Texaco, Beckman Institute, 3M,
Dow Chemical, Avery-Dennison, General Motors, Kellogg’s,
Asahi Chemical, and Nippon Steel.
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Hence, l(Bs – Bi)/l(Bs – Sii)’$@De(Bs – Bi)De(Sii)/De(Bs – Sii)2#/
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Shouldering in B diffusion profiles in Si: Role of di-boron diffusion

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Shouldering in B diffusion profiles in Si: Role of di-boron diffusion

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