CORRESPONDENCE BETWEEN SHEET RESISTANCE AND EMITTER PROFILE OF
PHOSHORUS DIFFUSED EMITTERS FROM A SPRAY-ON DOPANT
Andreas Bentzen and Arve Holt
Section for Renewable Energy, Institute for Energy Technology (IFE), P.O. Box 40, NO-2027 Kjeller, Norway
ABSTRACT
The evolution of the emitter sheet resistance upon
phosphorus in-diffusion from a spray-on dopant has been
studied in the temperature range 840-990°C. In
complement with investigations of emitter diffusion
profiles, by both electrochemical capacitance-voltage
profiling and secondary ion mass spectrometry, we find
that the sheet resistance is determined directly by the
depth of the flat plateau near the surface in profiles of
electrically active phosphorus. Thus, with respect to sheet
resistance, an emitter can be regarded as a constant
concentration abrupt box layer, with thickness and
concentration specified by the flat plateau, irrespective of
the actual profile at lower concentrations. Therefore,
independent optimization of the emitter profile at lower
concentrations is enabled.
INTRODUCTION
During multicrystalline silicon (mc-Si) solar cell
fabrication, an important process step is the formation of
the diffused emitter. In order to obtain optimal solar cell
performance, careful tuning of the emitter profile is
necessary. Particularly, to minimize the amount of light
absorbed within the highly doped region, and thus
increase the short wavelength response of the solar cell,
the emitter needs to be as thin as possible. However, this
generally results in a high sheet resistance, demanding
close spacing of the front contact fingers to avoid ohmic
losses. Moreover, a shallower emitter can affect the solar
cell to become more subjected to parasitic resistances,
due to over-firing of the contacts through the junction.
For simple emitter diffusion profiles, following
Gaussian or complementary error function (erfc)
distributions, sheet resistances can be readily calculated
by the well-known Irvin’s curves [1]. However, in Si solar
cell processing, emitter profiles generally deviate
significantly from such simple distributions. When P
diffused emitters are processed by in-diffusion from a
gaseous, liquid, or solid source of high concentration, the
characteristic kink-and-tail profiles are commonly obtained
[2,4]. Such profiles are distinguished by a shallow high
concentration region surpassed by a deeper tail at lower
concentrations. Moreover, when the concentration near
the surface is sufficiently high, as is often the case in solar
cell emitters, the profile of electrically active P deviates
from the chemical concentration, and a flat plateau near
the surface can be observed in the electrical profile [3,4].
0-7803-8707-4/05/$20.00 ©2005 IEEE.
To allow for optimization of emitter profiles in solar
cell processing, knowledge on the correspondence
between the emitter sheet resistance and the diffusion
profile is important. In the present study, we investigate
this correspondence for emitters diffused from a high
concentration spray-on source in an IR-heated belt
furnace.
EXPERIMENTAL DETAILS
2
Neighboring 10x10cm wafers from a ~1Ωcm B doped
mc-Si block were selected to ensure comparable material
properties in each sample. In order to remove surface
damage resulting from the wafer sawing, the as cut-wafers
were first etched in a heated solution of 20% NaOH. Then,
to further smoothen the surfaces, a chemical polish
consisting of HNO 3:HF:CH3COOH (10:2:5) was utilized,
resulting in a total thickness reduction of ~40µm.
Immediately after dipping in diluted HF and drying, the P
diffusion source Filmtronics P509 was applied by
pressurized air spraying, and the samples were baked at
120ºC to remove solvents from the film. Then, emitters
were formed by in-diffusion from the spray-on film in an
RTC-1210 IR-heated belt furnace in the temperature
range 840-990°C.
Following the diffusion, removal of the residual
diffusion source was achieved by etching in 10% HF.
Then, emitter sheet resistances were measured using a
four-point probe at 25 different positions across each
sample, in order to reduce the effect of variations in intergrain resistance. Finally, the diffusion profiles were
investigated by electrochemical capacitance-voltage
(ECV) profiling using a 0.1M NH4HF2 electrolyte, and
+
secondary ion mass spectrometry (SIMS) using Cs
primary ions with a net energy of 13.5keV, revealing the
electrically active and chemical P concentration profiles
respectively. All diffusion profiles were investigated in
equivalent grains on the different samples.
RESULTS AND DISCUSSION
The emitter sheet resistance of emitters diffused in
the temperature range 840-990°C is shown against the
inverse square root of the diffusion time in Fig. 1. The
error bars represent the standard deviation of all
measurements at equivalent diffusion parameters. It is
clearly seen from the figure that at a given diffusion
temperature, the sheet resistance is inversely proportional
to the square root of the diffusion time.
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Fig. 1. Emitter sheet resistance versus the inverse square
root of the diffusion time for different diffusion
temperatures and times.
Fig. 2. Emitter profile of electrically active phosphorus
(solid line) and total chemical concentration (circles) for an
emitter diffused at 840°C for 20 minutes.
Such time dependence of the sheet resistance is a
well-known result in planar Si technology, when emitters
are expressed by simple Gaussian, erfc, or abrupt box
profiles. In the latter example, i.e. a simple planar abruptly
doped emitter of constant concentration, the well-known
definition of the sheet resistance, Rs, is written as
Rs =
ρ
,
d
(1)
where ρ is the resistivity in the layer and d is the layer
thickness. In the case of Gaussian or erfc distributions,
Irvin showed that the same relation for the sheet
resistance could be used if employing the junction depth
for d and defining an average resistivity of the layer by
integrating each concentration contribution through the
profile [1]. In the case of simple diffusion profiles, such as
the Gaussian, erfc, or abrupt box distributions, it is easily
shown that the depth at any given concentration in the
profile can be expressed as
d = A Dt ,
(2)
where D is an apparent diffusivity, t is the diffusion time,
and A is a factor associated with the relation between the
concentrations at the surface and at the position
considered in the profile. In the following, we will let A be
contained within the apparent diffusivity, D, bearing in
mind that D is not to be regarded as an absolute diffusivity
of P in Si under the experimental circumstances in this
work. Combining equations (1) and (2) above then
demonstrates a time dependence of the sheet resistance
as observed above. Although actual solar cell emitters
normally deviate significantly from the simple profiles
considered above, we will nevertheless see later that such
simplifications have important relevance when analyzing
the emitter sheet resistance.
Fig. 3. Emitter profiles of electrically active phosphorus as
measured by ECV after diffusion at different temperatures.
In order to study the correlation between the sheet
resistance and the profile of diffused solar cell emitters, we
investigate the emitter profiles obtained after diffusion in
the previously mentioned temperature range for durations
between 4-40 minutes. Fig. 2 shows as an illustration of
the difference between the electrically active and chemical
concentration, an emitter profile obtained after diffusion at
840°C for 20 minutes, resulting in an emitter sheet
resistance of ~70Ω/sq. The profiles clearly express that
the concentration of electrically active P saturates at a
practically constant level at high concentrations, exhibiting
a flat plateau near the surface as mentioned earlier. At a
characteristic depth, the plateau ends abruptly and the
profile of electrically active P follows that of the chemical
concentration closely. Due to the very high concentration
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gradients in shallow diffused emitters, ECV profiling may
result in erroneous depth information caused by variations
in the etching regime during measurements [5]. To
account for this, all profiles were measured by both ECV
and SIMS, and discrepancies between the profiles, if any,
were corrected by slightly adjusting the depth scale of the
ECV profiles to match the SIMS measurements at low
concentrations.
Fig. 3 shows thus corrected ECV profiles of emitters
diffused from the spray-on source at 840, 890, and 940°C
for 20min. All profiles reveal the above-mentioned flat
plateau near the surface where the electrically active P
exhibits a practically constant concentration of about 220
-3
3x10 cm , in satisfactory agreement with previously
published values on the limit of electrically acti ve P in
equilibrium with inactive dopant [6,7]. For chemical
concentrations above this limi t, P exists in a mixture of SiP
precipitates and mobile neutral atoms [7].
By inspection of the ECV profiles, as exhibited in Fig.
3, it appears reasonable to argue that a significant majority
of the total amount of electrically active P is contained
within the region in the emitter comprised by the flat
plateau. This is especially the case for the shallowest
emitters, represented in Fig. 3 by the 20 minutes 840°C
diffusion, in which a very high concentration gradient can
be observed where the flat plateau ends. Reflecting this,
we will therefore attempt to simplify the emitters to consist
of an abrupt box-like shape with concentration and depth
given by the flat plateau in the real profiles, neglecting the
P concentration in the tails. This is, naturally, not
consistent with the true emitter profiles.
By combining equations (1) and (2) above, one gets
for the simple abrupt structure
D
1
= 2,
2
Rs t ρ
Although non-negligible standard deviations are
shown, especially at higher diffusion temperatures, Fig. 4
clearly reveals that the left hand side of equation (3)
indeed exhibits an Arrhenius behavior. The solid straight
line fitted through the data represents a pre-exponential
7
factor of 5.7x10 and apparent activation energy of 3.2eV.
As was noted previously, the depth at a given
concentration in the emitter profile can be expressed by
equation (2), where D is to be regarded as an apparent
diffusivity. Rearranging equation (2), one obtains
d2
= D,
t
(3)
where the temperature independent proportionality factor
A in equation (2) is now contained within the apparent
diffusivity as noted previously. Considering further an
activated diffusion mechanism, the apparent diffusivity can
be described by an Arrhenius behavior,
 −E 
D = D0 exp a  ,
 kB T 
Fig. 4. Arrhenius plots of the inverse square sheet
resistance divided by diffusion tim e (open squares) and
apparent flat plateau diffusivity (solid circles), revealing
parallel straight lines.
(4)
where Ea is an apparent activation energy, kB is
Boltzmann’s constant, and T is the absolute diffusion
temperature. An Arrhenius plot of the left hand side of
equation (3), i.e. plotted logarithmically as a function of
1/kBT, would reveal a straight line with a slope of –Ea and
a pre-exponential factor D0/ρ2 for an abrupt box profile. In
the case of Gaussian or erfc profiles, the resistivity would
be represented by the average through the profile as
discussed previously. Fig. 4 shows this Arrhenius plot,
where the open squares represent the mean value of all
measurements at the same diffusion temperature for
different diffusion times. The error bars indicate the
standard deviation in the measurements.
(5)
where D is described by an Arrhenius behavior through
equation (4), and the proportionality factor A has been
accounted for as previously mentioned. For the abrupt box
simplification discussed above, where d is chosen as the
depth of the flat plateau of electrically active P, an
Arrhenius plot of the left hand side of equation (5) should
then reveal a straight line, parallel to the data derived from
the sheet resistance and differing only from the latter by a
2
factor ρ .
The solid circles in Fig. 4 represent the apparent flat
plateau diffusivity as calculated with equation (5), where
the error bars denote the standard deviation from data at
differing diffusion tim es. The straight dashed line fitted
through the data correspond to a pre-exponential factor of
6.0 and apparent activation energy 3.2eV. As seen from
the figure, the two Arrhenius plots are indeed parallel,
revealing the same apparent activation energy. Moreover,
from the pre-exponential factors, an apparent emitter
-4
resistivity of ρ ≈ 3.24x10 Ωcm is implied, corresponding in
the box profile simplification to an electrically active dopant
concentration Cn ≈ 2.6x1020cm -3 [1,8]. This value is in
good agreement with the plateau concentration revealed
by the ECV profiles shown in Fig. 3, indicating validity of
the simple box profile analogy.
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profile at lower concentrations. Moreover, we find that the
depth of the flat plateau is described by an Arrhenius
behavior, exhibiting an apparent activation energy of
3.2eV. The results indicate that additional optimization of
the diffusion process to tailor the low concentration region
is both allowed and needed.
ACKNOWLEDGEMENTS
This project was financed by the Norwegian Research
Council. The authors would like to thank Dr. Radovan
Kopecek (University of Konstanz) for assistance with the
ECV profiling, and Dr. Margareta Linnarson (Royal
Institute of Technology) for assistance with SIMS.
REFERENCES
[1] J.C. Irvin, “Resistivity of bulk silicon and of diffused
layers in silicon”, Bell Syst. Tech. J. 41, 1962, pp. 387410.
Fig. 5. Depth of the flat plateau in profiles of electrically
active phosphorus versus the inverse emitter sheet
resistance.
Further indication on the validity of the abrupt box
profile simplification can be found by considering equation
(1) directly, i.e. the relation between sheet resistance and
the depth of the flat plateau. Fig. 5 shows the depth of the
flat plateau as found by the profiles of electrically active P
versus the inverse sheet resistance of the emitters.
It is clearly seen from Fig. 5 that an inverse relation
between sheet resistance and plateau depth exists, in
agreement with equation (1). The straight line fitted
through the data in Fig. 5 corresponds to an apparent
-4
emitter resistivity ρ ≈ 3.24x10 Ωcm, similar to what was
found above. Again, we thus find that the emitters can be
regarded as simple abrupt box layers of constant
concentration corresponding to the flat plateau in profiles
of electrically active P concentration.
This simplification, although rudely imprecise in
predicting the real emitter profiles, nevertheless shows
that the tail region of a shallow diffused emitter provide
minor contribution to the lateral current transport within the
emitter. The implications of this are two-fold. Firstly, it
shows that sheet resistance is not a good indication of the
true junction depth of a high concentration shallow
diffused emitter, as the tail penetration does not
significantly affect sheet resistance. Secondly, and more
important, the results indicate that the tail region of the
emitter profile can be tailored independently of the sheet
resistance, allowing further optimi zation of the solar cell
processing.
[2] J.C.C. Tsai, “Shallow phosphorus diffusion profiles in
silicon”, Proc. IEEE 57, 1969, pp. 1499-1506.
[3] E. Tannenbaum, “Detailed analysis of thin
phosphorus-diffused layers in p-type silicon”, Solid-State
Electronics 2, 1961, pp. 123-132.
[4] A. Bentzen et al., “Phosphorus diffusion and gettering
th
in multi-crystalline silicon solar cell processing”, Proc. 19
EUPVSEC, 2004, pp. 935-938.
[5] E. Peiner and A. Schlachetzky, “Anodic-dissolution
during electrochemical carrier-concentration profiling of
silicon”. J. Electrochem. Soc. 139, 1992, pp. 552-557.
[6] G. Masetti, D. Nobili, and S. Solmi, "Profiles of
phosphorus predeposited in silicon and carrier
concentration in equilibrium with SiP precipitates”, in
Semiconductor Silicon 1977, ed. H.R. Huff and E. Sirtl,
The Electrochemical Society, Pennington, 1977, pp. 648658.
[7] S. Solmi et al., “Dopant and carrier concentrations in
equilibrium with monoclinic SiP precipitates”, Phys. Rev.
B. 53, 1996, pp. 7836-7841.
[8] S.M. Sze and J.C. Irvin, “Resistivity, mobility and
impurity levels in GaAs, Ge, and Si at 300K”, Solid-State
Electron. 11, 1968, pp. 599-602.
CONCLUSIONS
We have shown that the sheet resistance of emitters
diffused from a high concentration spray-on source is
mainly dependent on the flat plateau of electrically active
diffusant, not significantly influenced by the tail region of
the diffusion profiles. From an electrical consideration, the
emitter can thus be regarded as a simple abrupt box layer
corresponding to the flat plateau, regardless of the emitter
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