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Volume 4, Issue 7, July 2016
Influence of the Depth base on the Electrical
parameters of a Parallel Vertical Junction Silicon
Solar Cell under Polychromatic illumination
1
Oulimata MBALLO, 2Boureima SEIBOU, 3Mamadou WADE, 1Marcel Sitor DIOUF, 3Ibrahima LY,
3
Seni TAMBA, 1Grégoire SISSOKO
1
Faculty of Science and Technology, University Cheikh Anta Diop, Dakar-Senegal
2
Ecole des mines de Niamey-Niger
3
Ecole Polytechnique of Thies, EPT, Thies, Senegal
ABSTRACT
In this paper, influence of the depth in the base on the Electrical parameters of a Parallel Vertical Junction Silicon Solar Cell
under Polychromatic illumination. From the excess minority carrier’s density in solar cell, the photocurrent density the
photovoltage and the capacitance are determined and studied for various depth in the base. From the I-V characteristic, the
series and shunt resistances are determined for different values of the depth in the base.
Keywords: parallel vertical junction – depth z – series and shunt resistances.
1. INTRODUCTION
The use of photovoltaic energy on a large scale is slowed down by poor efficiency of the solar cells. Indeed the
performance of a solar cell is related to its capacitance to collect maximum carriers and thus to limit the recombinations
in both in the bulk and the surface. In order to improve the performance of solar cells, a new generation of solar cells
called vertical junction solar cell was invented [1]. These solar cells are of two types: vertical junction solar cell series
and those parallel vertical junction [1], [2], [3]. For the characterization of solar cells much research have been carried
out on the behavior of carriers photocreated in a horizontal solar cell junction [4] and in a vertical junction solar cell
[5]. These types solar cell were studied in the presence of an electric field [6], [7], of a magnetic field [8], [9] or under a
simultaneous effect of both electric and magnetic field [10]. Our contribution in this article is to carry out a study based
on the minority carriers and the electrical parameters according to the depth of a parallel vertical junction silicon solar
cell. The advantage of this type of solar cell is the fact that the most important part of our study is based between two
junctions through which the carriers migrate to generate current.
Thus, after studying the influence of the depth on the minority carriers density, we will study the influence of the depth
on the photocurrent, the phototension, the capacitance and on the series and shunt resistances. The behavior of the
capacitance of the solar cell in short-circuit versus the depth will let us know the variation of the thickness of the
depletion zone and later on the influence of the depth on the performance of the solar cell.
2. THEORY
On figure 1 we present a series of photovoltaic cells with vertical junction connected in parallel and on figure 2 a
photovoltaic cell to the silicon of the n-p-n type to parallel vertical junction under polychromatic illumination
Figure 1 Series of parallel vertical junction photovoltaic cells.
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Figure 2 Structure of a photovoltaic cell of the type n-p-n to vertical junction under constant polychromatic
illumination
While being placed on the assumption of the Quasi Neutral Base (QNB) theory’s [11], the continuity equation which
the minority carriers in the base under steady state is given by:
G (z)  D 
 2 ( x )
 R (x)  0
x 2
(1)
With G(z) the carriers generation rate to depth Z for the polychromatic illumination and whose expression is given by
the equation [12]:
3
G(z) 
a e b
 i Z
(2)
i
i 1
where ai et bi are the overall radiation coefficients from the generation rate modelling in solar spectrum to A.M 1,5
[13] :
D 
 2 ( x )
is the term of diffusion where D is the diffusion coefficient of the carriers; R(x) is the
x2
recombination rate of the carriers to positon x [14] :
R( x) 
 ( x)

(3)
and (x) is the photo-generated minority carriers density in position X of the base
The solution of the equation (1) is given by the equation (4) below
x
x
 ( x , z )  Ach ( )  Bsh ( ) 
L
L
With
Ci 
a
i

3
C e b

i
Z
(4)
i
i 1
L2
D
where L is the diffusion length. Coefficients A and B of the equation (4) are determined by the use of the boundary
conditions [13], [15]:
At the junction base1-emitter1 (x=0)
At the middle of the base (x=H/2)
D
 ( x, z )
x
 Sf   ( x, z ) x 0
(5)
x 0
 ( x, z )
x
0
x
(6)
H
2
is the junction recombination velocity. It is equal to the sum of the intrinsic recombination velocity
(induced by
resistance shunt and depending only on the intrinsic parameters of the photovoltaic cell) and the recombination velocity
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which shows the leakage current induced by the external load and which defines the operating point of the
photovoltaic cell.
[16], [17].
To study the effect of depth on the parameters of the solar cell, we will work with a z depth between 20 and 50 microns.
Indeed for a good characterization of the solar cell it is important to have a low value of the series resistance whose
effect is reflected on the form factor and a large value of the photocurrent density [18, 19]. But the increase of the
depth z increases the series resistance and a decrease in the photocurrent. Hence the importance of working with low
values of the depth z.
2.1. Minority carriers density
Figure 3 represents the variation of the minority carriers density in the base versus thickness X for various depth Z.
Figure3: minority carriers density versus thickness X of the base for various depth Z (D=26 cm2.s-1 ; L=0,01cm)
On this figure, we note a symmetry of the various curves of the density at the middle of the base(X = H/2). Indeed our
photovoltaic cell model is in parallel vertical junction, therefore the basis of our study is done between two junctions
which contribute in the same way. Thus for a given curve, one observes three zones:
 x < H/2, the gradient of the carriers is positive: the electrons located in this zone cross junction 1 to generate
current.
 x=H/2, the null gradient of the density is corresponding to the maximum of the minority carriers density: carriers
cross the two junctions on both sides of the base.
 x > H/2, the gradient of the carriers is also positive compared to transmitter 2: the electrons located in this zone
cross junction 2 to take part in the photocurrent.
When the depth increases, the carrier density decreases. This is explained by the fact that it has a low generation of
carriers in the depth. The incident light attenuates in-depth involves a reduction in the rate of generation from where
reduction in the carriers density. The study of the density of the carriers in the base leads to the photocurrent density
generated within the solar cell.
2.2. Photocurrent density
The expression of the photocurrent density of a solar cell is given according to the gradient of the minority carriers
density by the relation:
J ph  2  q  D
 ( x, z )
x
(7)
x 0
with q the elementary charge.
On figure 4 we represent the photocurrent density profile versus the junction recombination velocity for various depth
and on figure 5 the photocurrent of short-circuit versus the depth
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Figure 4: Photocurrent density versus junction recombinaison velocity for various depth z (D=26 cm2.s-1 ; L=0,01 cm)
Figure 5: Short circuit photocurrent density versus the depth z (D=26 cm2.s-1 ; L=0,01 cm)
We note an increase of the photocourant at the figure 4 when the junction recombination velocity increases. In fact, as
the matter of fact, the recombination speed to the junction shows the amount of carriers that cross the junctions to be
part of the photocurrent. The more it increases, the more carriers are swept towards junctions, thus increasing, the
photocurrent density. To low values of the junction recombination velocity, the photocurrent density is almost nonexistent representing the situation of open circuit of the solar cell.
The photogenerated carriers are thus blocked to the junction. To high values of the junction recombination velocity, the
photocurrent density is maximal and corresponding to photocurrent of the short-circuit. The solar cell operates in
situation of short-circuit, where the maximum of carriers cross the junctions to be part of the photocurrent. This figure
shows again the decreasing of the photocurrent density of short-circuit when we go in depth, which is illustrated at
figure 5. Actually, the incident light intensity decreases in depth. In such case, there is less photo-generated carriers,
therefore, the photocurrent density decreases.
In the following paragraph, we are going to study the photovoltage, which characterizes the solar cell potential barrier.
2.3. Photovoltage
The solar cell photovoltage is given by the relation of Boltzmann:
 N
 
V ph  VT  ln  2B   (0, z )   1

 
 
  n i
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With VT is the thermal voltage:
NB the base doping density; ni the intrinsic carriers density at thermal equilibrium; k the Boltzmann constant ; T the
absolute temperature and q the electron charge.
Figures 6 and 7 respectively represent the variation of the photovoltage versus the junction recombination velocity for
various values depth and that of the photovoltage versus the depth.
Figure 6 : Photovoltage versus junction recombinaison velocity for various depth (D=26 cm2.s-1; L=0,01 cm)
Figure 7 : Open circuit photovoltage versus depth z (D=26 cm2.s-1; L=0,01 cm)
We notice in the figure 6 that the photovoltage is maximal and equal to the open circuit photovoltage for the low junction
recombination velocity (Sf) values then it decreases until tending to an almost null value with the great values of Sf (in the
vicinity of the short circuit). In fact for low Sf values, the charge carriers do not acquire a sufficient energy to cross the
junction. Thus, these carriers are blocked at the junction increasing the photovoltage consequently.
For the great values of the junction recombination velocity, the carriers manage to traverse the junction involving
thereafter the considerable fall of the photovoltage. When we advance in the depth, the carriers number decreases. We can
notice the reduction in the open circuit photovoltage what confirms figure 7.
2.4. I-V characteristics
We study in this paragraph the characteristics I-V of the photovoltaic cell. Figure 8 represents the I-V characteristics for
various depth.
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Figure 8: I-V Characteristics of the photovoltaic cell for various depth z (D=26 cm2.s-1; L=0,01 cm)
We notice on this figure that the photocurrent density is maximum with the low values of the photovoltage
corresponding to the short circuit photocurrent then it decreases for the great values of the photovoltage corresponding
to the open circuit situation of the solar cell. We also notice the reduction in the photocurrent density and the
photovoltage with the depth Z.
From the I-V characteristics of the solar cell, studies showed that the solar cell behaves like [18], [20].
i) an ideal voltage generator to the neighborhood of the open circuit,
ii) an ideal current generator to the neighborhood of the short circuit.
In each case, an equivalent electrical model of the solar cell was proposed. Using these electrical model the series and
shunt resistances can be determined.
2.4. Series resistance
The series resistance characterizes the ohmic and resistive effects of the material and the contact device. It is an
important parameter that affects the performance of a solar cell. It is therefore important to determine this parameter to
get a reliable characterization of the solar cell. There are several methods for determining the series resistance [18] –
[21].
To determine series resistance, we consider the solar cell operation in open circuit. Figure 9 below shows the equivalent
diagram of the solar cell in the vicinity of the open circuit [17], [20] where Rs is the series resistance; Rch is the
external load and Voc is the open circuit photovoltage.
Figure 9: Solar cell equivalent circuit operating in open circuit
The literal expression of the series resistance is given by:
R S ( Sf ) 
V
OC
V
J
ph
( Sf )
(9)
( Sf )
ph
Figures 10 and 11 respectively illustrate the profile of series resistance versus the junction recombination velocity for
various depth and the series resistance versus the depth.
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Figure 10: Series resistance versus junction recombinaison velocity for various depth (D=26 cm2.s-1 ; L=0,01 cm)
Figure 11: Series resistance versus depth z (Sf = 2 102 cm/s; D=26 cm2.s-1 ; L=0,01 cm)
On figure 10 the series resistance is low and almost. Series resistance increases with the depth z (figure 11). Indeed as
underlined previously, when the values of Z increases, the carriers generation rate decreases.
2.5. Shunt resistance
Shunt resistance characterizes the eddy currents within the solar cell. There are several methods for determining the
shunt resistance [20], [21].
To determine shunt resistance, we consider the solar cell operation in short circuit. Thus, the solar cell is regarded like
a generator of current in parallel with the shunt resistance Rsh and series whith the external charge Rch whose
equivalent electrical model is represented on the figure 12 [15], [ 22].
Figure 12: Solar cell equivalent circuit operating in short circuit
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By applying the nodes law, the shunt resistance can be expressed by:
R
Sh
( Sf ) 
V ph ( Sf )
J CC 
J
( Sf )
ph
(10)
We represent on the figure 13 the shunt resistance versus the junction recombination velocity for various depth Z. In
the expression of shunt resistance the currents Jph and Jcc as well as the Vph tension depend on depth Z, therefore we
represent on the figure 14 the profile of shunt resistance versus the depth Z
Figure 13 : Shunt resistance versus junction recombinaison velocity for various depth z (D=26 cm2.s-1 ; L=0,01 cm).
Figure 14: Shunt resistance versus depth z (Sf = 8108cm/s; D=26 cm2.s-1 ; L=0,01 cm).
At figure 13, we observe a considerable increasing in shunt resistance with the junction recombination velocity because
more the movement of the carriers in the base is accelerated, more the eddy current of the solar cell reduces. Besides,
we note also the raising in shunt resistance with the depth like illustrates on figure 14. Indeed, when the Z values
increases, the incident light intensity decreases involves the reduction in the leakage currents and the increasing of the
shunt resistance.
2.6. Capacitance
The solar cell capacitance under illumination is given by :
C
q  no
 (0, z)
q
VT
VT
(11)
Figure 15 illustrates the profile of the capacitance versus the junction recombination velocity for various depth and
figure 16 illustrates the capacitance of solar cell near the short circuit versus the depth.
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Figure 15 : Capacitance versus junction recombinaison velocity for various depth (D=26 cm2.s-1; L=0,01cm)
Figure 16 : capacitance of the solar cell operating in short circuit versus the depth Z (D=26cm2.s-1; L=0,01cm)
On these various curves, the capacitance is maximum in the vicinity of the open circuit (0< Sf< 2.102cm/s). This is due
to the blocking of the carriers to the junction when the junction recombination velocity is low. On the other hand the
capacitance decreases markedly in short-circuit (Sf > 5.105cm/s): almost all the carriers take part to photocurrent
generation. In addition, the decrease of the capacitance is noted when the Z values increases. Indeed the space charge
region varies with the depth.
It's reduces because of the weak generation in depth of the carriers. We notice also on figure 16 that the capacitance of
solar cell operating in short circuit decreases with the depth. From this figure we determined the values of capacitance
of solar cell operating in short circuit when the depth Z varies to see the influence of the depth on the widening of the
space charge region. We obtain the table below.
Table 1: values of capacitance of solar cell operating in short circuit when the depth Z varies
Depth Z (cm)
10 – 3
2 10 - 3
3 10 - 3
4 10 - 3
5 10-3
Capacitance in short
circuit Ccc (F/cm2)
2,337 10-8
1,189 10-8
7,478 10-9
5,461 10-9
4,406 10-9
We notice that the more the depth Z increases, weaker the capacitance of solar cell in short circuit becomes. This
reduction of the capacitance of solar cell in short circuit corresponds to a widening of the thickness X of the depletion
region which is comparable with a plane capacitor.
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3. CONCLUSION
The purpose of this work was to study influence of the depth base on the electrical parameters of a parallel vertical
junction solar cell under polychromatic illumination. The study showed that when depth Z increases the minority
carriers density as well as the electrical parameters such as the photocurrent density, the photovoltage and the
capacitance decrease because of attenuation of the incident ligth. This study showed also that the series and shunt
resistances increase when the depth increases.
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AUTHOR
Miss Oulimata Mballo was born in Oussouye, Senegal in 1988.She is working on her doctoral thesis in the
laboratory of semiconductors and renewableergy of the Faculty of Science and Technology of the University
Cheikh Anta Diop in Dakar, Senegal. His research interest is in the field renewable energy, Semiconductor
devices characterization and electronics
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