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The efficiency of a silicon solar cell is directly linked to the quantity of carrier photogenerated in its base. It increases with the increase of the quantity of carrier in the base of the solar cell. The carrier density in the base of the solar cell increases with the increase of the flux of photons that crosses the solar cell. One of the methods used to increase the flux of photon on the illuminated side of the solar cell is the intensification of the illumination light. However, the intensification of the light come with the increase of the energy released by thermalization, the collision between carriers, their braking due to the carriers concentration gradient electric field which lead to increase the temperature in the base of the solar cell. This work presents a 3-D study, of the effect of the temperature on the electronic parameters of a polycrystalline silicon solar under intense light illumination. The electronic parameters on which we analyze the temperature effect are:
the mobility of solar cell carriers
(
electrons and holes
),
their diffusion coefficient, their diffusion length and their distribution in the bulk of the base
. To study the effect of the temperature on electronic parameters, we take into account, the dependence of carriers (
electrons and holes
) mobility with the temperature (
μ_{n,}
(T)
_{ }μ_{p}
(T)). Then, the resolution of the continuity equation
,
which is a function of the carriers gradient electric field and the carriers mobility
,
leads to the expressions of the diffusion coefficient, the diffusion length, and the density of carriers which are function of the temperature. Then, we studied the effects of the temperature on the diffusion parameters in order to explain their effect on the behavior the carriers distribution in intermediate, short circuit and open circuit operating modes at several positions in the base depth. It appears through this study that the diffusion coefficient and the diffusion length decrease with the increase of the temperature. We observe also that with the increase of the temperature, the density of carriers in the base of the solar cell in short circuit and open voltage operating modes increases. In intermediate operating mode, the density of carriers increases also with the temperature but it is function of the base depth.

The efficiency of a solar cell is directly linked to the density of carriers in the base of the solar cell which is a function of the support material band gap of this solar cell, the illumination mode, the carriers diffusion parameters and recombination parameters. Several analytical and experimental studies have been done in monochromatic [

Even though the increase of the intensity of the light illumination leads to an increase of the carrier photogenaration and then to an increase of the density of carriers in the base [

In previous works [

In this work, we propose a three-dimensional (3D) study of a polycrystalline silicon solar cell (n-p-p^{+}) operating under an intense multispectral light. The polycrystalline silicon solar cell is made up of several grains with different sizes and forms separated by grain boundaries [_{x} = g_{y}) and a thickness H as shown in

The recombination planes are assumed to be thin surfaces between two adja-

cent grains and are located at

cular to the x and y axis of cartesian coordinates (O, x, y, z) [_{gb} is constant.

The polycrystalline silicon solar cell is illuminated by an intense light concentration (C > 50 suns), and then due to the intense photogeneration in the base of

the solar cell for this kind of illumination, we take into account the electric field due to the carriers concentration gradient in the base [

In this expressions: D_{n} and D_{p} are respectively electrons and holes diffusion coefficients, μ_{n}(T) and μ_{p}(T) are electrons and holes mobility depending on the temperature and δ(x) is the density of excess minority carrier in the base of the illuminated solar cell.

The contribution of the emitter is not taken into account and we work in the theory of the quasi-neutral base (QNB) [

Under the intense light illumination, the total current

- the diffusion current

- the conduction current

In Equation (2) the expression of the electric field given by Equation (1) is function of the electrons and holes mobility. The expressions of these mobilities are in turn functions of the temperature of the solar cell and they are expressed by Equation (3):

with μ_{0n} = 1500 cm^{2}∙V^{−1}∙s^{−1}, μ_{0p} = 475 cm^{2}∙V^{−1}∙s^{−1} and T_{0} = 300 K.

Taking into account the carriers photogeneration, their diffusion and recombination in the base of the solar cell, the expression, in steady state, of the carriers distribution in the base (p) of the solar cell is given by Equation (4) [

generation rate and their recombination rate at a position z.

Introducing the expressions of the total current

with:

The general shape of the solution of the partial derivative differential Equation (5) is given by Equation (8) [

with

In Equation (8), the expression of Z_{jk}(z) can be found using the orthogonality conditions of the functions

The expression of Z_{jk}(z) in these conditions is:

with:

The coefficients A_{jk} and B_{jk} are determined trough the boundary conditions at the junction (z = 0) and at the rear side at the position (z = H) given by Equation (15):

The expressions of the coefficients A_{jk} et B_{jk} are:

with

The expressions of the coefficient A_{jk} and B_{jk} lead to the solution of Equation (1) and the introduction of Equation (11) in Equation (8) leads to the solution of the continuity equation.

In this work, we study the temperature effect on a silicon solar under intense light illumination. For a multispectral light illumination, an intensification of the illuminated light means an increase of the quantity of photons which crosses the illuminated side of the solar cell. The consequence of this situation will be an increase of the carriers photogeneration in the base and then an increase of the density of carriers. The increase of the density of carriers in the base of the solar cell leads none the less to an increase of the collision between excess minority carriers but also to an increase of the quantity of the energy released by thermalization [

With the increase of the photogeneration due to the intensification of the illuminated light, another phenomenon which appears is the carriers concentration gradient electric field. His orientation is illustrated in

The expressions of carriers (electron and hole) mobility in function of the temperature are given in Equations (3) above. We present on the curves of

It appears trough these curves that the carriers mobility decrease when the temperature in the base of solar cell increase. The decrease of carriers mobility is the consequence of two phenomena:

- the increase of carriers density with the increase of light intensity, which comes

with an intensification of carriers collision in the base and then carriers slowing down.

- the increase of carriers density leads also to an increase of the carriers concentration gradient electric field which is opposed to the carriers movement toward the junction and then brake them.

The carriers slowing down due to their collision and braking lead to the decrease of the carriers mobilities. But, since carriers collision and braking come with the increase of the temperature in the base of the solar cell (energy released by collision and braking) we have the impression that it is the increase of the temperature which is responsible of the carriers mobility decrease.

The expressions of the diffusions coefficient of the silicon solar cell under an intense light illumination are given by Equation (7) and these expressions are functions of the electrons and holes mobility which are functions of the temperature. These coefficients are then functions of the temperature. We present on the curves of

We observe on the curves of

the increase of the carriers collision and braking, the decrease of the diffusion coefficients with the increase of the temperature mean also that the diffusion coefficients decreases when the carriers collision and braking increases. Indeed, the diffusion coefficient and the diffusion length are sensitive to any obstacle to the carrier movement in the base of solar cell. Then, the increase of collisions between carriers due to the increase of carriers density in the base and their slowing down due to the increase of carrier concentration gradient electric field lead to the decrease of the diffusion parameters.

We observe on

mode. The increase of carriers density in the region near the junction means an increase of the quantity of carriers present in this region. The increase of the density of the carriers comes with the increase of collisions between carriers and the increase of the quantity of energy releases by thermalization in this region. The increase of carrier density leads also to increase of the carriers concentration gradient electric field and then the increase of the energy released by braking. The increase of the temperature in the base of the solar cell is then the consequence of the energy which have been released by collisions, thermalization and braking with the increase of carriers density. It appears also on these curves that for the same base heating temperature, the density of carriers which contribute in open circuit operating mode is higher than ones of short circuit operating mode. This observation is the consequence of the operating mode. In short circuit and open voltage operating modes, the energy release by collisions, thermalization and braking exist. But contrarily to the open circuit operating mode where the carriers are blocked, in short circuit operating mode, the maximum of carriers crosses the junction and then that reduces the presence of carriers near the junction.

The curves of

state (junction recombination velocity S_{f} = 10^{4} cm/s). On the curves of

It appears on the curves of

In this work, we proposed a 3-D modeling study of the effects of the physical phenomena which contribute to heat the base of a solar cell and the effect of the temperature on the electronic parameters of a polycrystalline silicon solar cell under an intense light illumination. The resolution of the continuity equation leads to news expressions of carriers density, diffusion coefficient and diffusion length. It was proved through this study that, if the temperature in the base of the solar increases, the mobility of electrons and holes, the diffusion coefficient and the diffusion length decrease. The increase of the temperature is the consequence of

the energy releases by thermalization in the base of the solar cell, the collision between carriers due to the high photogeneration and the carriers braking due to the carriers concentration gradient electric field. The study of the temperature effect on the electronic parameters of the solar cell, put in evidence that, with the intensification of the illumination, it is the collisions between carriers and their braking that are responsible of carriers mobility and diffusion parameters decrease. It appears also through this study that the temperature in the base of the solar cell increases with the increase of carriers concentration at short circuit, open circuit and intermediate operating points. This situation is also the consequence of electrons collision and carriers concentration gradient electric field increase with the increase of carriers density.

All these results characterize the fact that the effect of temperature on the electronic parameters of a solar cell is in reality the effect of carriers thermalization, the collision between carriers due to the high photogeneration and the carriers braking due to the carriers concentration gradient electric field.

The authors wish to thank International Science Program (ISP) for funding our research group and allowing to conduct these works.

Soro, B., Zoungrana, M., Zerbo, I., Savadogo, M. and Bathiebo, D.J. (2017) 3-D Modeling of Temperature Effect on a Polycrystalline Silicon Solar Cell under Intense Light Illumination. Smart Grid and Renewable Energy, 8, 291-304. https://doi.org/10.4236/sgre.2017.89019