Indian Journal of Pure & Applied Physics
Vol. 50, September 2012, pp. 661-669
Effects of grain boundaries on the performance of
polycrystalline silicon solar cells
D P Joshi & Kiran Sharma1*
Department of Physics, D B S (PG) College, Dehradun, Uttarakhand, India
1
Department of Physics, Graphic Era University, Dehradun, Uttarakhand, India
*E-mail: dpj55@rediffmail.com; *kkiransharma@rediffmail.com
Received 28 Frbruary 2012;revised 10 May 2012; accepted 6 July 2012
A comprehensive carrier recombination model under optical illumination near grain boundaries (GBs) is proposed by
considering the asymmetric Gaussian energy distribution of GB interface states model. A new recombination velocity S(Ln)
is proposed to study the dependence of effective diffusion length of minority carriers on grain size and GB interface state
density. The dependence of GB space charge potential barrier height (qVg), the recombination velocities, and polycrystalline
silicon (PX-Si) solar cell parameters on grain size, illumination level, and GB interface state density have also been studied.
It is observed that the efficiency of solar cells is mainly determined by the potential barrier height qVg. Considering the
effect of vertical GBs in the junction depletion region of a solar cell, it is also observed that their effect is smaller in the
small grain size range as compared to that in the large grain size range. A reasonably good agreement is obtained between
the theoretical predictions and the available experimental data.
Keywords: Grain boundary, Solar cells, Polycrystalline silicon
1 Introduction
The need of the hour is to develop alternative
energy options in the form of non- conventional
resources particularly solar energy so that the pressure
on the conventional resources is reduced to a large
extent. This in turn will give us conducive
environment to grow and flourish. Solar cell is a clean
and eternal energy source, since it generates
electricity from clean and inexhaustible sunlight
without producing any contamination. At present,
silicon and polycrystalline silicon (PX-Si) are the
chief candidates for fabrication of solar cells, and it
should remain so in the future as well. This is because
silicon is an abundant, relatively cheap and harmless
material.
Heterojunction solar cells have proved to be
superior over conventional p-n junction solar cells.
The MS (metal semiconductor), MIS (metal insulator
semiconductor), SIS (semiconductor insulator
semiconductor) are the commonly used structures of
PV cells. The photovoltaic properties of MIS/SIS
solar cells are, in general, intermediate between those
of Schottky barrier cells and p-n junction cells.
Several researchers have investigated the effects of
GBs on the performance of polycrystalline silicon
solar cells by considering the concept of effective
diffusion length1-7. However, these theories have
some inadequacies8. Recently, authors have proposed
an electrical conduction model of carrier transport
across the grain boundaries in PX-Si and explained
the electrical characteristics of thin film transistors
(TFTs) and metal oxide semiconductor field effect
transistors (MOSFETs) fabricated using PX-Si
materials by considering Gaussian energy distribution
of GB interface states model9. In the present paper, an
attempt is made to study the dependence of effective
diffusion length of minority carriers and solar cell
parameters on grain size and GB interface state
density by using the above mentioned Gaussian
energy distribution of GB states model and carrierrecombination model under optical illumination
developed by Joshi and Bhatt10.
2 Theory and Discussion
2.1 Theory of grain boundary recombination
polycrystalline silicon under optical illumination
in
It is well known that due to the presence of GBs in
PX-Si semiconductor, the electrical and photovoltaic
properties of PX-Si material are, in general, different
than that of monocrystalline material. The electrical
transport properties of PX-Si play an important role in
determining the efficiencies of solar cells fabricated
by this material. The GBs generally contain a high
density trapping centers and impurities that have been
segregated from grain during growth11. The GB
interface states density plays an important role in
662
INDIAN J PURE & APPL PHYS, VOL 50, SEPTEMBER 2012
determining the space charge potential barrier height
(qVg). The distribution of GB interface states is
determined by the nature of the disorder by dangling
bonds, and by the local electrical fluctuations
producing stress field in the region of structural
irregularities12. Thus, in order to study the carrier
transport in PX-Si under optical illumination, it is
necessary to develop a comprehensive quantitative
theoretical model of GB recombination under
illumination.
2.2 Assumptions
Figure 1 shows the energy band diagram of n-type
PX-Si under optical illumination. In the present study,
the following assumptions are made to analyze the
GB recombination processes:
(1) PX-Si transport properties are one dimensional
and PX-Si film is composed of cubical grains
with an average grain size d.
(2) The parameters Ngs (GB interface states density),
ET (average energy of GB states), and s
(distribution parameter) are independent of
doping density (N) and grain size.
(3) All the GB states have equal capture cross-section
irrespective of their origin and for a
recombination there are two carrier capture crosssections of different magnitude ıN and ıC.
(4) Under sufficient illumination condition, the dark
hole concentration is negligible and the quasiFermi level of the majority carriers EFn is flat
everywhere but the quasi-Fermi level of the
minority carriers EFn is allowed to vary with
distance 16.
2.3 Grain boundary potential
recombination current density
barrier
height
and
Under optical illumination, the presence of high
electric field in the space-charge region drifts the
photo generated minority carriers towards the GB
surface. The electric field therefore, enhances the
recombination of excess minority carriers with
trapped majority carriers at the GBs. As a result of
this, a new interface charge at the GB is established
due to S-R-H capture and emission processes17.
Consequently, GB space-charge potential barrier
height (qVg) is reduced from its dark value (qVgo) and
the Fermi level splits up into electrons Fermi level
(EFn) and hole Fermi level (EFp). Considering Sharma
and Joshi9 GB interface states model, the barrier
height qVg can be calculated by the following relation:
ET + 3 s / 4
(8İNqVg)1/2 = q
³
N gs (E) f(E) dE
…(1)
ET − s / 2
where N is the doping density, E the energy of a GB
interface state with respect to intrinsic Fermi level
Ei, s the distribution parameter, ET the average energy
of GB states, İ the permittivity, and f(E) is the
occupation function for GB states given by:
f(E)=[ıN n(o) + ıc ni ȕ−1]/ [ıNn(o)+ıN ni ȕ+ıc p(o)
+ ıc ni ȕ-1]
…(2)
Here n(o) and p(o) are the electron and
hole densities at the GB, respectively and
ȕ = exp[(E−Ei)/kT].
The total photo generated minority carrier density
inside a cubic grain can be expressed as10:
qGd3 = 3d2 [Jr(o) + 2Jr(Wg)] + Jb (d-2Wg)2
…(3)
where G is the photo generated rate of electron-hole
pairs, Wg the width of the GB space charge depletion
region, Jb the recombination current density in the
bulk part of the grain (x>Wg), and Jr(Wg) is the
recombination current density at the edge of depletion
region. The recombination current Jb is defined as3 :
d /2
Jb = ( 2q / IJb)
³
p ( x) dx
…(4)
Wg
where IJb is the minority carrier life time in the bulk
part of the grain. From Eqs. (5) and (6), the GB
recombination current density is expressed as:
Fig. 1 — Energy band diagram of n-type PX-semiconductor under
optical illumination representing Gaussian energy distribution of
mid gap states
Jr(o) = qM[Gd–{(d-6Wg)(p(o)/ IJb)} exp(−qVg/ kT)]
…(5)
JOSHI & SHARMA: POLYCRYSTALLINE SILICON SOLAR CELLS
When grain size is much larger than the bulk
diffusion length of minority carriers (i.e. d>>Lb) and
the bulk diffusion length itself is much larger than the
depletion width (ie Lb>>Wg) Eq. (7) reduces to:
Jr(o) § 2q{Lb/IJb) [GIJb – p(o) exp(− qVg/kT)
…(6)
If we assume that the transition rate of a carrier bound
to a trapping center is much smaller than the rate of
the conduction or valance band, where many quantum
states are available for the transition18, then the
recombination current density at the GB can also be
obtained by using S-R-H theory19.
Jr(o) = q ıc ıN vth ni2 { exp(¨EF(o) / kT) – 1}
ET + 3 s /4
×
³
{N gs (E) dE / [ıN n(o)+ıNniȕ
ET − s / 2
+ıcniȕ-1+ıcp(o)]}
…(7)
where vth is the thermal velocity of the carriers.
Equating Eqs (8) and (9), and using Eq. (1), one can
study the dependence of ¨EF(o) is the separation of
quasi Fermi level at the GBs, and hence Vg on various
parameters such as illumination level, grain size, bulk
diffusion length etc.
The variation of qVg as a function of optical
illumination level is shown in Fig. 2. A good
agreement is obtained between the theoretical
predictions and available experimental results14,16. The
values of parameters used to compare theory with the
Fig. 2 — Computed variation of barrier height with illumination
level. Experimental points are taken from Refs (14, 16)
663
available experimental data are presented in
Table 1. Figure 3 shows the computed variation of
qVg with illumination level as a function of grain size.
The plot show that the value of qVg decreases as
illumination level or grain size increases. It is also
observed that at low illumination the dependence of
qVg on G is less as compared to that at high
illumination level. It is further noted that in the large
grain size range (d>>Lb), qVg is independent of d.
However, when grain size is small the sensitivity of
qVg on d increases (Fig. 4). The above mentioned
dependence of qVg on grain size and illumination
level can be explained by considering the variation of
ǻEF(o) with these parameters. At very low illumination
level, GB recombination current density Jr(o) is very
small and consequently ǻEF(o) § 0. On increasing the
illumination level, more GB states act as
recombination centers. As a result of this, ǻEF(o)
increases on increasing G. It is also observed that
ǻEF(o) increases with increasing the grain size, and in
Table 1 — List of parameters used in Fig. 2 to compare theory
with available experimental data
Parameters
−3
N (cm )
Ngs (cm−2)
ET (eV)
d (µm)
s (eV)
IJb (S)
ıN (cm2)
ıC (cm2)
DN(cm2s−1)
Lb (µm)
Values Ref. (16)
16
3×10
1.47×1012
0.3
103
4.0
4.11×10−6
1.5×10−17
10-15
20.461
2.44
Values Ref. (16)
3×1015
2×1013
0.4
103
5.0
4.11×10−6
10−15
10−14
20.461
102
Fig. 3 — Calculated variation of barrier height as a function of
illumination level at different grain sizes
INDIAN J PURE & APPL PHYS, VOL 50, SEPTEMBER 2012
664
large grain size range it becomes independent of d.
This variation of ǻEF(o) with grain size is attributed to
the fact that for large grain sizes Jr(o) is
approximately independent of d. It is also predicted
that as GB interface states density increases, the
trapping of free charge carriers near GB region
increases and hence qVg increases. On the other hand,
on increasing doping density, qVg decreases because
the numbers of free charge carriers near GB region
increases on increasing N, however at very high
illumination level it becomes independent of doping
density.
Jr(Wg) =(qWg/2IJb){[ni2/N] [exp(qVg/kT) –1]
×[exp(¨EF(o) / kT) ]−[(Jr(o) / 4qDp)
×Wg (ʌkT/qVg)1/2 erf(Ș) ] [1 + (2Wg / 2IJb)
×(Wg/4qDp) (ʌkT/qVg)1/2 erf(Ș)]-1}
…(10)
The dependence of recombination velocity S(o) on
illumination level as a function of grain size is shown
in Fig. 4. Present computations predict that on
increasing the illumination level the recombination
velocity first increases, attains a maximum value and
then decreases. This dependence of S(o) on G is
because in the low illumination level range qVg is
maximum and on increasing G, qVg start decreasing.
The sensitivity of S(o) to G also depends on the
parameters Lb, d, Ngs, s, and ET. It increases on
increasing the grain size due to the strong dependence
of recombination current density on d. Computations
also demonstrate that S(o) decreases on increasing
Ngs. This is due to the increase in qVg on increasing
the trapping state density. However, for
Ngs=5×1011cm−2, the dependence of S(o) on
illumination level is less because at this value of Ngs,
qVg attains a constant value whatever be the
illumination level. It is also observed that S(o)
increases with increasing the doping concentration.
Present study also predicts that the dependence of
S(o) and S(Wg) on s and ET is almost negligible since
qVg shows the same dependence on these parameters.
Figure 5 shows the computed variation of S(Wg)
with optical illumination level at different grain sizes.
Computed variation show that at low illumination
level S(Wg) has maximum value because in this range
qVg is independent of G and hence, S(Wg) has its
maximum value (§vth). As G increases, S(Wg) start
decreasing. It is also observed that S(Wg) decreases
with increasing the grain size since at low grain size
p(Wg) decreases and approaches to p(o). The
Fig. 4 — Dependence of recombination velocity S(o) on
illumination level as a function of grain size
Fig.5 — Dependence of recombination velocity S(Wg) on
illumination level at different grain sizes
2.4 Recombination velocities
The two recombination velocities of minority carriers
for PX-semiconductors are S(o) (recombination
velocity at the GB surface) and (SWg) (effective
recombination velocity at the depletion edge). These
velocities can be defined by the following relations:
S(o) = Jr(o) / q p(o)
...(8)
and
S(Wg) = [ Jr(Wg) + Jr(o) ] / [2q p(Wg) ]
…(9)
The recombination current density8 at the edge of
depletion region (Jr(Wg)) is given by :
JOSHI & SHARMA: POLYCRYSTALLINE SILICON SOLAR CELLS
predictions of present work are in agreement with the
experimental study of Sundaresan and Burk20. It is
observed that S(Wg) increases with increasing the
trapping state density and the doping concentration
this is due to the same dependence of qVg on Ngs and
N. It should be noted that for N=7×1017 cm-3, S(Wg) is
independent of illumination level. This is due to the
fixed value of qVg (=0.05 eV) at this doping
concentration, and over all ranges of illumination
level. The parameters used for theoretical
computations in Figs. 3 to 5 are presented in Table 2.
Many GB recombination models have used a
constant value for the recombination velocity at and
near the GB region1. However this concept seems to
be incorrect10,12. Present work predicts that for small
grain size, S(o)<<S(Wg) but for large grain sizes S(o)
may not be negligible as compared to S(Wg). This fact
shows that the minority carrier recombination near the
depletion region varies from S(o) to S(Wg). As a result
of this, minority carrier diffusion length (Ln) in a
PX-material is not constant in the GB depletion
region Wg. This prediction is in agreement with the
study of Koliwad and Daud21. The study22 of also
suggests that the electrical width of the GB is of order
of Ln and not the depletion width Wg. Hence, it would
be more appropriate to define a new effective
recombination velocity S(Ln) at the distance Ln from
the GB surface to consider the electrical width of the
GBs. This new recombination velocity is expressed
as:
S(Ln) = S(Wg) Ln / (d/2)
...(11)
Table 2 — List of parameters used to compare theory with
available experimental data
Parameters
−3
N (cm )
Ngs (cm−2)
ET (eV)
s (eV)
IJb (s)
ıN (cm2)
ıC (cm2)
DN (cm2s−1)
Dp (cm2s−1)
Lb (µm)
G (1 SUN)
Vth (cm2s−1)
T (K)
×j (cm)
Vb (eV)
Rs (ȍ-cm−2)
Sp (cms−1)
H (µm)
Values Figs ( 3-14)
7×1015
3×1012
0.51
4.2
4.11×10−6
1.5×10−17
10−15
20.461
13.5
91.747
3×1019
107
300
2×10−5
0.8
2.2
104
300
665
Note that Eq. (11) is valid under the condition,
S(o)<<S(Wg). If this condition is not satisfied, then:
S(Ln) = [S(Wg) + S(o) ] Ln / (d/2)
…(12)
2.5 Effective life time and effective diffusion length
Various approaches have been suggested to define
the effective minority carrier life time23 (IJn*) (for
PX-semiconductors). Assuming that GB defects are
distributed over the length Wg 4,24. IJn* can be expressed
as :
1/ IJn* = 1/IJb + 1/IJng + 1/IJAN,
...(13)
where IJb is the bulk life time of minority carriers and
IJAN is the Auger life time of minority carriers defined
as IJAN = 1/CpNA, here Cp=10−31 cm6s is the band to
band Auger recombination coefficient25 which
becomes significant26, 27 when the base doping density
(NA) is greater than 1017 cm−3. In Eq. (15), IJng is the
surface component of minority carrier life time in a
p-type PX-material. Considering the concept of new
recombination velocity S(Ln), authors propose the
following expression for the parameter IJng :
IJng = f6 Wg / S(Ln) IJng = [f6 Wg d] / [2 S(Wg) Ln]
...(14)
where f6 is a fitting parameter having different values
for different materials. Present study also assumes
that for the same material f6 may have different values
in the different grain size range because the minority
carrier concentration in the base region of a PX-Si
solar cell depends on the GB geometry. This fact is
supported by the study of Green28. According to his
calculation, the effective life time parameter depends
on the GB’s geometry and activity. If GB is very
active, minority carriers are more likely to be captured
by it, than the junction. It is well known that, in
general, there are three separate types of GBs in solar
cells. However, authors have considered only
columnar grains in the present work. Therefore, it is
necessary to consider the effect of vertical GBs in the
junction depletion region on the effective life time
especially when grain size is very small (d<<Lb).
Furthermore, present work does not consider the
effect of GB material and band edge states on the
recombination of the minority carriers. Keeping all
these facts in mind f6 is assumed to have values 6 and
16 for small (d<<Lb) and large (d>>Lb) grain size
ranges, respectively. In other words, it is assumed that
as grain size decreases, the effect of vertical GBs
decreases and hence f6 decreases.
INDIAN J PURE & APPL PHYS, VOL 50, SEPTEMBER 2012
666
The minority carrier diffusion length constitutes the
most important figure of merit for a photovoltaic
material. The diffusion length of electrons in PXfilms is expressed as:
The variation of IJn* with grain size for PX-Si solar
cell is shown in Fig. 6. Present computations are
found to be in good agreement with the available
experimental data5. It is noticed that, in the small
grain size range (d<<Lb), IJn* is controlled by the
component IJng. In this grain size range, IJn* is
approximately proportional to the grain size. As grain
size increases, the effect of GB recombination process
increases, and, hence qVg or S(Wg) or S(Ln) decreases
(Figs 3 and 5). As a result of this, IJng* increases with
increasing the grain size (Eq. 18) and approaches to
IJb. Note that, in very large grain size range (d>>Lb)
bulk recombination process is a dominant process,
therefore IJn* becomes approximately independent of
grain size. Computations also demonstrate that, in the
low and in the intermediate illumination level range,
IJn* increases slowly, but at very high illumination
level, IJn* increases sharply with increasing d. It is also
found that on increasing the interface state density, IJn*
decreases. It is observed that IJn* is almost independent
of distribution parameter, but it decreases on
increasing parameter ET. Present theory assumes that
the parameters N, ıc, ıN, Ngs, and qVg have the same
values for all devices prepared under widely different
conditions. Note that the methods used for the
measurement of IJb may not always be correct29.
Computations of Fig. 6 are made by considering the
parameters given in Table 2.
The variation of effective diffusion length of the
minority carriers in PX-Si solar cells with grain size
under AM1 illumination is shown in Fig. 7. Present
calculations are done by using Eq. (19). Present
theoretical calculations are found to be in good
agreement with the available experimental data21,22,30.
It is noticed that for large grain size, Ln* increases
rapidly with increasing grain size since at large grain
size IJn* increase and qVg decreases. Computed results
demonstrate that for d<Lb, Ln* is controlled by the GB
recombination processes. It is noted that, in the low
illumination level range, Ln* is independent of G, in
the intermediate range of G, Ln* starts increasing, and
for high illumination level Ln* increases rapidly. It is
also observed that Ln* decreases on increasing the
interface state density.
Fig. 6 — Dependence of effective life time on grain size.
Experimental points are culled from Ref. (5)
Fig. 7 — Variation of effective diffusion length as a function of
grain size. Experimental points are taken from Refs (21, 22, 30)
Ln = (Dn IJn)1/2
...(15)
where Dn is the diffusion constant of the electrons.
From Eqs. (16) and (17), we get:
IJng = [ f6 Wg d / 2 S(Wg) ]2/3 (Dn)−1/3
...(16)
In solar cells, we must consider an effective
diffusion length Ln* that includes additional device
parameters. Thus from Eq.(16) the effective diffusion
length is given by:
Ln* = (Dn IJn*)1/2.
...(17)
JOSHI & SHARMA: POLYCRYSTALLINE SILICON SOLAR CELLS
2.6 Short circuit current density and Open circuit voltage
The short circuit current density is calculated by
considering the relation given in the existing
literature33:
Jsc = Jn + Jdr + Jp
...(18)
Jdr = ¦ q M F(λ) exp(−αxj){1 –exp (−αWb)}
…(19)
λ
and
Jp = ¦ q α F(λ)Lp* (α2 Lp*2 −1)−1{[(Sp Lp*/Dp) + αLp*
667
observed that the value of n2 decreases with decrease
in grain size due the effect of vertical GBs in the
junction depletion region, effect of GB material and
band edge states on the recombination of the minority
carriers. This assumption is found to be in agreement
with the results of Neugrochel and Mazer36. Figure 10
shows the computed variation of Voc with grain size.
Present computed results show that in large grain size
range, Voc is controlled by both space-charge and
recombination current density. On the other hand in
small grain size range it is controlled by
recombination current density.
λ
−exp(−αxj)⋅{(SpLp*/Dp)cosh(xj /Lp*)+sinh(xj/Lp*)}]
×[(Sp Lp*/Dp) sinh(xj /Lp*) + cosh(xj / Lp*)]−1
−αLp*exp(−αxj)
…(20)
The open circuit voltage of an ideal solar cell is
calculated by the following relation:
Jsc = Jo1L [exp(qVoc /kT)−1]+Jo2L[exp (qVoc/n2kT)−1]
...(21)
Eq. (21) assumes a fix value for diode quality
factor n2(=2). However, it is found that the
dependence of Voc on the grain size cannot be
explained by this ideal expression. Present work
predicts that to match the available experimental
data5,21,22,34,35, the dependence of n2 on the grain size
must be considered. Figure 9 shows the variation of n2
with grain size. Note that it is necessary to consider
the variation of n2 with d because present theoretical
results are in good agreement with the experimental
observed value of IJn*, Ln*, and Jsc (Figs 6-8). It is
Fig. 8 — Variation of n2 with grain size
Fig. 9 — Variation of open circuit voltage with grain size.
Experimental points are taken from Refs ( 5, 21, 22, 34, 35)
Fig. 10 — Computed variation of fill factor as a function of grain
size. Experimental points are taken from Refs ( 5, 21, 22, 34, 35)
668
INDIAN J PURE & APPL PHYS, VOL 50, SEPTEMBER 2012
2.7 Fill factor
The Fill Factor (FF) of an ideal solar cell is
expressed as:
FFo = Jm Vm / Jsc Voc
…(22)
where Jm is the current density and Vm is the voltage
density at the maximum power point. Neglecting the
effect of series and shunt resistances, following
relation is used to calculate Vm :
Jsc=Jo1L(1+qVm/kT)[exp(qVm / kT)−1]
+Jo2L(1+qVm /n2KT)[exp(qVm /n2kT)−1]
…(23)
The effect of series and shunt resistance on ideal
fill factor FFo can be estimated approximately by
using the following relation:
FF = FFo (1-1.5 r) +[ r2 / 8.4]
…(24)
Fig. 11 — Variation of efficiency with grain size. Experimental
points are culled from Refs (5, 21, 22, 32, 34, 35)
where r = (R′s Jsc)/Voc, FFo is the ideal curve factor in
the absence of series resistance and R′s = 2.2 ȍ-cm2.
This relation is in accordance with Green’s relation37.
Figure 11 shows the variation of FF with the grain
size. A deviation between the theoretical results and
experimental data5,21,22,34,35 is observed. One should
note that, Eq. (27) is actually derived from single
crystal silicon solar cells. Many researchers23 have
used this relation as such to study the dependence of
FF on the grain size for PX-Si solar cells without
considering the presence of GBs part in the junction
space-charge region. However, one must consider this
fact in order to study the performance of PX-Si solar
cells, therefore, the deviation between present theory
and experimental data may be attributed to the above
mentioned fact.
2.8 Efficiency
The efficiency (Ș) for converting incident solar
radiation into electrical power is calculated by using:
Ș = [(Jsc Voc FF) / Pin ] x 100%.
…(25)
For AM1 illumination, the incident power density
(Pin) is taken as 100 mW/cm2. The computed variation
of efficiency with grain size is shown in Fig. 12. A
good agreement is obtained between computed results
and available experimental data5,21,22,32,34,35 without
considering any reflection loss. The present work
demonstrates that efficiency is mainly governed by
the height of GB potential barrier (qVg). The variation
of efficiency with parameter qVg is shown in Fig. 12.
Fig. 12 — Calculated variation of efficiency versus potential
barrier height
Present work thus clearly indicates that to get higher
efficiency of a solar cell device, GB states must be
passivated and the base doping density should be
properly selected. The computations show that cell
with 10% AM1 efficiency can be fabricated only
when the thickness of the device and grain size are
greater than 100 ȝm, and qVg § 0.
3 Conclusions
The proposed GB recombination model for PX-Si
is able to explain the dependence of GB space charge
JOSHI & SHARMA: POLYCRYSTALLINE SILICON SOLAR CELLS
potential barrier height (qVg), effective diffusion
length of minority carriers, and solar cell parameters
on grain size and GB interface state density. The
important conclusions of present analysis are:
(1) The effective diffusion length decreases on
increasing the doping density. For N§1016 cm−3
Ln* is almost independent of N if d is small.
(2) The diode quality factor n2 is found to vary with
grain size.
(3) In small grain size range (d<<Lb) the effect of
vertical GBs in the junction depth on effective life
time becomes appreciable, as a result of which
empirical parameter f6 is found to have different
value for different grain size range of same
material.
(4) The efficiency of PX-Si solar cells depends not
only on the doping density, grain size, effective
diffusion length, and trapping state density, but
also on the nature of the GB interface state
distribution. Efficiency decreases on increasing
the potential barrier height.
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