IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
Determination Of The Junction Surface recombination
Velocity Limiting The Open Circuit (Sfoc) For A Bifacial
Silicon Solar Cell Under External Electric Field.
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Marcel Sitor DIOUF, 1Gohan SAHIN , 1Amary THIAM, 1Khady FAYE 1Moussa Ibra NGOM, 2Doudou
GAYE, 1Grégoire SISSOKO
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University of Cheikh Anta Diop, Dakar/Senegal, Faculty of Sciences and Techniques, Physics Department.
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University of Cheikh Anta Diop, Dakar/Senegal, Polytechnic High School
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* Corresponding author: Grégoire SISSOKO (gsissoko@yahoo.com - 00221776329041).
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Abstract
In this paper, we study the influence of the electric field on the junction recombination
velocity limiting the open circuit. The excess of minority carrier’s density in the base is
determined from the continuity equation. The photovoltage and the open circuit voltage are
derived from the excess minority carrier’s density. From the photovoltage study, the junction
recombination velocity limiting the open circuit and the open circuit voltage are determined
and studied for different values of electric field and simultaneous illumination mode.
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Keywords : Solar Cell – Electric field – Junction recombination velocity – Open circuit
voltage
I. Introduction
Photovoltaic conversion is a direct transformation of light energy into electrical energy
through a device called solar cell. Because of their modest performance, many studies have
been developed in order to improve their efficiency by different processes [1] and through
different characterization techniques. The solar cell can be placed under static condition [2]
and dynamic mode (transient and frequency) [3], then the electrical and recombination
parameters [4-8] are deduced. As part this work, our contribution is to study the effect of
polarization electric field on the junction surface recombination velocity limiting the open
circuit through the open circuit voltage. The study will be done on the solar cell remained
under simultaneous polychromatic illumination of the two sides.
II. Theory
In this study, we consider an n+-pp+ solar cell type [9], double side surface illuminated and
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under external polarization by applying a voltage. The effect of external electric field
resulting from the polarization behavior of the charge carriers in the base is studied by help
with the assumption of the quasi-neutral base (QNB) [10]. theory’s. Figure 1 shows the
structure of the solar cell depending on the model under study.
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
Figure 1: Bifacial solar cell structure to the n+pp+ type under electric polarization and polychromatic
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illumination.
II.1. Détermination of the minority carrier’s density
The continuity equation for the excess minority carrier’s density photo-genered in the base
under influence of the electric field is:
∂ 2δ ( x) µ .E ∂δ ( x) G (x ) δ (x )
+
⋅
+
− 2 =0
D
D
∂x
∂x 2
L
(1)
δ(x) is the excess minority carriers density according to the depth x in the base of the solar
cell, following the simultaneous double side surface illumination mode.
E represents the electric field, D the diffusion coefficient, L the diffusion length, µ the carrier
mobility.
Posing in:
LE =
µ .E.L2
D
(2)
Equation (1) becomes:
∂ 2δ ( x) LE ∂δ ( x) G ( x ) δ (x )
+ 2⋅
+
− 2 =0
∂x
D
∂x 2
L
Ln
(3)
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
The expression of G (x) depends on the x depth of light absorption in the base and can be
written in the form of the following equation [11].
(
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G ( x) = ∑ ai ⋅ e −bi + e −bi ( H − x )
)
i =1
(4)
The parameters a i and b i stem from the modeling of the incident illumination as defined by
under A.M 1.5 condition [12].
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H is the thickness of the base.
Where, a 1 = 6.13x1020 cm-3/s; a 2 = 0.54x1020 cm-3/s; a 3 =0.0991x1020 cm-3/s; b 1 = 6630 cm-1 ;
b 2 = 103 cm-1; b 3 =130 cm-1;
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The solution δ(x) of the carriers’ diffusion equation (1) is obtained in the following forms:
δ ( x) = e ⋅ [A ⋅ ch(φ ⋅ x) + B ⋅ sh(φ ⋅ x)] + ∑ ci ⋅ (e −b . x + e −b .( H − x ) )
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βx
i
i
i =1
(5)
With the different coefficients expressed as:
1
( L2 E + 4 ⋅ L2 n ) 2
φ=
2 ⋅ L2 n
ci = −
β=
,
− LE
2 ⋅ L2n
a i ⋅ L2 n
Dn ⋅ [ L2 n ⋅ b 2 i − L E ⋅ bi − 1]
The coefficients A and B are solved with the boundary conditions at the emitter – base junction
and at the back surface of the cell [12, 13]:
-at the junction (x=0):
Sf =
D n ∂δ ( x)
⋅
δ (0) ∂x
(6)
x =0
-at the back surface (x=H) :
Sb = −
Dn ∂δ ( x)
⋅
δ ( H ) ∂x
x=H
(7)
Sf and Sb are respectively the junction and back surface recombination velocity [10, 11].
We plot in figure 2, the minority carrier’s density versus base depth for different values of
electric polarization field
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
Figure 2 : Minority carrier’s density versus base depth for different values of electric polarization
field
(Sf=4.104cm/s, µ=103cm2V-1s-1, L=0.02cm, H=0.03cm, D=26cm2.s-1)
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II.2. Photovoltage
The expression of the photovoltage is obtained from the following relation
N

V ph = VT ln b2 δ (0) + 1
 ni

(8)
V T is the thermal voltage, n i the intrinsic carrier density at thermal equilibrium and N B the
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base doping density.
We plot in figure 3, the photovoltage versus junction recombination velocity.
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
Figure 3 : Photovoltage versus junction recombination velocity for different values of electric
field
(µ=103cm2V-1s-1, L=0.02cm, H=0.03cm, D=26cm2.s-1)
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II.2. Determination of the junction recombination velocity limiting the open circuit
voltage
For low values of the junction recombination velocity, the photovoltage is maximum and
constant. The excess minority carriers are then stored at the junction. Taking into account
previous work [14] and keeping our interest in this flat part of the photovoltage curves, we
can deduce the condition yielding the junction surface recombination limiting the open circuit
voltage by the following equation.
Vph(Sf) - Voc =0
(9)
Voc represents the open circuit voltage and is given as:
Voc = lim Vph( Sf )
(10)
Sf →Sfoc
(D.β .E − F ).(D.bi E.e −b .H + G ) − (G − D.bi .E )(. D.β .E − F )
Sfco =
E (D.β .E − F )e −b . H + E (E.D.bi e b . H + G )
i
i
E = (Sb + D.β ).Sh(φ .H ) + D.φ .Ch(φ .H )
i
(11)
(11-1)
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
F = [(Sb + D.β ).Ch(φ .H ) + D.φ .Sh(φ .H )].φ .D
(11-2)
G = φ .D(Sb + D.bi ).e − H ( β +bi )
(11-3)
µ .E.D.φ .Ch(φ .H ) − [D 2 .α 2 − (µ .E + D.β ).D.β ].Sh(φ .H )
Sb =
D.φ .Ch(φ .H ) − (µ .E + D ).Sh(φ .H )
(11-4)
We plot in Figure 4, the relative values of junction recombination velocity limiting the open
circuit and the open circuit voltage versus the electric field
Figure 4: Relative values junction recombination velocity and open circuit voltage versus electric
field
2
(D=26cm /s, µ=103cm2.V-1s-1, τ=10-5s )
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Figure 4 shows the evolution of the relative values of the recombination velocity at the
junction as that of the open circuit voltage according to the electric field as described above.
We obtain the value of the electric field when the relative value of the open circuit voltage intercepts
with the relative value of junction recombination velocity
The values of the open circuit voltage and the recombination rate obtained are higher than
those obtained for the illumination from the front side [15].
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
Conclusion
In this work, the excess of minority charge carriers density in the base is determined and its
curve according the base depth for different values of electric field and for simultaneous
illumination mode is presented. The excess of the photovoltage is deducted from that of
minority carrier’s density and their profile depending the junction recombination velocity for
different values the electric field and for proposed illumination mode. Thus, the junction
recombination velocity limiting the open circuit voltage is determined for the solar cell under
electric polarization.
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IJISET - International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 9, September 2015.
www.ijiset.com
ISSN 2348 – 7968
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