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Volume 1, Issue 3, September – October 2012
ISSN 2278-6856
EFFECT OF IRRADIATION ON THE
TRANSIENT RESPONSE OF A SILICON
SOLAR CELL
I. Gaye 1, R. Sam 2, A.D. Seré 2, I.F. Barro 1 , M.A. Ould El Moujtaba 1, R. Mané 1, G. Sissoko1
1
Faculté des Sciences et Technologies, Université Cheikh Anta Diop de Dakar
BP 5005, Dakar-Fann, Sénégal
2
Département de Physique, Institut des Sciences Exactes et Appliquées,
Université Polytechnique de Bobo Dioulasso, Burkina Faso
Abstract: A theoretical study of a silicon solar cell under
multispectral illumination and particles (electrons,
protons…) irradiation is presented. The solar cell is placed in
a fast switch interrupted circuit and the transient decay is
obtained between two steady states. The transient variation of
minority carriers’ density is presented and we show how
diffusion
length,
transient
photovoltage,
transient
photocurrent, and transient capacitance depend on the
of particles).
Keywords:
Irradiation.
Solar
cell,
Transient
variation,
1. INTRODUCTION
Photovoltaic solar energy is the main energy source for
satellites and other space stations. Most solar panels are
embedded in silicon semiconductor materials. They are
subjected to ionizing radiation, which are able to change
their electrical behaviour. When there is absorption of a
dose of ionizing radiation, the concentration of electrons
and holes is modified and the solar cells operation could
be strongly modified. The harmful radiation sources for
semiconductors are of two sorts: natural phenomena and
those related to human activity.
The first one is mainly brought due to the space
environment: solar flare, solar wind, cosmic radiation and
the radiation belts. Phenomena resulting from human
activity are similar but the energy and flow of radiation
are higher.
Radiative emission is found in civil (nuclear power
plants) and military (nuclear explosion, etc ...)
applications.
All these phenomena generate emissions of particles and
radiation which interact with matter and introduce
disturbances in the atomic structures and the electrical
balance in the solar cell. Particles that interact are
charged particles (ions, electrons, protons etc ...),
neutrons and photons [1].
When energetic particles go through the atomic lattice of
the material, they transfer their energy to the network
through events in which ionizing electrons in the network
are temporarily excited to higher energy levels and events
Volume 1, Issue 3, September – October 2012
in which non-ionizing collisions between the incident
particle and the target atoms causes displacement of the
atoms in the lattice. It is the permanent displacement
produced by non-ionizing events incident (protons and
electrons) that degrades the performance of the
semiconductor devices [2].
The purpose of this study is to show the influence of the
irradiation energy and the nature of the radiation Kl on
silicon solar cell, particularly on the following
parameters: minority carriers’ density, transient
photovoltage, transient photocurrent density and transient
capacitance.
2. DEVICE OPERATION
Figure 1 show the experimental setup used to obtain the
transient response of the solar cell.
Figure 1: Experimental setup
This setup includes a square wave generator (BRI8500)
which drives a RFP50N06 MOSFET type, two adjustable
resistors R1 and R2, a silicon solar cell, a digital
oscilloscope, a computer and multi-spectral light source
[3], [4].
The I-V curve of the solar cell is given in Figure 2 [5].
At time t < 0 (Figure 1), the solar cell is under
constant multispectral illumination, MOSFET T is
turned off and the solar cell is loaded only by resistor
R2: this correspond to operating point F2 in steady
state.
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Volume 1, Issue 3, September – October 2012
ISSN 2278-6856
At t = 0 (Figure 1), MOSFET T turning on and after
a very short time (600-800ns) it is fully turned on so
that resistor R2 is in parallel with R1 + Rdson. Rdson
is the drain (D) - source (S) resistance. For a
sufficient Gate voltage, the value of Rdson is very low
(less than one ohm) and can be neglected compared
to that of R1 (10
at the operating point F1 in steady state (Figure 2).
L is the diffusion length of minority carriers in the base
depend on the irradiation energy
and the damage
coefficient Kl through the following expression [7], [2],
[8]:
(4)
L ( Kl ,
1
)
1
L
Kl
2
0
L0 is the diffusion length without irradiation.
We present on figure 3 the diffusion length versus
particles energy for various damage coefficients.
0.01
9.5 10
9 10
3
3
Figure 2: I-V curve photovoltage of a silicon solar cell
The transient decay occurs between the operating points
F1 and F2. The transient voltage across the solar cell is
recorded by a digital oscilloscope (Tektronix), coupled
with a computer for processing and analysis.
Varying R1 and R2, lead to changing operating points F1
and F2 respectively; this allow us to perform the transient
decay at any operating point of the solar cell.
3. THEORY
3.1 Excess minority carrier density
This study is done on a n+pp+ BSF silicon solar cell.
Given that the base contribution is more important, our
analysis will be conducted only in this region of the solar
cell.
The solar cell is under constant multispectral
illumination. At time t and at the depth x in the base, the
distribution of the minority charge carriers is represented
by n (x,t) in transient state.
Let n (x) be the distribution of minority charge carriers in
the steady state and (x, t) the excess minority carriers at
time t from the final state, we have [6]:
(1)
Distribution of minority carrier’s n(x, t) at time t satisfies
the continuity equation on the charge carriers given by:
(2)
D is a diffusion constant and L is the diffusion length of
the minority carriers.
G (x) is the carrier generation rate at the depth x in the
base.
G ( x)
n
3
ame
bm x
(3)
m 1
n is the illumination level, H is the thickness of the base,
am and bm are coefficients tabulated from overall AM1.5
solar radiation [2].
Volume 1, Issue 3, September – October 2012
8.5 10
3
Kl=5 cm^2/s
Kl=10 cm^2/s
Kl=15 cm^2/s
Kl=25 cm^2/s
0
0.5
1
1.5
2
Figure 3: Profile of the variation of the diffusion
length depending on the irradiation energy
The diffusion length decreases as the particle energy
increases. The diffusion length also decreases with the
coefficient damage, but this decrease is more marked for
higher irradiation energy. Since the diffusion length is
strongly influenced by irradiation. It is clear that the
behaviour of the solar cell will also be influenced by
irradiation.
Equation (1) is solved by taking into account the
boundary conditions at the junction and at the back side
of the solar cell [9], [10]:
At the junction (x = 0):
D
( x)
x
Sf
(5)
(0)
x 0
At the back surface (x = H):
D
( x)
Sb
(5’)
(H )
x x H
Sf and Sb are respectively the minority carrier’s
recombination velocities at the junction and at the back
side of the cell.
Expressions (1), (2) and (3) represent Sturm Liouville’s
system.
The excess minority carrier’s density can be written in the
following form:
(6)
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Volume 1, Issue 3, September – October 2012
ISSN 2278-6856
The solutions of these differential equations in X(x) and
T(t) lead to the following general terms:
(7)
And
(8)
An , Bn and Tn(0) are constants.
c,n is the decay time constant and is related to the
minority carriers lifetime by the following expression.
(9)
n is the Eigen value of the transcendental equation
below.
We can establish the following transcendental equation,
taking into account the expression of L
(10)
This equation is valid only if:
(11)
We present on figure 6 the transient decay and also the
series expansion of equation (6) limited to one, two, and
three terms.
Figure 8: Variation of the carrier density versus time for
different values of damage coefficient Kl
We note in Figures 7 and 8 that the particle irradiation
energy affects the transient variation of the carrier
density. When the irradiation energy increases, the carrier
density decreases, and the variation in time is faster.
Thus, for a given value of the energy of radiation, we feel
the same effects with the increase in the coefficient of
damage. The passage of a charged particle, including an
ion through the material generates a region damaged
along its path; irradiation creates defects inherent in
interactions between charged particles and electrons of
silicon. The charged particles lose their energy in the
material and the electron density decreases [12], [13].
We present in figure 9 the excess minority carriers
density versus irradiation energy for various damage
coefficients
Figure 6: Transient decay versus time
This figure show that the different terms of the series
expansion decrease very quickly and after a certain
amount of time t0, the fundamental mode corresponding
to n=0 predominates and is equal to the excess minority
We can write that [11].
(12)
The excess minority carrier’s density versus time is
presented on figures 7 and 8 respectively for various
irradiation energies and various damage coefficients.
Figure 9: Carrier density versus irradiation energy
various damage coefficients
We can observe that the density of minority carriers
decreases with the irradiation for a damage coefficient.
And it’s more perceptible for higher irradiation energy
and higher damage coefficient.
3.2 Transient photovoltage
The transient photovoltage is determined from the
Boltzmann relation:
(13)
VT is the thermal voltage
Or
Figure 7: Variation of the carrier density versus time for
different values
Volume 1, Issue 3, September – October 2012
Let
(13’)
for
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Volume 1, Issue 3, September – October 2012
ISSN 2278-6856
transient photovoltage.
(14)
Figures 14 and 15 below represent the transient
photocurrent profiles for various radiation energies and
damage coefficients Kl.
Figure11: P
We can observe that Transient voltage increases with the
carriers are
increasingly blocked at the junction.
Figures 12 and 13 below present the transient
Figure 14: Profile of the photocurrent density versus time
for different values of
coefficients Kl.
Figure 12: Profile of the transient voltage between
two operating points for different values of the radiation
Figure 15: Profile of the photocurrent density versus
time for different values of the damage coefficient Kl
The transient photocurrent density decreases when the
amplitude level of radiation increases. Irradiation affects
the density of the carriers, the carriers passing through
the space charge zone decreases, so it is a decrease of the
amplitude of the transient photocurrent density and
therefore.
3.4 Transient capacitance
Transient capacitance is given by the following relation:
(15)
Figures 16 and 17 below present the transient capacitance
for various irradiation energy
and damage coefficient
Kl respectively.
Figure 13: Profile of the transient voltage between two
operating points for different values of damage
coefficient Kl
We note in Figures 12 and 13 that photovoltage decreases
in time. The magnitude of the transient voltage remains
constant when the irradiation energy increases and also
when the damage coefficient increases. This means that
irradiation does not affect the carriers trapped at the
junction.
3.3 Transient Photocurrent
The transient photocurrent is given by the equation below
Volume 1, Issue 3, September – October 2012
Figure16: Profile of the transient capacity versus time for
different values of the irradiation energy
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Volume 1, Issue 3, September – October 2012
ISSN 2278-6856
illuminated I-V characteristic. World Renewable
Energy Congress, pp.1848-1851, 1998.
[6] G. Sissoko, C. Museruka, A. Corréa, I. Gaye, A. L.
Ndiaye. Light spectral effect on recombination
parameters of silicon solar cell World Renewable
Energy Congress, part III, pp.1487-1490, 1996
Figure17: Profile of the transient capacity versus time for
different values of damage coefficient Kl
When the irradiation energy increases, ie when the
radiation level increases, as the increase in the coefficient
of injury, the number of particles interactions increases,
and the carrier density is affected which reduces the
number of carriers stored on either side of the junction,
and there is a widening of the space charge zone. This is
what explains the decrease in the amplitude of the
transient capacitance with increasing irradiation energy
and damage coefficient.
4. CONCLUSION
This study based on a silicon solar cell irradiated by
energetic particles shows that the diffusion length
depends strongly on the irradiation energy but also on the
damage coefficient of these particles. The study also
showed that the minority carriers density, transient
photovoltage, transient photocurrent density and transient
capacitance, are influenced by both the irradiation energy
and the damage coefficient. We can also extend this study
to a bifacial solar cell.
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AUTHOR
Since 2006: Professor of physical
sciences in High School Malick Sy,
Thiès-Sénégal. 2010-2012: PhD in
physics (2nd registration), University
Cheikh Anta Diop Dakar-Sénégal
2010-2011: Certificate in secondary
education, University Cheikh Anta
Diop Dakar-Sénégal 2009-2010: Master II in Physics and
Applications, University Cheikh Anta Diop Dakar 20032004: Master II in Systems, Networking and
Telecommunication, High School of Sciences computers,
Dakar-Sénégal 2002-2003: Master in Electronics
sciences, University Mohamed 1er Oujda-Morocco.
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