International Journal on Power Engineering and Energy (IJPEE)
ISSN Print (2314 – 7318) and Online (2314 – 730X)
Vol. (7) – No. (1)
January 2016
Electrical Power under Influence of the Solar
Cell Thickness
Nfally DIEME
Laboratory of Semiconductors and Solar Energy, Department of Physics, Faculty of Science and
Technology, Cheikh Anta DiopUniversity, Dakar, Senegal.
nfallydieme@yahoo.fr
Abstract-The aim of this work is to show the effects
of solar cell thickness on the electrical parameters
such as Short -circuit current density (Jsc) Open
circuit photovoltage (Voc) and Power.
This theoretical study of a parallel vertical junction
silicon solar cell under a multi-spectral illumination in
static regime has been done under impact of the
thickness of this solar cell. Based on the diffusionrecombination equation, the expression of electrons,
Jsc, Voc and power are then deduced.
Keywords: Short -circuit current density (Jsc),
Open circuit photovoltage (Voc) ,
Power,
temperature.
Figure (1): Parallel vertical junction solar cell
I. INTRODUCTION
The vertical junction solar cell is made by an
alternative junction base -emitter-base-emitter. Both sides
have the same thickness. [1] Each base and emitter is
bordered by an aluminum collector as shown in the
following figure1. The incident rays simultaneously touch
the base, the junction and the emitter.
The bases are interconnected by a connecting wire to
define the positive electrode and the emitters are
connected together to form the negative electrode.
But for the rest of our study we assume that the following
hypotheses are satisfied.
• The illumination is uniform and is made with
polychromatic light in steady state
The contribution of the emitter and space charge region is
neglected, so this analysis is only developed in the base
region.
• There is no electric field without space charge regions.
The aim of this work is to show the effects of solar
cell thickness on the electrical parameters such as Short circuit current density (Jsc) Open circuit photovoltage
(Voc) and Power.
Knowing the evolution of these quantities based on the
thickness is a good indicator for us to comment on the
impact on the performance of solar cells.
II. ELECTRONS DENSITY
Taking into account the generation, recombination
and diffusion phenomena in the base, the equation,
governing the variation of the electrons in static regime
can be written as [1]
∂
2
G n
n(x)
n(x)
−
= −
2
2
D
∂x
L
(1)
D is the diffusion constant [2], [3]
D =  .
K
.T
q
(2)
with q the elementary charge, k the Boltzmann constant
and T the temperature.
Gn= g(z)+gth is the carrier generation rate.
g(z) is the carrier generation rate at the thickness z in the
base and can be written as:
Reference Number: JO-P-0071
619
International Journal on Power Engineering and Energy (IJPEE)
ISSN Print (2314 – 7318) and Online (2314 – 730X)
g ( z) = ∑ ai e−biz
(3)
ai and bi are obtained from the tabulated values of
AM1.5 solar illumination spectrum and the dependence of
the absorption coefficient of silicon with illumination
wavelength.
gth is the thermal generation rate. But in the absence of
temperature gradient gth is uniformity compensated by
the thermal recombination rate [4]
It is given by:
2
(4)
th
i
Vol. (7) – No. (1)
January 2016
III. ELECTRICAL PARAMETERS
Short-circuit current density: The photocurrent Jph
is obtained from the following relation given that there is
no drift current:
J
ph
Eg
)
2 KT
x0
=
Isc
lim
Sf
→ ∞
Jph
(12)
The figure2 shows the impact of the solar cell thickness
on the Short -circuit current density.
with
n i = An .T . exp(
(11)
Short -circuit current density is defined by [7]
g = c.n
3
2
n( x)
x
 qD
(5)
ni refers to the intrinsic concentration of minority
carriers in the base, An is a specific constant of the
material (An=3.87x1016 for silicon)
Eg is the energy gap ; it is given by [ 4 ] :
a.T 2
b+T
(6)
1
C .N B
(7)
Eg = Eg 0 −
(Eg0=1.170 eV; a=4.9 10-4 eV.K-2 ; b=655K for silicon)
And
 =
NB is the base doping concentration in impurity atoms
and C is the proportionality coefficient.
n(x), L, τ, and μ are respectively the excess minority
carriers density, diffusion length, lifetime and mobility.
The solution of equation (1) is:
ai 2 −biz L2
x
x
Eg
n(x) = Asinh( ) +Bcosh( ) +∑ L e + C.An.T3.exp( )
L
L
D
D
KT
(8)
Coefficients A and B are determined through the
following boundary conditions [5], [6]
Boundary conditions:
• at the junction (x=0):
∂n ( x )
∂x
•
=
x=0
Sf
D
n (0)
w
x=
2
=0
Reference Number: JO-P-0071
Figure2 shows the profile of the Short -circuit current
density (Isc) versus temperature for various values of the
solar cell thickness. For higher temperature, the electrons
flow through the junction increases so that the generated
photocurrent also increases [8]: In this figure we note that
Isc increases as operating temperature increase. Such
increase of Isc is all the more important that the Thickness
is low.
Open circuit photovoltage: The photovoltage
derives from the Boltzmann relation:
(9)

n (0) 
V ph = k .T ⋅ ln  N B . 2 + 1
q
ni


(13)
Open circuit photovoltage is defined by [7]
in the middle of the base (x=W/2) :
∂n ( x)
∂x
Figure (2): Short-circuit current density versus
temperature
(10)
Voc
=
lim
Sf
→
0
Vph
(14)
The figure3 shows the impact of the solar cell thickness
on the Open circuit photovoltage.
620
International Journal on Power Engineering and Energy (IJPEE)
ISSN Print (2314 – 7318) and Online (2314 – 730X)
Vol. (7) – No. (1)
January 2016
Moreover high thickness increases rate imperfection of
the junction. All these malfunctions are the reals causes of
the decrease of photocurrent, photovoltage and power.
IV. CONCLUSION
A theoretical study of a vertical junction solar cell has
been presented. Electrical parameters such as
photocurrent density, photovoltage, have been determined
and we showed the effects of solar cell. This study exhibit
the fact that photocurrent density and photovoltage
depend on solar cell thickness. We can estimate that high
solar cell thickness decreases performance solar panels.
This study can be confirmed by studying the diffusion
capacitance under the influence of thickness.
Figure (3): Open-circuit photovoltage versus temperature
REFERENCES
Figure3 shows that the open circuit voltage rapidly
decreases as the temperature prevailing in the solar cell
increases. With the increase of the temperature a lot of
electrons through the junction to participate in the output
current [8]. This decrease is all the more important than
solar cell thickness is high
1
Ideal power: Figure4 below shows the evolution of
the ideal power depending on the average temperature
prevailing in the solar cell for various values of solar cell
thickness.
3
2
4
5
6
7
Figure (4): Ideal power versus temperature
Figure4 shows that power reaches maximum level
with low temperature and decreases with increasing
temperature. This decrease is all the more important than
solar cell thickness is high, accordance with Isc and Voc
Indeed High thickness retains heat for a long time and the
solar cell considerably loses its ability to store charge
carriers at the junction with increasing temperature [9].
Moreover the increase in thickness increases defects in
structuring and traps center for photogenerated electrons.
Reference Number: JO-P-0071
8
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