LAMELLA SILICON OPTIMUM WIDTH DETERMINATION UNDER TEMPERATURE

Geometric parameters are an important data for the choice of solar cell architecture, for better conversion performance. As poor opto-electronic material is used, i.e. short minority carrier’s diffusion length and under concentrated light which increases the temperature, it is then important to optimize the width of the lamella in order to have better photogenerated charge collection. Thus the intent of this work is the determination of the width of the lamella structure, presented through phenomelogical parametersmodeling study. These are the diffusion length and coefficient, as well as the surfacerecombination velocity of the photogenerated carriers in the base of the lamella silicon. The result gives a mathematical relationship between the optimum width and the operating temperature of the lamella solar cell, allowing to influence the industrial manufacturing process for the material economy.


ISSN: 2320-5407
Int. J. Adv. Res. 8(06), 1409-1419 1410 The operatingshort-circuit situation of thesolar cellcorresponds to the high values of the carriers'recombination velocity (Sf) at the junction, and therefore gives the density of short-circuit current, which is constant for a given temperature. Expressions of back surface recombinationvelocity (Sb) are deduced [16,32,33].
Thus the analysis of the expressions of this recombination velocity (Sb), through its representation as function of the width of the lamella leads to the extraction of the optimum width (Hopt), which is modeled according to both the temperature and the effective diffusion coeffient.

Theory:
The vertical multi-junction(VMJ) solar cells are successionof series-connected (n+-p-p+) lamella [10,11]. The structure of the seriesvertical multi-junction solar cells is represented by figure .1.They are illuminated by a polychromatic light and subject to temperature variation.   The illumination arrives parallel to the junction of the lamella under the influence of temperature. There is absorption of photons, generation of electron-hole pairs, which can diffuse or recombine in the bulk and on surfaces (front and rear). These physical mechanisms are governed by the following continuity equation [5,11]: Coefficients A and B are determined from the following boundary conditions as: i) At the junction(n + /p): S f is the minority carrier recombination velocity at the junction, imposed by the external load. It also characterizes the solar cell operating point, varying from the open circuit to the short circuit [16,32,35,44] ii) At the back surface(p/p + ): S b is theexcess minority carrier's recombination velocity at the back surface. It is the result of the electric field produced by the p/p + junction and characterizes the behaviour of the density of the charge carriers at the(p/p + )junction [16,30,31]. Photocurrent density is defined by the following relationship: For high values of excess minority carrier's recombination velocity at the junction (S f ≥ 10 4 cm. s −1 ), the photocurrent density is constant, and corresponds to the short-circuit density current (J SC ). In this solar cell operating condition, the derivative of Jph (Sf, z,T) with respect to Sf, vanishes, and allows to establish the following equation: The resolution of this equation, gives two solutions Sb1 (H, T) and Sb2 (H, T) which are expressions of the excess minority carrier's recombination velocity at the back surface. They are dependent on the geometric parameter (H) 1412 (which is the width of the lamella), the parameters of diffusion and recombination in the bulk, as well as the temperature (T). They are given by [19,20,45]: (12) Results and Discussions:-Density of excess minority carriers in thelamella: Figure (3) produces the profile of the carriers'densitywith the width of the lamella under short circuit. The minority carriers'maximum density increases under thermal agitation, in accordance with the Umklapp process [20,25,26,46,47].    The optimum thickness values are extracted from Figure 6 and are shown in Table 1 below. They are represented, for each temperature, by the abscess of the intersection of the two curves representing the recombination velocity expressions [19,20,27,45,49,50,51,52], one of which also represents the intrinsic velocity at the junction [11], allowing to obtain the maximum of extracted photocurrent density The results of Table 1

1416
On the other hand, Figure 8 gives the optimum width (Hopt) of the lamella as an increasing function of the effective diffusion coefficient (D) of excess minority carriers, through the following modeling relationship: With: applied magnetic field [19,20] doping rate [49] magnetic field and temperature [50,51] flow and intensity of irradiation by charged particles [27,45] the excess minority carrier's recombination velocity at the backunder the action of: the variation in the monochromatic absorption coefficient [52].

Conclusion:-
The results of this work are an important contribution to optimize the performance of the lamella solar cells, under the conditions of temperature variation. The width of the lamella depending on the temperature, will lead to the determination of the electrical parameters of the solar cells. Thus the application of these results, combined with the previous ones constitute references in the choice of the width of the base of the lamella in the process of its industrial manufacture.
Further work will be carried out by combining the different experimental conditions of the study of the solar cells, including the use of monochromatic incident light in frequency modulation.