STUDY OF THE CAPACITY OF A MANOFACIAL SOLAR CELL BASED ON CIGS UNDER HORIZONTAL MONOCHROMATIC ILLUMINATION IN FREQUENCY DYNAMIC MODE: THE EFFECT OF THE WAVELENGTH

Jean Jude Domingo, Alain Kassine Ehemba, Demba Diallo, Ibrahima Wade and Moustapha Dieng. Laboratory of semiconductors and solar energy, physics department, faculty of science and technology, university cheikh anta diop – Dakar. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

In the present work, we make a theoretical study of the wavelength effect on the capacity of a solar cell based on CIGS subjected to horizontal monochromatic light in frequency modulation. Based on the expression of the density of minority charge carriers, we study the photovoltage and capacity. A gap of 1.34eV corresponding to gallium ratio of 0.28 is selected. We find that efficiency is reduced by the increase in wavelength. Thus diffusing capacity results from the variation of the minority charge carriers in the base of the solar cell. The results show that the effectiveness of capacity decreases when the wavelength increases.
The electrical properties are based generally on the determination of the photocurrent, the photo voltage, series and shunt resistors and the capacity of the solar cell [3]. The parameters usually employed are: the diffusion length (L), the diffusion coefficient (D), the recombination rates at the front side (Sf) and the rear side (Sb), the reflection coefficient (R) and the absorption coefficient (α) [4]. In this present article, the ability of a CIGS solar cell and effectiveness will be determined from the density of minority charge carriers. The influence of the wavelength is highlighted.

Theoretical study:-
In our study, we consider a solar cell presented by the figure 1. The contribution of the transmitter is ignored and we consider the quasi-neutral basis (QNB). When the solar cell is illuminated, there is creation of electron-hole pairs in the active database. The density of generated minority charge carriers follows the next continuity equation [4]: Corresponding Author:-Alain Kassine Ehemba. Address:-Laboratory of semiconductors and solar energy, physics department, faculty of science and technology, university cheikh anta diop -Dakar. 712 δ (x, t) and G (x, t) are respectively, the density and the generation rate of minority charge carriers in function of the thickness x and the time factor t. Their expressions are [4]: are the respective spatial components of the density and the generation rate. The generation rate of electron-hole pairs per the wavelength is equal to the photons rate of disappearance of the material [5]: L 0 and D 0 represent the intrinsic diffusion length and the intrinsic diffusion coefficient. The term D 0 is given by the Einstein formula [7]: with  which represents the mobility of the material, The coefficients A and B are obtained from the following boundary conditions: [4] -At the junction at x = 0 -At the rear side of the cell: S respectively represent the recombination speeds at the front side and the rear side of the absorber.

Absorption coefficient:-
CIGS is used in photovoltaic devices due to its direct gap [8]. Thus, we represent the CIGS absorption coefficient as a function of the wavelength of the incident photons in Figure 2 This figure shows that the absorption coefficient decreases with increasing wavelength. Consequently the generation of electron-hole pairs increases with the increasing of the wavelength. The magnitude of the CIGS absorption coefficient is of 104cm -1 , which explains its use in thin layer. Therefore, it takes some micrometer CIGS to absorb the entire incident light [9].

Study of the density of minority charge carriers:-
We present in the following four figures the density of minority carriers according to the base thickness x with different wavelengths of visible range and infrared range respectively open circuit and short circuit.

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To Figures 3 and 4, all the curves start with a maximum and then decrease gradually. The maximum density corresponds to a gradient of carries equal to zero. Then this density decreases with the depth x in the database of the base. Therefore, carriess can not cross the junction to generate a photocurrent. They will recombine. This decrease or the negative gradient corresponds to the recombination of minority carriers in the basis. [11] To Figures 5 and 6, for a given wavelength, we find two levels: At the first level, the density of minority carriers increases with the thickness in the basis to a maximum; this corresponds to the crossing of minority carriers at the junction to participate in the generation of photocurrent. [12] At the second level, the density of minority carriers decreases with the basis thickness; this corresponds to the recombination surface and volume of carriers that do not cross the junction. [12] The modulus of the density of minority carriers at short-circuit as open-circuit increases with the wavelength. The increase in the module of the density with wavelength corresponds to an increase of the carriers generated in the basis since the absorption decreases with the increasing wavelength. It is also seen that for low values of the wavelength (λ), the absorption is near the junction while for large values of λ, the absorption moves in depth. The obtained profiles of the figures 3, 4, 5 and 6 are due to the fact that CIGS has a reduced thickness in the micrometer range. [4] To  The figures 7 and 8, the thickness of the cell where the modulus of the density of minority carriers is maximal corresponds to the extension of the space charge zone. It is noted that the thickness of the latter expands with increasing the recombination rate at the junction Sf. This is due to the fact that carriers are stored in open circuit in short circuit [5]. To a recombination velocity value Sf junction fixed in the vicinity of the short circuit (figure8) enlargement of the space charge zone is more important with large wavelength values. We can say that the short wavelengths provide a thickness of the space charge region reduced compared to longer wavelengths.

Photovoltage:-
The photovoltage is given by the following Boltzmann equation [4]: (11) b N and i n are respectively the doping density and the intrinsic density of minority charge carriers is given by the following relationship [6]: The photo voltage influences the diffusion capacity.

Diffusion capacity:-
When excess minority carriers diffuse into the base of a solar cell, they do not pass through all, the junction. Therefore they induce in the base equivalent capacity which is diffusing capacity whose expression is given as follows [5]: where: By Q substituting its value is obtained: From the expression of the photo voltage, we finally get the following equation:

Effectiveness of capacity:-
The area of collection of minority charge carriers corresponds to an extension of the space charge zone 0 X which depends on the rate of recombination at the junction. However, when the space charge region is considered a planar capacitor, we can write:  The Table 1 summarizes the values of the maximum density of the minority carriers, the thickness of the space charge zone and the capacity for different values of the wavelength. The capacity in open circuit as short-circuit decreases as the wavelength increases. This ability is very low short circuit. It is also noted that the thickness of the space charge zone in open circuit as short circuit increases as the wavelength increases. We also find that the performance of the capacity for long wavelengths is higher than for short wavelengths.

Conclusion:-
In this work, we presented a simulation study using the wavelength effect on the ability of a solar cell based on CIGS subjected to horizontal monochromatic light frequency modulation. The result obtained in this study is the reduction of the efficiency of cell capacity with the increase in wavelength. Thus diffusing capacity results from the variation of the minority charge carriers in the base of the solar cell. Usually the considered parameter in diffusion capacity studies is the characteristics of the junction. In the end we can say that the capacity, which is proportional to the density of minority charge carriers increases with the wavelength