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* Corresponding author. Tel.: #965 4811188, xtn 5850; fax: #965 4817451; e-mail: alomar@
cairo.eng.kuniv.edu.kw.
Solar Energy Materials and Solar Cells 52 (1998) 107 124
Optimum two-dimensional short circuit collectionefficiency in thin multicrystalline silicon solar cells
with optical confinement
A.S. Al-Omar*, M.Y. Ghannam
Department of Electrical and Computer Engineering, Kuwait University, P.O. Box 5969, 13060 Safat, Kuwait
Received 21 January 1997; received in revised form 7 October 1997
Abstract
The two-dimensional short-circuit AM1.5 collection efficiency is studied in thin multicrystal-
line silicon solar cells with optical confinement. The collection efficiency is calculated by linking
an optical analytical generation profile with the two-dimensional collection probability in pn
junction solar cells. The calculations are carried out for variable grain boundary recombination
velocity, cell thickness, grain width, diffusion length, and back surface recombination velocity.
The role of optical confinement leading to a strong dependence of the collection efficiency on
the cell thickness in very thin cells is confirmed. The optimum cell thickness for maximum
collection efficiency increases in cells with low back reflection or poor back surface passivation.
Also, the optimum thickness in very thin cells increases significantly with increasing the
diffusion length. It is also found that the effect of grain boundary recombination is predominantif the cell thickness is larger than the diffusion length and if the diffusion length is larger than
half the grain width, especially, in cells with unpassivated grain boundaries. On the other hand,
back surface recombination dominates the response in cells with unpassivated back surface if
the thickness is smaller than or comparable to the diffusion length. 1998 Elsevier Science
B.V. All rights reserved.
Keywords: Short circuit collection; Efficiency; Silicon solar cells
0927-0248/98/$19.00 1998 Elsevier Science B.V. All rights reserved
PII S 0 9 2 7 - 0 2 4 8 ( 9 7 ) 0 0 2 7 5 - 4
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1. Introduction
There has been a growing commercial interest in thin multicrystalline Si solar cells
[1]. Solar cell thickness affects the following energy conversion efficiency-loss mecha-
nisms: (1) voltage factor, (2) fill factor (FF), and (3) collection efficiency. The voltagefactor increases in thinner cells due to increased open-circuit voltage from reduced
Auger recombination [2]. Degraded collection efficiency and light trapping in thin
solar cells result in smaller short-circuit current (J
), which reduces its overall
efficiency. Recombination at grain boundaries produces further reduction in the
collection efficiency of thin multicrystalline solar cells. In these cells, higher efficiencies
are achieved through effective light-trapping [3], bulk passivation, grain boundary
passivation, and both back and front surface passivation. With the exception of light
trapping; all previous passivation techniques are affiliated with the enhancement of
carrier collection produced by reduced bulk recombination or surface recombination.
The magnitude of the last recombination mechanisms have a profound effect on the
collection efficiency in thin multicrystalline solar cells; especially, grain boundary and
surface recombination.
Recently, it has been shown that the collection probability, f(x, y), defined as the
fraction of those carriers generated at a point (x, y) that are collected in the external
circuit [410] is governed by the same equations governing the excess dark minority
carriers. The two-dimensional collection efficiency has been calculated from the
collection probability and used to study the impact of the grain size and of grainboundary recombination on the short-circuit performance of thick polycrystalline
silicon (poly-Si) pn junction solar cells [9].
In the present paper, a similar procedure is carried out for thin poly-Si pn-junction
solar cells with optical confinement. The spectral response, the AM1.5 collection
efficiency, and the short-circuit current are determined from spatial numerical integra-
tion of the collection probability f(x, y) over rate of carrier photogeneration g(x)
throughout the cell. The advantage of the method used here is twofold: (1) solar-cell
characteristics are determined by numerical integration, which is more accurate than
numerical differentiation of finite-difference calculation as usually done for the deter-
mination of the current, and (2) calculation of collection probability density is
decoupled from position dependent carrier generation rate g(x), which removes short
wavelength convergence problems. Optical confinement obtained by light trapping is
essential in thin cells to maintain a relatively high efficiency [11,12]. Light trapping,
usually studied with ray tracing methods [1315], is a computationally intensive task.
The analytical approximation for the optical generation rate introduced by Basore
[16] and extended by Brendel [12] to account for the absorption in the emitter and
for light trapping is adopted in this work. This model applies to a cell having a frontsurface covered with infinitesimally small grooves and a diffused back reflector and is
introduced in the present analysis through a back surface reflectivity (R
) and
a surface roughness parameter ().
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Fig. 1. Schematic representation of a perfectly columnar grain PN junction poly-crystalline silicon solar
cell. In the blowup an isolated single grain cell is sketched. Due to the symmetry around the central axis
only half of the cell is analyzed.
2. Summary of methodology
2.1. Transport model
The model detailed in Ref. [9] is summarized here for convenience. Thetwo dimensional carrier collection probability density f
(x, y) is to be determined
at any point (x, y) inside an ideal pn junction solar cell at low-level injection
[17] which is adequate for one sun illumination. As shown in Fig. 1, the cell is
divided into three regions: (1) an active (neutral) n> emitter region, (2) a depletion
region, and (3) an active (neutral) p base region. Light generates minority carriers in
the three regions. In the depletion region a 100% collection probability is attained.
Therefore,
f"1 for x
)x)x
and !
2)y)
2, (1)
where x
is the edge of the depletion region in the active n> emitter region and x
is
the edge of the depletion region in the active p base region. The two-dimensional
partial differential equation for the collection probability in the n> emitter region is
given by
f"f
, (2a)
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where
is the minority carrier (hole) diffusion length. The solution of Eq. (2a) is
subject to the boundary conditions
f"1 at x"x
,
jf
jx"
S
D
f
at x"0 and 0(y)
2
,
jf
jy"!
S
D
f
at y"
2
,
jf
jy"0 at y"0,
(2b)
where S
is the recombination velocity at the front surface, S
is the recombination
velocity at the vertical edge boundaries, and D
is the minority hole diffusion
coefficient in the emitter region. Note that Eqs. (2a) and (2b) for the collection
probability is similar to the steady-state continuity equation of excess minority carrier
concentration in Refs. [710]. The collection probability is unity at the depletion
region edge, and follows the same boundary conditions as that for excess minority
carriers at other boundaries. The analysis is made simpler by assuming constant
effective surface recombination velocities, S [18,19], which is assumed to be identical
at dark and under illumination. The boundary condition at y"0 results from thesymmetry around the central vertical axis.
Similarly, the two-dimensional partial differential equation of the collection prob-
ability in the p base region is given by
f"
f
, (3a)
where
is the minority carrier (electron) diffusion length. In this case, the boundary
conditions are
f"1 at x"x
,
jf
jx"!
S
D
f
at x"H,
jf
jy"!
S
D
f
at y"
2
,
jf
*y"0 at y"0,
(3b)
where S
is the recombination velocity at the back surface and D
is the minority
electron diffusion coefficient in the base. The boundary condition at y"0 results from
the symmetry around the central vertical axis.
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The collection probability in the entire solar cell is determined by combining
condition, (1) with the separate numerical solutions of the sets of Eq. (2a) and Eq. (3b).
Such numerical solutions are carried out using the finite-difference approximation
on uniform rectangular grids [20,21] in each region. As a result of symmetry
around the central vertical axis, the calculations are performed for only one-half ofthe cell.
2.2. Optical model
The optical generation model used here follows a carrier generation profile g(x, )given by [12]
g(x, )"g(x)#R()
cos
exp
!
()(H!x)cos
#RR
;()
cos L
exp(!()x/cos L)#
LR
Lexp(![()(H!x)]/cos
L)
1!RL
RLL
,
(8)
where
g
(x, )"
(1!R)
()
cos exp
!
()x
cos
, 0)x)x
()cos
exp!()x
cos
!()(x!x
)
cos
, x) x)H,where x
is the edge of the depletion region on the base side, H is the total cell
thickness, R
is the front surface reflectance, is the angle at which light is transmitted
through the emitter,
is the angle at which light is transmitted through the base for
the first pass, for the second pass,
L for the nth pass, R is the back surfacereflectance for the first pass, R
Lfor the nth pass, R
is the first internal front surface
reflection, RL
is the nth internal front surface reflection. The transmittance of the first
pass
is given by
"exp
!x
cos !
(H!x
)
cos
, (9)and the nth pass diffuse light transmittance factor
Lis given by
L"exp
!Hcos
L"2
sin cos exp!H
cos d. (10)The second pass transmittance factor
is given by
"exp
!Hcos
"L#(1!), (11)
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where is the surface roughness parameter.
represents an average of the diffuse
transmittance and the specularly reflected light transmittance
given by
"exp
!H
cos
(12)
2.3. Internal spectral response and collection efficiency
The averaged internal spectral response [5,6], (), corresponding to a photo-generation rate g(x, ) (that may take light confinement into account) is given by
()"2
5
&
f(x, y)g(x, ) dx dy, (13)
where the front and back surfaces define the integration limits along the x-axis. The
collection probability density f(x, y) at point (x, y) calculated earlier is used to carry
out the integration in Eq. (13) along the y-axis leading to the averaged response over
the illuminated region.
The average short-circuit collection efficiency, G, defined as the ratio of the total
collected carrier density to the total generated carrier density in the cell assuming
a unity quantum yield under short circuit condition, is determined from
G"1()2+"H+
H
(
)F+
(
) d
H+H
F+
() d , (14)
where F+
() is the AM1.5 radiation spectrum, the wavelength +
is set to 1103 nm
which corresponds to the energy band gap of Si, and
is 325 nm. No effect of front
contact shadowing was accounted for. The numerator of Eq. (14) represents the
AM1.5 photo-generated (short-circuit) current density per unit electronic charge, J*
,
while the denominator denotes the AM1.5 photon flux absorbable in Si. Thus, the
short-circuit current is related to the averaged collection efficiency G
by
J*"q
GH+
H
F+
() d"58.6G
mA/cm. (15)
3. Results
The collection efficiency at AM1.5 in thin poly-Si cells with optical confinement is
investigated. Optical model parameters are fixed at R"20%, R
"60%, "0.5,
R"92.8%, R"62%, which are typical for highly efficient light confinement ofRef. [12]. The grain width
and the surface recombination velocity at the grain
boundary S
are the main variables shaping grain boundary recombination in poly-Si
solar cells. Other parameters such as the cell thickness H, the minority electron
diffusion length in the base
, and the back surface recombination velocity S
are also
considered. The minority hole diffusion length in the emitter
and the front surface
recombination velocity S
shape carrier collection in the emitter. The latter has
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a weaker dependence on grain boundary recombination than the collection in the
base [9]. Therefore, the last two parameters are assumed to be secondary and are fixed
at "5 m and S
"100 cm/s which are typical values for n> emitters of silicon
solar cells with high- quality oxide-passivated surface. Grain boundary recombination
velocities of 100 and 10 cm/s are assumed for well-passivated and unpassivated grainboundaries, respectively. Back surface recombination velocity of 500 and 10 cm/s are
assumed for well passivated (e.g. back surface field contact) and metal back contact,
respectively.
3.1. Dependence of collection efficiency on substrate thickness and grain width
The AM1.5 collection efficiency is calculated according to the model described by
Eq. (13), which includes the combined effect of collection probability and optical
generation, as a function of substrate thickness (H) and grain width (). The
collection efficiency is evaluated for cells with different passivation conditions.
3.1.1. Cells with grain boundary passivation and back surface passivation
The AM1.5 collection efficiency (G) contours in cells with grain boundary passiva-
tion and back surface passivation are plotted in Fig. 2a for an optical back reflection
of 60% and Fig. 2b for a zero back reflection as a function of substrate thickness (H)
and grain width (). In these plots, the electron diffusion length (
) was fixed at
50 m.Fig. 2a shows that the collection efficiency contours are almost vertical for films
thinner than 10 m. Vertical contours indicate that the collection efficiency is inde-
pendent of the grain width but is very sensitive to the film thickness. Thickness
dependence of the collection efficiency mainly occurs through high sensitivity to
optical generation or to back surface recombination. In the present case, the back
surface is well passivated and the pronounced efficiency degradation for film thickness
below 10 m is mainly due to the highly reduced optical generation resulting from the
highly attenuated light intensity crossing the cell beyond the second reflection.
At a grain width of 100 m (twice the diffusion length), the collection efficiency
exhibits a peak value slightly larger than 66% at an optimum thickness slightly larger
than 30 m. At this point the collection probability density f
is close to unity because
S
is small and the thickness is shorter than the diffusion length. As the cell thickness
exceeds this optimum thickness, the collection efficiency decreases very slowly with
cell thickness and almost saturates once the thickness reaches 100 m. In such
relatively thick cells optical confinement has a marginal role, and the behavior of the
collection efficiency versus cell thickness is divided into two streams. First, if the cell
thickness is smaller than or comparable to the diffusion length, the collection efficien-cy is mainly controlled by back surface recombination. In the case under study, S
is
small which explains the very weak degradation observed in the collection efficiency
as the cell thickness exceeds the optimum thickness. Second, in cells much thicker than
the diffusion length, the carriers photogenerated at the back surface cannot be
collected which leads to a thickness-independent behavior as observed in cells thicker
than 100 m. For such cells, the role of grain boundary recombination takes over
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Fig. 2. (a) The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and grain
width () for
"50 m, passivated grain boundary (S
"100 cm/s), and passivated back surface (S
"500 cm/s) with highly efficient light confinement: R
"20%, R
"60%, "0.5, R
L"92.8%, and
R"62%. (b) The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and
grain width () for
"50 m, passivated grain boundary (S
"100 cm/s), and passivated back surface
(S"500 cm/s) with no light confinement: R
"20%, R
"0%.
leading to horizontal efficiency contours. Note that the efficiency degradation due to
grain boundary recombination is relatively weak, especially in the range 'because of the small grain boundary recombination velocity assumed in the case
under study (S"100 cm/s).
In cells without optical confinement (R"0), the position of the peak collection
efficiency is shifted towards larger thickness as depicted in Fig. 2b. The peak efficiency
occurs in this case at a film thickness of 50 m and its value at a grain width of 100 m
is slightly greater than 63%. The collection efficiency contours displayed in Fig. 2b
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Fig. 3. The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and grain width
() for
"50 m, unpassivated grain boundary (S
"10 cm/s), and passivated back surface
(S"500 cm/s) with highly efficient light confinement: R
"20%, R
"60%, "0.5, R
L"92.8%, and
R"62%.
exhibit an abrupt transition from a thickness-dependent behavior (vertical contours)
to a grain-size-dependent behavior (horizontal contours). This indicates that the peak,
if any, is very marginal, which is in agreement with previously reported one-dimen-
sional results for cells with very small back surface recombination velocity [5]. For
a film thickness of 10 m, the collection efficiency for a cell with 60% back reflection is61% compared to 55% for a cell without back reflection.
3.1.2. Cells with unpassivated grain boundaries but with back surface passivation
The collection efficiency contours for cells with unpassivated grain boundaries and
well-passivated back surface are displayed in Fig. 3 as a function of cell thickness and
grain width. These contours can be identically obtained by vertically shifting the
contours of Fig. 2a upwards. Below a certain critical grain size given by approximately
twice the diffusion length, the role of grain boundary recombination is very dominant.
For larger aspect ratios (ratio of grain size to thickness), the collection efficiency
becomes mainly dependent on the cell thickness primarily due to the significant role of
optical generation since in the present case back surface recombination is negligible.
The optimum film thickness corresponding to the peak collection efficiency is 30 m
like in the result of Section 3.1.1 also dealing with cells with back surface recombina-
tion. The value of the peak collection efficiency at the critical grain size of 100 m,
however, is only 62.5% compared to 66% for cells with passivated grain boundaries.
3.1.3. Cells with grain boundary passivation and unpassivated back surfaceThe collection efficiency contours for cells with grain boundary passivation and
unpassivated back surface are displayed in Fig. 4 as a function of cell thickness and
grain width. The vertical contours highly dominating the plot for cells thinner than
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Fig. 4. The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and grain width
() for
"50 m, passivated grain boundary (S
"100 cm/s), and unpassivated back surface
(S"10 cm/s) with highly efficient light confinement: R
"20%, R
"60%, "0.5, R
L"92.8%, and
R"62%.
30 m indicate a strong dependence of the collection efficiency on the optical genera-
tion. The corresponding value of the collection efficiency is significantly degraded dueto the very high back surface recombination velocity. This result demonstrates the
importance of back surface passivation for maintaining a relatively high efficiency in
thin cells with relatively high-quality bulk material. As the cell thickness exceeds one
diffusion length, the influence of optical confinement and back surface recombination
is weakened out leading to a collection efficiency almost solely dependent on the grain
width. Due to high back surface recombination, the maximum collection efficiency at
the critical grain size of 100 m is smaller than in cells with passivated back surface
(less than 63% compared to 66%), and the optimum cell thickness is shifted towards
larger values exceeding 100 m.
3.1.4. Cells with unpassivated grain boundary and unpassivated back surface
The collection efficiency contours for cells with unpassivated grain boundaries and
unpassivated back surface are displayed in Fig. 5 as a function of cell thickness and
grain width. These contours can be understood based on the detailed discussions
presented above and need no more elaboration. Actually, these contours can be
generated by shifting those of Fig. 2a diagonally upwards to the right. At the critical
grain size, the peak collection efficiency in the high recombination scheme studied inthis section slightly exceeds 59%.
3.2. Optimum cell thickness and maximum collection efficiency
The optimum cell thickness (H
) corresponding to the maximum collection effi-
ciency G
is plotted in Fig. 6a together with G
as a function of grain width () for
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Fig. 5. The internal AM1.5 collection efficiency contours as a function of cell thickness (H) and grain width
() for
"50 m, unpassivated grain boundary (S
"10 cm/s), and unpassivated back surface
(S"10 cm/s) with highly efficient light confinement: R
"20%, R
"60%, "0.5, R
L"92.8%, and
R"62%.
a cell with grain boundary passivation and back surface passivation having a
base diffusion length
of 50 m, taking the back reflection factor R
as an in-
dependent parameter. The curves for R"0.6 correspond to the results displayed
in Fig. 2a. Larger back reflection leads to a more efficient optical confinement,
a shallower generation profile and an enhanced absorption in thin substrates.
Such a reasoning is confirmed in Fig. 6a showing a higher maximum collection
efficiency at a smaller cell thickness when the back reflection factor is increased. In
general, Fig. 6a indicates that the optimum cell thickness is inversely proportional to
the back reflection ratio R
while the maximum collection efficiency is directly
proportional to R. In practice, plots like those displayed in Fig. 6a can be used to
determine the optimum film thickness for specific passivation and back reflection
schemes assuming that the grain width and bulk diffusion length of the resulting films
are reproducible.
The behaviors displayed in Fig. 6a of the optimum thickness and of the maximum
efficiency with respect to the grain width can be divided into two distinct regions. For
wide grains ('2
) grain boundary recombination is less influential; especially, in
cells with efficient grain boundary passivation. In such a case, the optimum cellthickness and the maximum collection efficiency are almost independent of the grain
width, and the solar cell behaves practically as single crystalline cell. On the other
hand, for narrow grains ()2
), the optimum cell thickness and the maximum
collection efficiency are proportional to the grain width . This result can also be
visualized by following the trajectory of the bottoms of the contours in Fig. 2a as the
grain width is reduced below 100 m (2
). Since the efficiency dependence on grain
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width is caused by grain boundary recombination, grain boundary recombination
continues to affect the maximum collection efficiency and the optimum thickness in
cells with unpassivated grain boundaries even if the grain width exceeds the 2
limit
described above, which is illustrated in Fig. 6b.
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Fig. 6. (a) Optimum cell thickness versus grain width
for cells with "50 m, passivated grain
boundary (S"100 cm/s), passivated back surface (S
"500 cm/s) and different back reflections ratio R
.
The right y-axis is the value of maximum internal AM1.5 collection efficiency at the optimum thickness. Theoptical model parameters are: R
"20%,"0.5, R
L"92.8%, and R
"62%. (b) Optimum cell thickness
versus grain width
for cells with "50 m, R
"60%, and different passivation schemes: (A) grain
boundary only (S"100 cm/s and S
"10 cm/s), (B) neither (S
"10 cm/s and S
"10 cm/s), (C) grain
boundary and back surface (S"100 cm/s and S
"500 cm/s), (D) back surface only (S
"10 cm/s and
S"500 cm/s). The right y-axis is the value of maximum internal AM1.5 collection efficiency at the
optimum thickness. The optical model parameters are: R"20%, R
"60%, "0.5, R
L"92.8%, and
R"62%.
3.3. Dependence of optimum cell thickness on diffusion length
3.3.1. Very wide grain (monocrystalline silicon) cells
The optimum cell thickness (H
) and the maximum collection efficiency G
of very
wide grain cells with grain boundary passivation simulating monocrystalline siliconwith back surface passivation are plotted in Fig. 7a as a function of the base diffusion
length (
) for different back reflection ratios R
. The results show that the maximum
collection efficiency and the optimum thickness increase with increasing diffusion
length. For
exceeding 100 m, the maximum collection efficiency tends to converge
to an asymptote with weakly dependence on both R
and
. The calculated values
represent a very good estimate for H
and
in most practical cases for films with
a diffusion length lying in the range 10100 m. In such cases, the calculated optimum
thickness lies between 5 and 60 m which are typical values for silicon film techno-
logy.
The theoretical dependencies ofH
and G
on the diffusion length are generated forR
"60% for cells without back surface passivation and plotted in Fig. 7b together
with the results of Fig. 7a for cells with back surface passivation. As expected,
enhanced back surface recombination leads to degradation of the maximum collec-
tion efficiency and to a strong increase in the optimum thickness of the cell. Note that
the continuous influence of back surface recombination even at very small values of
is due to the dependence of the optimum cell thickness on
.
3.3.2. Polycrystalline silicon cells with equal grain width and cell thickness
The maximum collection efficiency is determined for cells with equal grain width
and film thickness from the two-dimensional contour tangent to the line representing
the condition "H
. Such a condition is reasonable for thin multicrystalline
silicon films, where grain widths are similar to thickness. From Fig. 2a, the highest
collection efficiency that can be obtained when"H
lies between 65% and 66%
and occurs approximately at"H
"30 m. Such values are checked and con-
firmed at "50 m in Fig. 8 displaying the calculated optimum cell thickness
H
(with H") and its corresponding maximum collection efficiency as a function
of the diffusion length
for polycrystalline silicon cells with grain boundary and
back surface passivation. The results of Fig. 8 are very close to those of Fig. 7a, since
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cells with grain boundary passivation behave very similarly to very wide grain cells.
However, at long diffusion lengths, the effect of grain boundary recombination is not
totally negligible leading to a smaller maximum collection efficiency than that of very
wide grain cells. Furthermore, the optimum cell thickness (H
) disappears as
exceeds a certain critical value above 100 m. In the last situation, increasing
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Fig. 7. (a) Optimum cell thickness versus base diffusion length
for very wide grain cells "1 cm
(practically perfect grain boundary passivation or single crystalline cell) with passivated back surface(S
"500 cm/s) and different back reflections ratio R
. The right y-axis is the value of maximum internal
AM1.5 collection efficiency at the optimum thickness. The optical model parameters are: R"20%,
"0.5, RL"92.8%, and R
"62%. (b) Optimum cell thickness versus base diffusion length
for very
wide grain cells "1 cm (practically perfect grain boundary passivation or single crystalline cell) with
(S"500 cm/s) or without (S
"10 cm/s) back surface passivation, and R
"60%. The right y-axis is the
value of maximum internal AM1.5 collection efficiency at the optimum thickness. The optical model
parameters are: R"20%, "0.5, R
L"92.8%, and R
"62%.
Fig. 8. Optimum grain dimension of equal thickness and width ("H) versus base diffusion length
for passivated grain boundary (S"100 cm/s), passivated back surface (S
"500 cm/s), and different
back reflections ratio R
. The right y-axis is the value of maximum internal AM1.5 collection efficiency at
the optimum dimension. The optical model parameters are: R"20%, "0.5, R
L"92.8%, and
R"62%.
above this critical value does not produce a curve with maximum G
at a finite
thickness; maximum efficiency occurs at the largest possible cell thickness H. It should
be noticed that collection efficiency enhancement through reduction of grain size is
similar with what is observed with porous photochemical cells [22]. There, the effect
of bulk recombination on the collection efficiency is minimized in nanostructure
semiconductor with structural units equal to or smaller than twice the diffusion length
given that surface recombination is reduced, which is achieved by the aqueous
electrolyte solution interface.
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Fig. 9. Optimum cell thickness versus back surface recombination velocity S
for very wide grain cells
"1 cm (practically perfect grain boundary passivation or single crystalline cell) with
"50 m,
Sb"500 cm/s and different back reflections ratio R
. The right y-axis is the value of maximum internal
AM1.5 collection efficiency at the optimum thickness. The optical model parameters are: R"20%,
"0.5, RL"92.8%, and R
"62%.
3.4. Dependence of optimum cell thickness and maximum collection efficiency on back
surface recombination
The optimum cell thickness and the maximum collection efficiency are plotted as
a function of back surface recombination velocity in Fig. 9 for very wide grain(monocrystalline) cells and in Fig. 10 for grain boundary passivated polycrystalline
cells for which the grain width is equal to the thickness. Cells in both figures had
"50 m. Cells with grain boundary passivation are treated in order to emphasize
the effect of back surface recombination. As long as S
is smaller than 1000 cm/s its
effect is marginal. On the other hand, when S
exceeds 1000 cm/s H
increases
drastically with S
and saturates for S
larger than 10 cm/s. The opposite behavior is
observed for G
which exhibits a strong decrease in the range 1000(S(10 cm/s
and saturates for larger S@
values. Such behaviors can be explained by a reduced
collection probability f
at large S
values with skewed distribution that requires
a much thicker substrate to obtain the maximum collection efficiency. The differences
between the values of the maximum collection efficiency for different values of R
are
strongly reduced at large S
values because the optimum thickness becomes large
enough to minimize the influence of optical confinement.
Although the difference between the maximum collection efficiency and the opti-
mum thickness of monocrystalline cells and of polycrystalline cells is reduced at large
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Fig. 10. Optimum grain dimension of equal thickness and width ("H) versus back surface recombina-
tion velocity S
for L"50 m, passivated grain boundary (S
"100 cm/s), and different back reflections
ratio R
. The right y-axis is the value of maximum internal AM1.5 collection efficiency at the optimum
dimension. The optical model parameters are: R"20%, "0.5, R
L"92.8%, and R
"62%.
values ofS, a smaller maximum collection efficiency and a larger optimum thickness,
resulting from the two-dimensional distribution of the collection probability, charac-
terize the polycrystalline cells (even with grain boundary passivation), as deduced by
comparing Figs. 9 and 10. It should be noted that since the thickness is varying in cells
of both figures, relative significance of back surface recombination should be nor-
malized to D
/H. The last statement was transparent in both figures, where large
surface recombination velocity effects occurred for S'D
/H.
4. Conclusions
For thin poly-Si solar cells with effective back surface passivation and optical
confinement the optimum cell thickness is strongly dependent on the back reflection,diffusion length, and back surface recombination velocity. Higher back reflectionR
results in smaller optimum thickness and larger collection efficiencies
G. The
maximum collection efficiency and the optimum thickness increase with increasing
the diffusion length. The former saturates for
above 100 m while the latter has to
be determined from its value at the border value of"100 m. Small back surface
recombination velocity below 1000 cm/s practically has no effect on optimum cell
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thickness and on the maximum collection efficiency. Larger back surface recombina-
tion velocities ('D
/H) significantly increase the optimum thickness and reduce the
maximum collection efficiency. An optimum grain size of one diffusion length is
recommended for cells with passivated grain boundaries and a size larger than twice
the diffusion length is necessary if the grain boundaries are not passivated.
Acknowledgements
This work was supported by Kuwait University research Grants EE-048 and
EE-079.
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