Influence of Temperature and Frequency on Minority Carrier Diffusion Coefficient in a Silicon Solar Cell under Magnetic Field

In this study, the effects of temperature and frequency on minority carrier diffusion coefficient in silicon solar cell under a magnetic field are presented. Using two methods (analytic and graphical), the optimum temperature corresponding to maximum diffusion coefficient is determined versus cyclotronic frequency and magnetic field.


Introduction
Minority carrier diffusion coefficient is a recombination parameter which has a big impact on photovoltaic conversion efficiency. His determination is fundamental for different techniques characterization of solar cells. Many studies have been conducted on the minority carrier diffusion coefficient under the influence of temperature, damage coefficient, irradiation flux and magnetic field in static regime [1] [2] [3] or dynamic frequency regime [4] [5] [6] [7].
In this work, the maximum diffusion coefficient in silicon solar cell is determined according to the optimum temperature for different frequency and magnetic field values.

Study of the Diffusion Coefficient
The expression of minority carrier diffusion coefficient in solar cell under dynamic frequency regime versus the magnetic field and the temperature is given 2  2  2  2  2   2  2  2  2  2 2   1  1  , ,  ,  1 , D B T is the minority carrier diffusion coefficient under influence temperature T and applied magnetic field B [2].  For the rest of the work, Table 1 will allow us to set the value magnetic field for each cyclotronic frequency. Figure 2 represents the minority carrier diffusion coefficient according to temperature for different pairs' values cyclotronic frequency and the magnetic field.

Determination of the Optimal Temperature by Graphic Method
The minority carrier diffusion coefficient increases with temperature up to a maximum value Dn max (ω, B) corresponding to temperature called optimum temperature T opt (ω, B) for a given cyclotronic frequency and magnetic field. Indeed, when the temperature is lower than the optimal temperature T opt (ω, B). Indeed, when the temperature is lower than the optimal temperature T opt (ω, B), From the curves in Figure 3, the values of optimum temperature and maximum diffusion coefficient for each pair cyclotronic frequency and magnetic field are determined and presented in the following Table 2. Table 3 allowed to represent the following figures.
The curve obtained can be assimilated to an affine function of equation: The constants a and b are determined from the curve, the following equations is obtained: These results obtained by the graphical method can be verified by an analytical method.

Determination of Optimal Temperature by Analytical Method
The minority carrier diffusion coefficient curve versus temperature admits a The relation allows deducing the values of optimum temperature T opt (ω, B) for different values cyclotronic frequency and magnetic field.
Log-log maximum diffusion coefficient versus optimum temperature is presented by Figure 4.
For a comparative study of two methods, we represent in Figure 5, on log-log scale, profiles of amplitude diffusion coefficient versus optimum temperature.
Note that two curves are almost confused. Thus, the relation obtained will make it possible to justify the choice the values temperature, magnetic field and   frequency in the study of different parameters a silicon solar cell.

Conclusion
The study of minority carrier diffusion coefficient in silicon solar cell has shown that the choice of parameter values such as temperature, magnetic field and frequency must obey certain conditions for a good performance of solar cells. Thus, the optimum temperature T opt (ω, B) for a maximum minority carrier diffusion coefficient is obtained using the pairs of cyclotronic frequency and magnetic field values presented in Table 2 and Table 3.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.