Diffusion and Segregation Model for the Annealing of Silicon Solar Cells Implanted With Phosphorus

Abstract

We present a fully calibrated model for the diffusion, segregation, and activation of phosphorus for typical annealing conditions of implanted silicon solar cells. In contrast to existing process simulation software, this model allows the quantitative prediction of doping profile distributions, and, thereby, sheet resistances, surface concentrations, and junction depths. The model also provides an intuitive understanding of the dependence of these quantities on the parameters of the annealing process. A post-print version of the article can be found at publica.fraunhofer.de/documents/N-322023.html

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IEEE JOURNAL OF PHOTOVOLTAICS 1
Diffusion and segregation model for the annealing
of silicon solar cells implanted with phosphorus
F. A. Wolf, A. Martinez-Limia, D. Grote, D. Stichtenoth, and P. Pichler, Senior Member, IEEE
Abstract—We present a fully calibrated model for the diffusion,
segregation and activation of phosphorus for typical annealing
conditions of implanted silicon solar cells. In contrast to existing
process simulation software, this model allows to quantitatively
predict doping profile distributions, and thereby sheet resistances,
surface concentrations and junction depths. The model also
provides an intuitive understanding of the dependence of these
quantities on the parameters of the annealing process.
I. INTRODUCTION
CURRENT studies of implanted n-type Si solar cells for
industrial production use P implantation with subsequent
annealing for the formation of a back surface field (BSF) as
well as to facilitate contact formation [1, 2]. A major open
question in this context is whether an efficient process flow
can be realized [1], and in particular, whether a B-implanted
emitter and a P-implanted BSF can be coannealed. High-
dose non-amorphising B implants lead to massive structural
defects [3, 4], which can only be annealed with high thermal
budgets [4, 1]. By contrast, P implants amorphize and need
much lower thermal budgets [1] to anneal implant damage.
Due to the fast diffusion of P [5] and the necessity of high
surface concentrations for the BSF, they even require low
thermal budgets. Defining an efficient coanneal process is
therefore a non-trivial task that can be optimized with the
help of simulation. Simulation of B annealing with current
tools [6] is predictive for standard implantation conditions and
since recently even for fluorine containing plasma implantation
[7]. The situation is very different for P, for which post-
implantation annealing has not been as thoroughly investigated
due to the lower relevance of P for the formation of ultra
shallow junctions, and for which modeling is particularily
complicated as both interstitials and vacancies contribute to
diffusion. Complementary studies of P diffusion from glasses
or spray-on sources [8, 9, 10] provide valuable information
but are also not conclusive for post-implantation conditions
due to the very different state of intrinsic defects at the onset
of the annealing process. For the latter situation, only very few
simulation studies have been published [11, 12].
F. A. Wolf was, at the time of this work, with Corporate Research,
Robert Bosch GmbH, Robert-Bosch-Platz 1, 70839 Gerlingen-Schillerh¨
ohe,
Germany. He now is with LMU Munich.
A. Martinez-Limia is with Corporate Research, Robert Bosch GmbH,
Robert-Bosch-Platz 1, 70839 Gerlingen-Schillerh¨
ohe, Germany.
D. Grote and D. Stichtenoth are with SolarWorld Industries Th¨
uringen,
Arnstadt, Germany.
P. Pichler is with the Fraunhofer Institute for Integrated Systems and Device
Technology, Schottkystrasse 10, 91058 Erlangen, Germany and with the
Chair of Electron Devices, University of Erlangen-Nuremberg, Cauerstrasse
6, 91058 Erlangen, Germany.
Manuscript received August 2014, published by IEEE JPV Nov 2014, DOI:
10.1109/JPHOTOV.2014.2362358.
In this paper, we present a model that yields quantitatively
correct results for a wide range of experimental conditions, in
particular, for solar cell processing conditions. The paper is
structured as follows. Sec. II discusses diffusion, Sec. III pre-
cipitation and Sec. IV interface segregation. Sec. V compares
simulation results with experiment and Sec. VI concludes the
paper. The parameters of the model are found in the appendix.
II. DI FFU SI ON O F PH OS PH ORU S
As the calibration of the diffusion model for P is highly non-
trivial so that even state-of-the-art models yield qualitatively
wrong results (see Appendix B), we provide a detailed expla-
nation of the fundamental mechanism of high-concentration P
diffusion, as is relevant for solar cell production. This provides
one with both a clear strategy and an intuition, of how P
diffusion models can be recalibrated to address a particular
set of experiments.
We consider the following model for the diffusion of P via
P-interstitial (PI) and P-vacancy (PV) pairs [13]:
∂tCtotal
P=∂t(CP++CPI +CPV) = X
X=I,V
(−∂xJPX),(1a)
∂tCtotal
I=∂t(CI+CPI) = −∂xJI−∂xJPI −RIV +RIclus ,
(1b)
∂tCtotal
V=∂t(CV+CPV) = −∂xJV−∂xJPV −RIV ,(1c)
Therein, Cand Ctotal stand for the individual and total con-
centrations of quantities identified by the index: phosphorus in
any configuration (P), substitutional (active) phosphorus (P+),
isolated self-interstitials (I), vacancies (V), as well as PI and
PV pairs. Concentrations depend on position x(depth in the Si
wafer) and time t.JPXdenotes the currents of the PXpairs
(X=I,V) and JXthe currents of the isolated point defects.
The reaction of Is with I-clusters is contained in RIclus, for
which we assume the model of [14]. The implementation of
the recombination rate RIV for Is with Vs follows Ref. [13].
RIclus and RIV are not relevant for the following discussion.
The reduced model of Eq. (1), which is the basis for all what
follows, assumes the pairing reaction of P with point defects to
be in equilibrium. This results in a simple product relation [15]
for the concentration of pairs CP+
Xz=kP+
XzCP+CXz, where
zdenotes the charge state of the point defect that binds to
phosphorus [16]. Due to the product relation, the currents JPX
in Eq. (1) can be expressed in terms of contributions from the
substitutional dopant atoms CP+and the respective intrinsic
point defects CXzin the pair. Defining the total currents JPX
and JXas the sum over all charge states, JPX=PzJP+Xz
and JX=PzJXz, it remains to specify the contributions to

IEEE JOURNAL OF PHOTOVOLTAICS 2
Fig. 1. Intrinsic diffusivity Dintr
Pof P. Symbols depict literature data[19, 20,
21, 22] taken from the compilation of [5, p. 320]. The solid line corresponds
to the value of Dintr
Pobtained for our parameters for DP+I0,DP+I−,DP+V=,
which are specified in Appendix A. The contributions from P+V−and P+V0
pairs can be neglected and therefore are omitted. For comparison, we plot the
fit obtained by [5] described by 1.03e−3.507 eV/kT .
each charge state
JP+
Xz=−DP+
Xzn
ni−zCP+
C∗
X0
∂xCX0+αf
CX0
C∗
X0
∂xCP+,
(2a)
JXz=−DXzn
ni−z
∂xCX0,(2b)
where the field enhancement factor [17] αfis
αf= (1 + CP+(C2
P++ 4n2
i)−1
2),(3)
with ndenoting the electron concentration and nithe in-
trinsic concentration of charge carriers. C∗
X0stands for the
equilibrium concentration of point defect Xin charge state
z= 0, and DXzand DP+
Xzdenote the diffusion constants
of the charged intrinsic point defects Xand charged PX
pairs. Values for DXzhave been well-studied experimentally
[18] and we simply assume the default values of Sentaurus
Process [6] for them. Values for DP+
Xz, by contrast, show
a considerable spread over the literature [5], and we discuss
their calibration in the following.
a) Low-concentration diffusion: The concentration of
intrinsic point defects in the bulk is determined by the inter-
play of two complementary processes: P diffusion transports
intrinsic point defects Xvia the mobile PXpairs into the
bulk while the transport back to the surface goes via self-
diffusion of X. At low P concentrations, the former process
is negligible in comparison to the latter. P diffusion then
causes only insignificant deviations of the concentrations of
intrinsic point defects from equilibrium so that the gradients
∂xCX0= 0 vanish. In this approximation, summing over the
charge states of PI and PV pairs as defined in Eq. (2), one
obtains a single effective diffusion equation
∂tCtotal
P=∂xX
X,z αfDP+
Xzn
ni−zCX
C∗
X∂xCP+,(4)
which for intrinsic conditions, where n=niand αf'1,
gives
∂tCtotal
P=Dintr
PI
CI
C∗
I
+Dintr
PV
CV
C∗
V∂2
xCP+.(5)
Fig. 2. Details of P diffusion after an implant of 4.5·1015 cm−2at
10 keV annealed at 900 ◦C for 34 min. The concentration of Is increases
when going deeper into the bulk, while the inverse is true for Vs. Note that
CX/C∗
X=CX0/C∗
X0. A similar figure has been shown in Ref. [23].
where we defined the intrinsic diffusion coefficients
Dintr
PX=X
z
DP+
Xz.(6)
In this work, we assume that P diffusion is mediated by
P+I−, P+I0, P+V=, P+V−and P+V0pairs, as is assumed in
Ref. [6]. Fig. 1 compares our calibration for DP+I0,DP+I−,
DP+V=and the resulting value for Dintr
Pwith experimental
data. The parameters DP+I0,DP+I−,DP+V=can be found
in Appendix A. We do not show the parameters DP+V−and
DP+V0, which we leave as in the calibration of [6] where they
only contribute for temperatures clearly below 800 ◦C, which
is outside the temperature range we are interested in. As seen
in Fig. 1, our choice of parameters yields an intrinsic diffusion
coefficient close to the fit of Ref. [5], obtained by fitting many
experimental results.
b) High-concentration diffusion — kink concentration:
For high-concentration diffusion, the diffusion of P has a
strong influence on the intrinsic point defect concentrations
in the bulk [23, 24]. This leads to strongly inhomogeneous
intrinsic point defect distributions and the gradient ∂xCX0in
the PXcurrent (2a) can no longer be neglected. To understand
the physical mechanism that leads to this contribution, con-
sider the typical example shown in Fig. 2. The figure allows
to qualitatively interpret the terms in the coupled diffusion
equations (1b) by realizing that currents are, via the gradients
in Eq. (2), proportional to the slope of the concentration
profiles shown in Fig. 2: Clearly, JPI transports Is deeper
into the bulk, while JItransports Is back to the surface.
The qualitative behavior of JV, by contrast, is not as clearly
defined, as the concentration profile for Vs is quite flat for
the parameter regime shown in Fig. 2. Generally, comparing
the current contributions JPXwith JX, one observes that JPX
in Eq. (2a) grows strongly w.r.t. CP+, while JXin Eq. (2b)
does not. For high values of CP,JPXtherefore dominates
over JX, and high amounts of Is are transported into the bulk,
whereas close to the surface, the I concentration is still around
its equilibrium value (see right ordinate of Fig. 2). This implies
(compare (5)) a high effective P diffusion coefficient deeper
in the bulk, and a normal P diffusion coefficient close to the
surface. This separates two regions in which P diffusion occurs

IEEE JOURNAL OF PHOTOVOLTAICS 3
Fig. 3. Panel (a): The contribution of P to I diffusion increases much
faster than the one for V diffusion. The estimates for the kink concentration
Ckink,estim
Pare given by the positions of the intersection of the transport
quotient for Is with an ordinate value of unity, as defined in Eq. (9). The
numerical values of these estimates are shown for four different temperatures.
The legend for the temperatures is given in panel (b). Panel (b): Comparison
of the estimate for the kink concentration with a simulation for a P dose
of 1·1015 cm−2implanted at 10 keV (see also experimental data in the last
section).
at qualitatively different strengths, which leads to the typical
kink in high-concentration P diffusion profiles.
The value of the kink concentration can be estimated with
the following argument. The ratio of the currents of Xthat
diffuse via PXand the the currents of Xthat diffuse isolated
equals the ratio of their respective transport capacities [5,
Sec. 3.4.7] DPXCP+
DXC∗
X
(7)
where the effective diffusion coefficients of PXpairs has been
introduced as
DPX=X
z
DP+
Xzn
ni−z
.(8)
The kink concentration, i.e. the P concentration at which
the two qualitatively different diffusion regions are separated,
roughly appears when the transport capacity of the PXpair
becomes higher than the transport capacity of the isolated X.
The ratios of transport capacities (7) are shown in their
dependences on the P concentration in Fig. 3(a) for our
calibrated parameters of Appendix A. The transitions from
the domination of self-diffusion to the domination of impurity-
atom diffusion are given by intersections of the ratios of the
transport capacities with the constant line at an ordinate value
of unity. These intersections occur for typical P concentrations
as observed in Fig. 2 in the case of I. In the case of V, these
Fig. 4. Equilibrium P activation model. Upper panel: The free (active)
P concentration Cfree
Pis obtained from the total P concentration CPvia
Eq. (11). The exact value for CPfree is obtained by usage of Eq. (10) and the
approximated value by usage of Eq. (11) for the plateau annealing temperature.
The temperature used for the panel is 850 ◦C. Lower panel: Solubility Css
Pof
electrically active P. The literature data is taken from the compilation of [5]
and shows measurements of [25], [26], [27], [28] and [29].
intersections occur for so high P concentrations, that their
effect can usually not be observed. It is therefore the case
of Is, for which the intersection yields an approximation for
the appearance of the typical kink,
Ckink,estim
Pdefined by DPICkink,estim
P
DIC∗
I
= 1,(9)
where it should be remembered that DPI and DIdepend on CP
via n
ni. Isolation of Ckink,estim
Pin Eq. (9) is therefore tedious.
The values for Eq. (9), as obtained for our parameters, are
explicitly shown for Is in Fig. 3(a). In Fig. 3(b) we plot these
values as horizontal lines together with the simulated P con-
centration profiles. Agreement is good even on a quantitative
level, only for the lowest temperature, it is poorer. Such an
analysis provides a systematic strategy to narrow down the
calibration of diffusion constants to a small regime that is
compatible with a comparison of own experimental data of
kink concentrations.
III. CLUSTERING AND PRECIPITATION
The active P concentration in P profiles is in the literature
found to be best characterized as a plateau, which extends
rather deeply into the wafer [see e.g. 10, 30]. Current models
[31] implement a dynamical clustering reaction to describe
insufficient activation, which leads to results that contradict
this experimental evidence: the concentration profile of a

IEEE JOURNAL OF PHOTOVOLTAICS 4
dynamically modeled cluster reduces the active concentration
only up to the shallow depth of the as-implanted profile, as the
modeled clusters remain immobile throughout the anneailng
process. By contrast, with the equally well-established steady-
state clustering model, we can directly reproduce the plateau
shape. The steady-state model defines a solubility for active P
that obeys an equilibrium relation: The fraction of P below this
solubility is assumed active and participates in diffusion, the
fraction above this solubility is assumed inactive and does not
participate in diffusion. In practice, in the diffusion equations
of Sec. II, where substitutional P appeared as CP+, we now
replace it with the concentration of free phosphorus CPfree ,
obtained from some total P concentration CP.
Taking the solubility model literally, one would define the
relationship between CPfree and CPrigidly in the form
CPfree 'Css
Pfor CP≥Css
P,
CPfor CP≤Css
P.(10)
However, this function is not smooth and was found to lead
to non-converging numerical solutions. Instead, we use the
approximation
Cfree
P=Css
PCP
Css
P+CP
(11)
which corresponds to the activation model Solid of Sentaurus
Process [6].
In the upper panel of Fig. 4, we show the approximation of
the free P concentration together with the rigid formulation
(10). One observes a significant mismatch for the region
around CP=Css
P+. The solid solubility as used with the
approximate expression (11) has thus to be considered an
effective parameter, employed to satisfy the necessity to use
a smooth functional dependence of Cfree
Pon CP. Therefore, to
calculate the sheet resistance after the simulation, we employ
the rigid relation, fitted to well-checked experimental values
as shown in the lower panel of Fig. 4, and evaluated for the
plateau annealing temperature.
IV. INTERFACE SEGREGATION OF PHOSPHORUS
In the case of interface segregation, current models [31]
qualitatively overestimate segregation for the experimental
conditions studied here. In particular, they do not show a
reversible segregation [32] that should occur for the high
temperatures used in typical solar cell processing conditions:
After ion implantation, the high amount of implantation-
induced Is leads to transient enhanced diffusion already at
low temperatures, where the energy-driven segregation is
much stronger than at high temperatures, where entropy-driven
redistribution usually becomes so strong that the segregated P
is again released from the interface traps.
Models for the dynamic segregation of P at the SiO2/Si
interface approximate the interface as an infinitely thin layer
[33, 34]. The traps in this layer can in principle dynamically
capture and release P to both sides of the interface. This
model is described by the fluxes in (Jt) and out (Je) of the
interface, leading to the following time evolution equation for
the number of trapped P atoms NP[35, 6]
∂tNP=Jt−Je(12)
Jt=kt(Nt−NP)CP+(13)
Je=keNP(Css,seg
P−CP+)(14)
Here, CP+≡CP+(x)|x=0 is the P concentration on the silicon
side of the interface that is situated at x= 0.Css,seg
Pis a
limiting concentration in the bulk, usually at least the solid
solubility, and ktand keare trapping and emission rates.
In general, the interface can exchange dopants with both
neighboring materials, and one has a sum in Eq. (12) that reads
∂tNP=Pa=Si,SiO2Jt
a−Je
a. In practice, almost no dopant is
exchanged with the oxide side [31]: Jt
Ox '0and Je
Ox '0.
With this we can keep the simple notation of Eq. (12) and do
not have to account for the material-dependent terms.
In equilibrium, Eq. (12) yields
NP
Nt−NP
=CP+
Css,seg
P−CP+
kt
ke
,(15)
which implies that kt
kecan be associated with a segregation
free energy ∆G,
kt
ke
=e∆G/kT .(16)
One must have ∆G > 0to observe segregation of P for
sufficiently low temperatures. From this one concludes that,
if ktand keboth follow Arrhenius laws, the activation energy
of kemust be higher than that of kt, which is a rigorous
constraint for these parameters. We finally note that interface
segregation has a major influence on the surface concentration,
which determines contact properties as well as charge carrier
recombination at the surface.
V. EX PE RI ME NTA L VALIDATIO N
We compare the simulation results of our model with
typical solar cell processing experiments in Figs. 5 and 6,
and find good agreement in all cases, which vary over a wide
range of temperatures and implantation doses. While the high-
temperature conditions of Fig. 6 do not pose a difficult case,
for the lower temperature conditions of Fig. 5, the interplay
of transient enhanced diffusion, segregation and activation
phenomena has to be correctly captured by the model, in order
to reproduce the typical benchmarks of kink position, junction
depth and surface concentration.
A prominent feature in the experimental profiles are the
peaks at the SiO2/Si interface, which are signatures of inactive
interface-segregated P atoms. As already mentioned at the
beginning of Sec. IV, interface segregation is reversible and
can therefore be strongly influenced by the detailed annealing
protocol. We show the time evolution of the segregated P dose
in Fig. 7(a), where for the lowest temperature, the segregated
dose increases during the whole annealing process. For higher
temperatures, the dose is partly recovered, i.e. it reenters
the bulk when reaching the plateau annealing temperature.
Only at the end of the annealing process, during the low
temperatures that occur during ramp-down, the segregated
dose increases again. This increase of the segregated dose

IEEE JOURNAL OF PHOTOVOLTAICS 5
Fig. 5. P concentration profiles for annealing of implanted Phosphorus
at 10 keV and doses of 1·1015 cm−2and 4.5·1015 cm−2. Symbols depict
experimental results obtained at Bosch Solar Energy, lines depict simulation
results. The annealing temperatures and times are given in the panels. Heating
and cooling ramps proceed at 10 K/min, starting at 600 ◦C. The interface to the
oxide is at 0 µm. Simulations performed using the calibrated model described
in Sec. A.
during ramp down can degrade the quality of the back surface
field, as it considerably reduces the P surface concentration.
Finally, in Fig. 8, we show experimental and simulation
results for the sheet resistances obtained for the dopant profiles
shown in Fig. 5. We find very good agreement using the
Fig. 6. P concentration profiles after implantation and annealing. Parameters
are given in the figure. Experimental data from [36] (upper panel) and [37]
(lower panel). Simulations performed using the calibrated model described in
Sec. A.
Fig. 7. The segregated P dose for the concentration profiles of the
1·1015 cm−2dose in Fig. 5. Upper panel: Simulated time evolution. Lower
panel: Comparison with experiment. Lines and filled symbols depict the
simulation, open symbols the experiment. The ramp up and down proceeded
with 10 K/min, starting and ending at 600 ◦C. 800 ◦C are therefore reached
after 20 min of annealing. Up to this time and slightly longer, all curves agree.

IEEE JOURNAL OF PHOTOVOLTAICS 6
Fig. 8. Sheet resistance measurements compared to values calculated from simulated profiles, using the the mobility values of Sentaurus Process [6]. The
corresponding concentration profiles for the cases with P doses of 1·1015 cm−2and 4.5·1015 cm−2have been shown in Fig. 5.
method explained in Sec. III. Again, we find the signature
of segregation: the values of Rsfor the 800◦C data points
are significantly higher than the values of Rsobtained for
higher temperatures, separated by a step that can be associated
with the irreversible segregation at 800◦C and the reversible
segregation for higher temperatures (Fig. 7(a)). The non-
trivial activation phenomena can therefore be explained with
segregation, whereas the influence of precipitation is easy
to understand: precipitation only contributes for very high P
concentrations and shows a very weak and smooth temperature
dependence as shown in Fig. 4.
VI. CONCLUSION
We presented a predictive model for the diffusion and seg-
regation of P in Si for typical solar cell processing conditions.
We clarified important physical mechanisms and their relation
to profile form and sheet resistance. The presented model is
suitable to optimize processing conditions in the emerging
field of implantation in photovoltaics.
APPENDIX
A. Parameters of the model
The diffusion model of (1) is termed Charged Pair in
Sentaurus Process [6]. The full dynamical model Charged
React leads to equivalent results for the conditions studied
in this paper, similarly to the observations of Ref. [13].
Implantations have usually been simulated with the Sentau-
rus Process Monte Carlo implantation in its default configura-
tion [6]. In order to speed up calculations, for the simulations
shown, we used an analytical implantation, using a “+1.4
model”. This leads to the same net number of implantation-
induced interstitials behind the amorphous-crystalline bound-
ary, as obtained in the Monte Carlo implantation. It therefore
leads to the same results for the diffusion profiles.
We use the parameters of the Advanced Calibration of
Sentaurus Process [31] as a starting point. In the following,
we only specify the parameters that we changed. We used the
I clustering model of [14], which turned out to be sufficiently
accurate for the conditions discussed in this paper. More so-
phisticated I clustering (dislocation loop) models [38] yielded
almost equivalent results, but required more computational
time. An extended discussion of the following parameters can
be found in Ref. [38].
The changed diffusion coefficients read DP+I−= 8.25·101·
e−4.1eV/kT cm−2/s, DP+I0= 7.80 ·101·e−4.0eV/kT cm−2/s
and DP+V== 1.83 ·10−5·e−2.9eV/kT cm−2/s. The less
relevant diffusivities of DP+V−and DP+V0are left unchanged.
We furthermore change one pairing rate: kP+V== 2.1·10−26 ·
e1.0eV/kT cm2.
The solid solubility used to solve the diffusion model is set
to 2.0·1021 ·e−0.1eV/kT cm−3while the solid solubility used
to evaluate the simulated data, e.g. for obtaining Rs, is taken
as 0.51 ·1022 ·e−0.3eV/kT cm−3.1
Concerning interface segregation: The emission rate is set to
ke= 1.04 ·10−9·e−3.4eV/kT cm3/s for T < 850 ◦C and ke=
1.66·10−11 ·e−3eV/kT cm3/s for T≥850 ◦C. The trapping rate
is set to kt= 2.1·10−29 ·e−0.7eV/kT cm3/s. The dissolution
rate for an auxiliary clustering reaction P ↔P2in the interface,
defined in [31], is set to kdis = 1.2·1028 ·e−3eV/kT cm−2.
While the preceding parameters are a general calibration
that correctly describes very broad experimental conditions
[38], the high precision shown in Figs. 5 and 6, is related
to a particular recalibration, for which we changed two
diffusivities: DP+I−= 1.07 ·102·e−4.1eV/kT cm−2/s for
T < 900 ◦C and DP+I−= 4.05 ·104·e−4.7eV/kT cm−2/s
for T≥900 ◦C. DP+V== 2.42 ·101·e−4eV/kT cm−2/s.
To obtain high precision also for the 4.5·1015 cm−2dose
simulation in Fig. 5, we again changed these two diffusivities:
DP+I−= 8.25 ·101·e−4.1eV/kT cm−2/s for T < 900 ◦C and
3.12 ·104·e−4.7eV/kT cm−2/s for T≥900 ◦C. DP+V==
9.59 ·10−4·e−3.3eV/kT cm−2/s.
1The justification and explanation of this difference is discussed at length
in Sec. III. The activation model discussed there is called solid in Sentaurus
Process [6], which is not the default of the Advanced Calibration.

IEEE JOURNAL OF PHOTOVOLTAICS 7
Fig. 9. P concentration profiles for annealing of implanted Phosphorus
at 10 keV and doses of 1·1015 cm−2and 4.5·1015 cm−2. Symbols depict
experimental results from Bosch Solar Energy, lines simulation results. The
annealing temperatures and times are given in the panels. Heating and cooling
ramps proceed at 10 K/min, starting at 600 ◦C. The interface to the oxide
is at 0 µm. Simulations were performed using [31]. Sentaurus Monte Carlo
implantation was used with its default options.
B. Results with Sentaurus Process Advanced Calibration
In Fig. 9, we show the predicition of a state-of-the-arte diffu-
sion model [31] for the typical solar cell relevant experiments
we studied. We note that the model of Ref. [31] is mainly
adapted to rapid thermal annealing conditions. To describe the
latter predictively was not the main focus of the present work.
However, several comparisons of the current model for much
shorter annealing times can be found in the dissertation of
Wolf [38].
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IEEE JOURNAL OF PHOTOVOLTAICS 9
F. Alexander Wolf obtained a M. Sc. in Physics in 2011 from the University
of Augsburg. At the time of this work, he was a PhD student at Bosch
Corporate Research, Gerlingen, Germany. He now is with the Ludwig-
Maximilians-Universit¨
at (LMU), Munich.
Alberto Martinez-Limia obtained his diploma in Nuclear Physics in 1994
from the Institute of Nuclear Sciences and Technology of Havana and his
PhD in 2002 from the Institute of Theoretical Chemistry of the University
of Erlangen-Nuremberg. Later he worked in several academic and scientific
organizations: the University of South Carolina, the University of Chemnitz
and the Fraunhofer Institute IISB in Erlangen. He investigated topics related
to material modeling and process simulation. In October 2008 he joined the
Robert Bosch GmbH as a Research and Development scientist.
Daniela Grote studied physics at the Universities of Marburg and Freiburg,
Germany. She received her diploma degree in physics in 2004 from the
University of Freiburg. In 2010 she obtained her Dr. rer. nat. from the
University of Konstanz. Both diploma thesis and dissertation focus on different
aspects of the characterization and simulation of silicon solar cells and were
realized at the Fraunhofer Institute for Solar Energy Systems ISE, Freiburg,
Germany. In 2010 Daniela Grote joined the Bosch Solar Energy AG, Arnstadt,
Germany, and is now with the SolarWorld Industries Th¨
uringen GmbH,
Arnstadt, Germany.
Daniel Stichtenoth studied physics at the University of G¨
ottingen, Germany
and Uppsala, Sweden. He received his diploma degree in physics in 2005 and
his Dr. rer nat in 2008 from the University of G¨
ottingen, Germany. Since 2009
he is with BOSCH Solar Energy AG, Arnstadt, Germany and works in the
field of silicon solar cell development. His main focus is on the interaction
of silicon with high-efficiency silicon solar cell processes.
Peter Pichler obtained the Dip.-Ing. degree in Electrical Engineering in 1982
and the Dr. techn. degree 1985 both from the Technical University of Vienna.
Since 1986 he has been Group Manager at Fraunhofer IISB, responsible
now for the doping and device simulation activities. In 2004 he obtained
the venia legendis from the University of Erlangen-Nuremberg. Dr. Pichler
contributed to various European projects and coordinated the EC projects
RAPID, FRENDTECH, ATOMICS and ATEMOX on diffusion and activation
phenomena in silicon and silicon-based materials, as well as on the modeling
of leakage currents and technologies for low-leakage ultrashallow junctions.
He is the author or coauthor of some 120 publications in international journals
and conference proceedings, and author of the book “Intrinsic Point Defects,
Impurities, and Their Diffusion in Silicon” published by Springer Wien-New
York.