Revue des Energies Renouvelables CER’07 Oujda (2007) 185 – 188
185
Influence of the base region drift field on the photovoltaic parameters of a polycrystalline silicon solar cell
A. Trabelsi *, A. Zouari et A. Ben Arab
Laboratoire de Physique Appliquée, Département de Physique, Faculté des Sciences de Sfax, Tunisie
Abstract - Polycrystalline silicon is a very promising material for the production of inexpensive and efficient solar cells for the terrestrial photovoltaic applications. In this paper, we use a three- dimensional model to study the performance of a polycrystalline silicon solar cell. The model takes into account the electric field due to non-uniform doping base region. The impurity profile is assumed to be exponential. For an elementary solar cell with constant dimensions and recombination velocity at the back contact, the results show an improvement of the solar cell parameters when we increase the electric field. On the other hand, for a constant electric field, the solar cell parameters are improved by an increase of the solar cell dimensions.
1. INTRODUCTION
Polycrystalline silicon is a very promising material for the production of inexpensive and efficient solar cells for the terrestrial photovoltaic applications [1]. However, the technological parameters and the conditions of elaboration of the material and of the cell, has an enormous influence on the photovoltaic parameters of the cell [2, 3].
In this work, we study the influence of the drift field obtained by a non-uniform doping base region on the variation of the solar cell parameters. We use a three-dimensional model for an elementary solar cell having a cubic geometry. The cell is under illumination or in obscurity.
2. THEORY
We considered a polycrystalline N+/P elementary solar cell formed by a cubic grain. The base doping profile takes an exponential form given a constant drift field in this region [4]. But the emitter doping is considered to be uniform.
Under these assumptions, the continuity equation for minority carrier generated by a monochromatic light is given as follows [5]:
( ) ( ) ( ) ( ) ( ) ( )
2 n T n
2 2 2 2
2 2 2
2 2
D z g L
z , y , x n z
z , y , x n U
E z
z , y , x n y
z , y , x n x
z , y , x
n −∆ = −
∂
∆ + ∂
∂
∆ +∂
∂
∆ +∂
∂
∆
∂ (1)
The term g
( )
z is the generation rate of minority carrier. In this study, we used the one presented by Mohammed Nour [6]:( ) ∑ ( )
=
α
−
= 4
1 i
i
iexp z
g z
g (2)
where αi and g values correspond to AM1 spectrum. The recombination velocity at the grain i boundaries is variable in function of the generation rate [7].
The boundary conditions in the base are:
(C1): At the junction edge side of the base region, the excess electron density is under the short-circuit condition [5]:
(
x,y,W W)
0n e+ =
∆ (3)
* abdessalem_trabelsi@yahoo.fr
A. Trabelsi et al.
186
(C2): At the back contact, the surface is characterized by a recombination velocity S , so the n excess electron density satisfies the following equation [5-8]:
H n z
n H T z
H z
D n n S
U E z
n
=
= =
∆
−
=
∆
∂ +
∆
∂ (4)
(C3): At the grain boundary, the excess minority carrier are governed by the grain boundary recombination velocity Vg,i [5]:
(
u xory)
D n 2 V u
n
n u d n i , g
2 u d
=
∆
±
∂ =
∆
∂
±
± =
=
(5)
The resolution of the continuity equation (Eq. (1)) allows to determine the photocurrent in the base region JBph. For the obscurity current in the base regionJ . We solve the same equation B0 (Eq. (1)) but without the generation term.
The photocurrent and the obscurity current in the emitter region JBph and J ; and in the B0 depletion region JRph and J are taken of references [9, 10]. R0
3. RESULTS
Figures 1.a) and 1.b) represent the effect of the drift field E on the variation of the photocurrent with respect to the grain thickness for two grain widths superior and inferior to the diffusion length respectively.
Fig. 1.a): Drift field effect on the photocourant variation with respect to the solar cell
thickness for d>Ln
Fig. 1.b): Drift field effect on the photocourant variation with respect to the solar cell
thickness for d<Ln
We notice that, for d>Ln (Fig 1.a) the photocurrent increases with the grain thickness until it becomes constant for all the values of the electric field E . The effect of the drift field is more important in the case of the thick grains. Also, we can note that the increase of the photocurrent with the electric field is not linear. In fact, the difference between the curves decreases when E increases.
CER’2007: Influence of the base region drift field on the photovoltaic parameters… 187 Figure 1.b shows a faster saturation when H increases for d<Ln. This is due to a small generation volume, so an important recombination at the grain boundaries. However, we notice that the difference between the curves becomes constant when E increases. So, in this case, the photocurrent increases by a linear form with the drift field.
Figure 2 represents the effect of the drift field E on the variation of the photocurrent with the grain width d . We notice that this variation presents a parabolic form for all the values of E . Also, the influence of the drift field is more important for the large grains.
Figures 3 and 4 give the variation of the open circuit voltage VOC and the solar cell efficiency η with respect to the grain width for different values of electric field. We notice a parabolic form for all the values of E . The effect of the drift field is, also, more remarkable for the large grains. In the other hand, the differences between the curves decrease when the electric field increases. So the variations of VOC and h with respect to E are not linear.
Fig. 2: Drift field effect on the photocurrent variation with respect to the grain width
Fig. 3: Drift field effect of the open voltage with respect to the grain width
Fig. 4: Drift field effect on the variation of the solar cell efficiency with respect to the grain width
4. CONCLUSION
In this work, we have showed that for an elementary solar cell with constant dimensions and recombination velocity at the back contact, the solar cell parameters are improved when we increase the electric field E .
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Also, for a constant electric field, the solar cell parameters are improved by an increase of the solar cell dimensions.
NOTATION L n Diffusion length of minority
carrier (electron) in the base region, cm
i ,
Vg Recombination velocity at the grain boundaries, cm.s-1 D n Diffusion constant of
minority carrier (electron) in the base region, cm2.s-1
S n Recombination velocity at the back contact, cm.s-1 H Total cell thickness, cm W b Thickness of the base
region, cm W e Thickness of the emitter
region, cm
d Grain width, cm W Width of the depletion
region, cm
REFERENCES
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[4] H. Samet et al., ‘Les Annales Maghrébines de l’Ingénieur’, Vol. 6, 1992.
[5] S. Elnahwhy et al., Solid State Electronics, Vol. 31, N°12, pp. 1703 – 1709, 1988.
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[9] S.M. Sze, Physics of Semiconductors Devices, Murray Hill New-Jersey, 1991.
[10] A. Ben Arab et al., Solar Cells, Vol. 29, pp. 49 – 62, 1990.
