Research Journal of Applied Sciences, Engineering and Technology 4(23): 5068-5073, 2012
ISSN: 2040-7467
©Maxwell Scientific Organization, 2012
Submitted: March 31, 2012 Accepted: April 26, 2012 Published: December 01, 2012
Abstract: This study aims to demonstrate the effects of particles irradiation on the silicon solar cell properties.
A theoretical study of a silicon solar cell under multispectral illumination and particles (electrons, protons…) irradiationis presented. The relative density is presented and we show that the space charge region width depend on the irradiation parameters (energy and nature especially). We also pointed out the influence of the irradiation on the following parameters: the photocurrent density, the open circuit voltage, the fill factor, the conversion efficiency, the shunt and series resistances and the diffusion capacitance of the solar cell.
Keywords: Electrical parameters, irradiation, solar cell
INTRODUCTION
Solarcell technology has been pioneered by space industry, essentially because solar energy is one of the main power sources for satellites. However, space environment is a very harsh environment for electronic devices, such as solar cells and other semiconductor based detectors. In this environment the devices mounted in or on satellites are subjected to large temperature variations, space dust and high-energy charged-particle irradiation.
Since high-energy charged-particle irradiation damage the semiconductor structure (Martin, 2006;
Fatemi et al ., 2001; Kreinin et al ., 2007), the solar cell performance under radiation exposure is a critical design parameter (Ohshima et al ., 2005) so that the relation between solar cell parameters and the radiation parameters has to be known.
The aim of this study is to show the influence of the energy and the nature of the irradiation on a silicon solar cell, especially for the following parameters: Relative excess minority carriers density, photocurrent density, open circuit voltage, fill factor, conversion efficiency, shunt and series resistances and last but not least the diffusion capacitance.
THEORY
Excess minority carrier density: This study is based on a back surface field silicon solar cell with n+-p-p+ structure (Fig. 1). Since the base has a greater contribution to photo conversion, the following analyses will be conducted only on this region. When the solar cell is illuminated with a multispectral light, the continuity equation relative to excess minority carriers (electrons) density photo generated in the base region can be written as:
 x
 
2

  
L
2

 
D

0 (1)
With D being the diffusion constant and L the diffusion length; and Amon (1985):
L
0
G (x) is the carrier generation rate taken to be Furlan
   n
 3 m

1 a e
 n is related to the illumination level: it is the ratio between the real operating power and the reference power for
AM1.5 (100 mW/cm 2 ), H is the base thickness; a m
and b m are coefficients obtained from modelling of the generation rate overall radiations in the solar spectrum (Mohammad,
1987).
The diffusion length L is related to the particles energy
M
and the type of particles (that is the nature of irradiation) Kl by the following relation (Kraner, 1983):

,






1
L
0
2
1

Kl
  


is the minority carrier diffusion length without particles irradiation.
(2)
(3)
Corresponding Author: M.A. Ould El Moujtaba, Faculté des Sciences et Technologies, Université Cheikh AntaDiop de Dakar
BP 5005, Dakar-Fann, Senegal
5068

Res. J. Appl. Sci. Eng. Technol., 4(23): 5068-5073, 2012
0.0130
0.0125
0.0120
0.0115
0.0110
0.0105
0.1
19.9 15 10 5
Fig. 1: Silicon solar cell
1.00
1.0
10 100
0.99
0.98
0.97

(MeV)
100 60 20 0.1
1 10
-3 
10
-3
Depth in case x (cm)

10
-3
Fig. 2: Relative excess carriers density versus depth in the base for various irradiation energy; Kl: 15 cm
2
/s; Sf: 4.10
3 cm/s; Sb: 10
3 cm/s; n: 1
Equation (1) is solved with the boundary conditions at the emitter-base junction and at the back surface of the cell (Sissoko et al ., 1996; Diallo et al ., 2008):
C
At the junction (x = 0):
D

 
 x x

0

Sf
 
(4)
C
At the back surface (x = H):
D

 
 x
 
Sb
   
(5)
Sf and Sb are respectively the junction and back surface recombination velocities.
Relative excess minority carrier’s density: The relative excess minority carriers density is defined to be the ratio between the minority carrier density and the maximum of the same excess minority carriers density for a given irradiation energy. We present in the Fig. 2 the relative excess minority carriers density versus depth in base for various irradiation energies.
This Fig. 2 shows that the excess carrier density first increase with the depth in the base until the maximum
5069
Fig. 3: Photocurrent density versus particles energy for various types of particle. n: 1 sun; Sf: 10
3 cm/s; Sb: 3.10
3 cm/s situated at a certain depth in the base; above this depth, the excess carrier density decrease. Since the cell is front illuminated, this behavior could be explained by the shape of the generation rate for this front illumination given that the maximum is near the front side. For increasing irradiation energy, the maximum is left shifted leading to a space charge region reduction. There is a reduction of carrier flow through the junction with increasing irradiation energy for the same operating point.
Let us express now the photocurrent density that can be extracted from the cell.
Photocurrent density: The excess minority carrier’s photocurrent density is given by:
Jph
 qD
 
 x x

0
(6) q is the elementary charge.
A plot of the photocurrent density versus particles energy is presented on Fig. 3 for various types of particle.
The photocurrent density is not very dependent on irradiation energy for lower irradiation energy; but for increasing irradiation energy, photocurrent begun decreasing.
As it can be seen on the Fig. 3, this decreasing is more marked for increasing damage coefficient Kl.
It seems that the important parameter here is the irradiation energy given that significant decrease cannot be observed since irradiation energy is below a certain threshold.
Open circuit voltage: The photo voltage across the junction is expressed by mean of Boltzmann’s relation; we have:
Vph

Vt
 ln



Nb
    n i
2

1



(7)

Res. J. Appl. Sci. Eng. Technol., 4(23): 5068-5073, 2012
0.624
0.622
0.620
0.618
0.616
0.1
1.0
19.9 15 10 5
10 100
17.0
16.5
16.0
19.9 15 10 5
15.5
15.0
100
3 4
Back surface recombination velocity Sb (cm/s)
1 10
5
Fig. 4: Photovoltage versus particle energy for various types of particle. n: 1 sun; Sb: 3.10
3 cm/s
0.834
0.833
0.832
2
K1 (cm /s)
5
10
15
19.9
0.831
0.830
0
4 
10
4 
10
4 
10
4
Back surface recombination velocity Sb
(cm/s)

10
4
Fig. 5: Fill factor versus back surface recombination velocity for various types of particle. n: 1 sun;
M
: 100 MeV
Vt is the thermal voltage, n i the intrinsic carrier density at thermal equilibrium and Nb the base doping density.
For very low Sf, there is no significant carrier crossing the junction; it is the open circuit condition. The open circuit voltage can be obtained by:
Sf
 o
Vph

Vph oc
(8)
The open circuit voltage versus particle energy is plotted on Fig. 4 for various types of particle.
The open circuit voltage decrease with increasing particle energy; this decrease depend on the type of particle given that the damage coefficient varies with the type of particle and the fluence of the radiation beam.
As for the photocurrent, the decrease of the open circuit photo voltage is more marked for important irradiation energy.
Fill factor and conversion efficiency: The fill factor and conversion efficiency are two important parameters of the solar cell. The fill factor indicates the quality of the pn junction while the conversion efficiency indicates the performance of the whole cell.
The expression for the fill factor is given by: recombination velocity for various types of particle. n:
1 sun;
M
: 100 MeV
FF

P max
(9)
P max is the maximum power, Vco the open circuit voltage and Jsc the short circuit current.
For the conversion efficiency, we have:
 
P
P reference
(10)
P reference
is the illumination power corresponding to one sun for AM1.5.
We plotted on Fig. 5 the fill factor versus irradiation energy for various damage coefficients.
We denote the fill factor decrease with the back surface recombination velocity and this decrease is more marked for increasing damage coefficient as for the open circuit voltage.
When back surface recombination increase, the losses at the back surface increase too so that the quality of the cell decrease. But this decrease is also related to the type of particles through the damage coefficient.
We plot now on Fig. 6 the conversion efficiency versus irradiation energy for various damage coefficients.
The conversion efficiency decreases with the back surface recombination velocity; when the damage coefficient increases, the conversion efficiency decreases also.
The conversion efficiency also decreases with the irradiation energy but this decrease is less than the observed decrease with the damage coefficient.
Shunt and series resistances: We want to study now the shunt and series resistances (Barro et al ., 2008; Mbodji et al ., 2012) of the solar cell; for deriving the expression of these parameters, let us show in the two following Fig.
7a, b the behavior of the cell in two particular situations based on the illuminated I-V curve: first near short circuit and second near the open circuit.
5070

Res. J. Appl. Sci. Eng. Technol., 4(23): 5068-5073, 2012
(a)
(a)
(b)
Fig. 7: (a) Illuminated I-V curve and, (b) corresponding equivalent electrical circuit near short circuit
Figure 7a presents the illuminated I-V curve of the solar cell, we can see that near short circuit (High Sf values) the solar cell behavior like a real current generator; it can then be represented as an ideal current generator Jcc shunted by a parasitic resistance Rsh as shown in Fig. 7b. Based on Fig. 7a, b, one can write that:
Vph ( Sf ) = Rsh .[ Jcc Jph ( Sf )] (11)
We then deduce an expression of the shunt resistance as:
Rsh

Vph
Jsc

Jph
(12)
This expression is valid only for high Sf values. Let us now take a look at the following Fig. 8a, b:
We consider here the open circuit region (low Sf values) of the illuminated I-V curve of the solar cell
(Fig. 8a); the solar cell behavior now as a real voltage generator so that it can be represented by an ideal voltage generator with a parasitic Resistance in series (Rs) as shown on Fig. 8b. Based on Fig. 8a, b, we can write that:
V
Rs
= Voc Vph ( Sf ) (13)
(b)
Fig. 8: (a) Illuminated I-V curve and, (b) corresponding equivalent electrical circuit near open circuit
This lead to the following expression of the series resistance:
Rs

Jph
(14)
Based on these two expressions given by Eq. (12) and
(14), we present the variation the parasitic resistances Rsh and Rs versus particle energy for various back surface recombination velocities respectively on Fig. 9 and 10.
The dependence of the shunt resistance on the irradiation energy is not perceptible for lower particle energy; for increasing particle energy we see that the shunt resistance decrease, especially for very high back surface recombination velocities.
An increase of the recombination at the back side leads to a decrease of the shunt resistance so that leakage current will increase also. That is, solar performance will decrease.
This Fig. 10 shows that an increase of the particle energy leads to an increase of the series resistance especially for high irradiation energy; the series resistance also increases with increasing back surface recombination velocities recombination. That is, solar performance will also decrease with both particle irradiation and back surface recombination velocity.
5071

Res. J. Appl. Sci. Eng. Technol., 4(23): 5068-5073, 2012
1.4 10
3
1.3 10
3
1.2 10
3
1.1 10
3
1.0 10
3
900
0.1
sb
3
10 cm/s
4
10 cm/s
5
10 cm/s
6
10 cm/s
1.0
10 100
Fig. 9: Shunt resistance versus particle energy for various back surface recombination velocities. Sf : 10 5 cm.s; Kl: 5 cm
2
.s
0.87
0.86
0.85
0.84
0.83
0.82
0.1
1.0
sb
10 cm/s
10 cm/s
10 cm/s
3
10 cm/s
10 100
Fig. 10: Series resistance versus particle energy for various back surface recombination velocities. Sf: 10 cm.s; Kl:
5 cm
2
.s
Diffusion capacitance: The diffusion capacitance of the solar cell is considered to be the capacitance resulting of a charge variation through diffusion process in the solar cell (Hu, 2010; Colinge and Colinge, 2002; Böer, 2010;
Mbodji et al ., 2010; Mbodji et al ., 2010; Mbodji et al .,
2011). This capacitance can be written as:
C

 dQ dV
(15)
Replacing the total charge Q by its expression, Eq. (15) becomes:
C

  d
  x

0
 dV
(16)
To facilitate calculations, let us rewrite Eq. (16) as following:
C

  d


 x dSf

0


1 dV
 dSf
(17)
5072

10
-3

10
-4

10
-4

10
-4
-4

(Mev)
0.1
20
60
100
0
1.0
10 100 1 10
3
Junction recombination velocity
Sf (cm/s)
1 10
4 5 a) Sb: 10 3 cm/s; Kl: 15 cm 2 /s

10
-4

10
-4

10
-4

10
-4
-4
Sb
4
10 cm /s
0
1.0
10 100 1 10
3
Junction recombination velocity
Sf (cm/s)
1 10
4 b) Kl: 15 cm 2/s;
M
: 60 MeV
5
Fig. 11: Diffusion capacitance versus junction recombination velocity
Based on the photo voltage expression we can definitely write the diffusion capacitance as:
C

  q ni
2

Vt
Nb  q


Vt
(18)
The diffusion capacitance is then composed of two terms; the first term is the intrinsic capacitance and the second depend on the operating point.
Let us now plot the diffusion capacitance versus junction recombination velocity for various particle energies (Fig. 11a) and various back surface recombination velocities (Fig. 11b)
It can be seen that the diffusion capacitance decrease with the junction recombination velocity; near open circuit (low junction recombination velocities) the whole part of excess minority carrier stored in the cell leading to a higher capacitance. When Sf increases, carriers flow through junction increase also and the charge stored in the cell decrease so that the associated capacitance decrease too.

Res. J. Appl. Sci. Eng. Technol., 4(23): 5068-5073, 2012
The diffusion capacitance decreases with increasing particle energy (or back surface recombination velocity) with a decrease more marked for low junction recombination velocity.
CONCLUSION
The simulation of a silicon solar cell under particleir radiation shows that electrical parameters of the cell present dependence on the irradiation energy and also on the type of irradiation particles.
The dependence on the particle type is more marked given that the damage type that means the type of defect caused by irradiation is not the same; the damage caused by the particle is also more marked for higher energy.
Beam fluence is supposed to be constant contrary to
(Kraner, 1983; Hu, 2010); they show that for a given energy, when increasing the fluence, the degradation factor increase so that the performance of the cell decreases. It is clear that even for lower energy, for an extended exposure to irradiation, the effect will become more and more marked.
REFERENCES
Barro, F.I., S. Gueye, M. Deme, H.L. Diallo, M.L. Samb,
A.M. Samoura, S. Mbodji and G. Sissoko, 2008.
Influence of grain size and grain boundary recombination velocity on the series and shunt resistances of a polycrystalline silicon solar cell.
Proceedings of the 23rd European Photovoltaic Solar
Energy Conference, pp: 612-615.
Böer, K.W., 2010. Introduction to Space Charge Effects in Semiconductors. Springer-Verlag, New York.
Colinge, J.P. and C.A. Colinge, 2002. Physics of
Semiconductor Devices. Kluwer Academic
Publishers, New York.
Diallo, H.L., A. SeïdouMaiga, A. Wereme and G.Sissoko,
2008. New approach of both junction and back surface recombination velocities in a 3D modelling study of a polycrystalline silicon solar cell. Eur.
Phys. J. Appl. Phys., 42: 203-211.
Fatemi, N.S., P.R. Sharps, M.A. Stan, D.J. Aiken, B.
Clevenger and H.Q. Hou, 2001. Radiation-hard highefficiency multi-junction solar cells for commercial space applications. Proceedings of the 17th
European Photovoltaic Solar Energy Conference, pp: 2155-2158.
Furlan, J. and S. Amon, 1985. Approximation of the carrier generation rate in illuminated silicon. Solid
State Electr., 28(12): 1241-1243.
Hu, C.C., 2010. Modern Semiconductor Devices for
Integrated Circuits. Pearson/Prentice Hall, New
Jersey.
Kraner, H.W., 1983. Radiation damage in silicon detectors. 2nd Pisa Meeting on Advanced Detectors,
Grosetto, Italy, June 3-7.
Kreinin, L., N. Bordin and N. Eisenberg, 2007. Spectral response of light biased Si solar cells at open circuit voltage. Proceedings of the 14th SedeBoqer
Symposium on Solar Electricity Production, pp:
71-76.
Martin, J.E., 2006. Physics for Radiation Protection: A
Handbook. 2nd Edn., Wiley-VCH, Weinheim.
Mbodji, S., B. Mbow, F.I. Barroand and G. Sissoko,
2010a. A 3D model for thickness anddiffusion capacitance of emitter-base junction in a bifacial polycrystalline solar cell. Global J. Pure Appl. Sci.,
16(4): 469-477.
Mbodji, S., M. Dieng, B. Mbow, F.I. Barroand and G.
Sissoko, 2010b. Three dimensional simulated modelling of diffusion capacitance of polycrystalline bifacial silicon solar cell. J. Appl. Sci. Tech., (JAST),
15(1-2): 109-114.
Mbodji, S., B. Mbow, F.I. Barro and G. Sissoko, 2011. A
3D model for thickness anddiffusion capacitance ofemitter-base junctiondetermination in a bifacialpolycrystalline solar cell underreal operating condition. Turkish J. Phys., 35(3): 281-291.
Mbodji, S., I. Ly, H.L. Diallo, M.M. Dione, O. Diasse and G. Sissoko, 2012. Modeling study of n+/p solar cell resistances from single I-V characteristic curve considering the junction recombination velocity (Sf).
Res. J. Appl. Sci. Eng. Techn., 4(1): 1-7.
Mohammad, S.N., 1987. An alternative method for the performance analysis of silicon solar cells. J. Appl.
Phys., 61(2): 767-772.
Ohshima, T., T. Sumita, M. Imaizumi, S. Kawakita, K.
Shimazaki, S. Kuwajima, A. Ohi and H. Itoh, 2005.
Evaluation of the electrical characteristics of III-V compounds solar cells irradiated with protons at low temperatures. Proceedings of the 31st IEEE
Photovoltaic Specialists Conference, pp: 806.
Sissoko, G., C. Museruka, A. Corréa, I. Gaye and A.L.
Ndiaye, 1996. Light spectral effect on recombination parameters of silicon solar cell. Proc. World Renew.
Energ. Cong., 3: 1487-1490.
5073