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Volume 1, Issue 3, September – October 2012                                    ISSN 2278-6856

                     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
                             Faculté des Sciences et Technologies, Université Cheikh Anta Diop de Dakar
                                                   BP 5005, Dakar-Fann, Sénégal
                                  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           in which non-ionizing collisions between the incident
multispectral illumination and particles (electrons,                  particle and the target atoms causes displacement of the
protons…) irradiation is presented. The solar cell is placed in       atoms in the lattice. It is the permanent displacement
a fast switch interrupted circuit and the transient decay is          produced by non-ionizing events incident (protons and
obtained between two steady states. The transient variation of        electrons) that degrades the performance of the
minority carriers’ density is presented and we show how               semiconductor devices [2].
diffusion   length,    transient    photovoltage,     transient
                                                                      The purpose of this study is to show the influence of the
photocurrent, and transient capacitance depend on the
                                                                      irradiation energy and the nature of the radiation Kl on
of particles).                                                        silicon solar cell, particularly on the following
Keywords:        Solar       cell,      Transient      variation,     parameters: minority carriers’ density, transient
Irradiation.                                                          photovoltage, transient photocurrent density and transient
                                                                      2. DEVICE OPERATION
Photovoltaic solar energy is the main energy source for
satellites and other space stations. Most solar panels are            Figure 1 show the experimental setup used to obtain the
embedded in silicon semiconductor materials. They are                 transient response of the solar cell.
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                            Figure 1: Experimental setup
are higher.
Radiative emission is found in civil (nuclear power                   This setup includes a square wave generator (BRI8500)
plants) and military (nuclear explosion, etc ...)                     which drives a RFP50N06 MOSFET type, two adjustable
applications.                                                         resistors R1 and R2, a silicon solar cell, a digital
All these phenomena generate emissions of particles and               oscilloscope, a computer and multi-spectral light source
radiation which interact with matter and introduce                    [3], [4].
disturbances in the atomic structures and the electrical              The I-V curve of the solar cell is given in Figure 2 [5].
balance in the solar cell. Particles that interact are
charged particles (ions, electrons, protons etc ...),                     At time t < 0 (Figure 1), the solar cell is under
neutrons and photons [1].                                                 constant multispectral illumination, MOSFET T is
When energetic particles go through the atomic lattice of                 turned off and the solar cell is loaded only by resistor
the material, they transfer their energy to the network                   R2: this correspond to operating point F2 in steady
through events in which ionizing electrons in the network                 state.
are temporarily excited to higher energy levels and events

Volume 1, Issue 3, September – October 2012                                                                            Page 210
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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           L is the diffusion length of minority carriers in the base
    a very short time (600-800ns) it is fully turned on so       depend on the irradiation energy        and the damage
    that resistor R2 is in parallel with R1 + Rdson. Rdson       coefficient Kl through the following expression [7], [2],
    is the drain (D) - source (S) resistance. For a              [8]:
    sufficient Gate voltage, the value of Rdson is very low                                                (4)
    (less than one ohm) and can be neglected compared            L ( Kl ,       )
    to that of R1 (10                                                                         1
    at the operating point F1 in steady state (Figure 2).                                 L   0

                                                                 L0 is the diffusion length without irradiation.
                                                                 We present on figure 3 the diffusion length versus
                                                                 particles energy for various damage coefficients.

                                                                   9.5 10

                                                                     9 10
 Figure 2: I-V curve photovoltage of a silicon solar cell
                                                                            3                                                        Kl=5 cm^2/s
                                                                   8.5 10
The transient decay occurs between the operating points                                                                              Kl=10 cm^2/s
                                                                                                                                     Kl=15 cm^2/s
F1 and F2. The transient voltage across the solar cell is                                                                            Kl=25 cm^2/s

recorded by a digital oscilloscope (Tektronix), coupled                         0                 0.5              1           1.5                  2

with a computer for processing and analysis.
Varying R1 and R2, lead to changing operating points F1               Figure 3: Profile of the variation of the diffusion
and F2 respectively; this allow us to perform the transient              length depending on the irradiation energy
decay at any operating point of the solar cell.
                                                                 The diffusion length decreases as the particle energy
3. THEORY                                                        increases. The diffusion length also decreases with the
                                                                 coefficient damage, but this decrease is more marked for
   3.1 Excess minority carrier density
This study is done on a n+pp+ BSF silicon solar cell.            higher irradiation energy. Since the diffusion length is
                                                                 strongly influenced by irradiation. It is clear that the
Given that the base contribution is more important, our
analysis will be conducted only in this region of the solar      behaviour of the solar cell will also be influenced by
                                                                 Equation (1) is solved by taking into account the
The solar cell is under constant multispectral
                                                                 boundary conditions at the junction and at the back side
illumination. At time t and at the depth x in the base, the
                                                                 of the solar cell [9], [10]:
distribution of the minority charge carriers is represented
by n (x,t) in transient state.
                                                                 At the junction (x = 0):
Let n (x) be the distribution of minority charge carriers in
the steady state and (x, t) the excess minority carriers at                 ( x)                                         (5)
time t from the final state, we have [6]:                        D                            Sf            (0)
                                                     (1)                    x       x 0
Distribution of minority carrier’s n(x, t) at time t satisfies
the continuity equation on the charge carriers given by:         At the back surface (x = H):

                                                     (2)                    ( x)                                                             (5’)
                                                                 D                                      Sb        (H )
D is a diffusion constant and L is the diffusion length of                    x x H
the minority carriers.
                                                                 Sf and Sb are respectively the minority carrier’s
                                                                 recombination velocities at the junction and at the back
G (x) is the carrier generation rate at the depth x in the
                                                                 side of the cell.
                                                                 Expressions (1), (2) and (3) represent Sturm Liouville’s
                         bm x                                    system.
G ( x)    n        ame                (3)                        The excess minority carrier’s density can be written in the
              m 1
                                                                 following form:
n is the illumination level, H is the thickness of the base,
am and bm are coefficients tabulated from overall AM1.5                                                                  (6)
solar radiation [2].

Volume 1, Issue 3, September – October 2012                                                                                                Page 211
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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:
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.
  n is the Eigen value of the transcendental equation
below.                                                       Figure 8: Variation of the carrier density versus time for
We can establish the following transcendental equation,             different values of damage coefficient Kl
taking into account the expression of L
                                                             We note in Figures 7 and 8 that the particle irradiation
                                                             energy affects the transient variation of the carrier
This equation is valid only if:                              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
                                                    (11)     the same effects with the increase in the coefficient of
We present on figure 6 the transient decay and also the      damage. The passage of a charged particle, including an
series expansion of equation (6) limited to one, two, and    ion through the material generates a region damaged
three terms.                                                 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

         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].                                       Figure 9: Carrier density versus irradiation energy
                                                      (12)                  various damage coefficients
The excess minority carrier’s density versus time is         We can observe that the density of minority carriers
presented on figures 7 and 8 respectively for various        decreases with the irradiation for a damage coefficient.
irradiation energies and various damage coefficients.        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:
                                                             VT is the thermal voltage
                                                             Or                                              (13’)

Figure 7: Variation of the carrier density versus time for   Let            for
        different values

Volume 1, Issue 3, September – October 2012                                                                  Page 212
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Volume 1, Issue 3, September – October 2012                                    ISSN 2278-6856

transient photovoltage.
                                                              Figures 14 and 15 below represent the transient
                                                              photocurrent profiles for various radiation energies and
                                                              damage coefficients Kl.

Figure11: P
                                                              Figure 14: Profile of the photocurrent density versus time
We can observe that Transient voltage increases with the           for different values of
                                            carriers are
increasingly blocked at the junction.
Figures 12 and 13 below present the transient

coefficients Kl.

                                                                 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
   Figure 12: Profile of the transient voltage between
                                                              the space charge zone decreases, so it is a decrease of the
 two operating points for different values of the radiation
                                                              amplitude of the transient photocurrent density and
                                                              3.4 Transient capacitance
                                                              Transient capacitance is given by the following relation:

                                                              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       Figure16: Profile of the transient capacity versus time for
junction.                                                            different values of the irradiation energy
3.3 Transient Photocurrent
The transient photocurrent is given by the equation below

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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

                                                                  [7] M.A. Ould El Moujtaba, M. Ndiaye, A.Diao,
                                                                    M.Thiame, I.F. Barro and G. Sissoko. Theoretical
                                                                    Study of the Influence of Irradiation on a Silicon
                                                                    Solar Cell under Multispectral Illumination.
Figure17: Profile of the transient capacity versus time for         Research Journal of Applied Sciences, Engineering
         different values of damage coefficient Kl                  and Technology ISSN
When the irradiation energy increases, ie when the                [8] R. K. Ahrenkiel, D. J. Dunlavy, H. C. Hamaker, R.
radiation level increases, as the increase in the coefficient       T. Green, C. R. Lewis, R. E. Hayes, H. Fardi Time-
of injury, the number of particles interactions increases,          of-flight studies of minority-carrier diffusion in
and the carrier density is affected which reduces the               AlxGa1-xAs homojunctions J. Appl. Phys. 49(12)
number of carriers stored on either side of the junction,           1986.
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and damage coefficient.                                             2001.
                                                                  [10] A. Ricaud Photopiles solaires. Presses
4. CONCLUSION                                                       polytechniques et universitaires romandes, 1997.
This study based on a silicon solar cell irradiated by            [11] Saïdou Madougou, Mohamadou Kaka and
energetic particles shows that the diffusion length                 Gregoire Sissoko Silicon solar cells: recombination
depends strongly on the irradiation energy but also on the          and electrical parameters. Solar Energy, Book edited
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