OPTIMUM BASETHICKNESS DETERMINATION OF A BACKILLUMINATED SILICON SOLAR CELL: IRRADIATION EFFECT

Amadou Sarr Gning, Mamadou Lamine Ba, Mamour Amadou Ba, Gora Diop, Ibrahima Diatta, El Hadji Sow, Oulimata Mballo and Gregoire Sissoko Laboratory of Semiconductors and Solar Energy, Physics Department, Faculty of Science and Technology, University Cheikh Anta Diop, Dakar, Senegal. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History Received: 05 May 2020 Final Accepted: 10 June 2020 Published: July 2020

In this paper, we propose a method to determine the optimum thickness of a bifacial silicon solar cell back illuminated and under irradiation. The expressions of back surface recombination velocity of excess minority carrier depending on both irradiation energy (ϕp) and damage coefficient (kl) are established. From their plots, base optimum thickness is deduced, and its relationships with bothirradiation energy (ϕp) and damage coefficient (kl) are modeled.
Our study concerns the silicon solar cell (n + /p/p + ) previously subjected to various doses of radiation and illuminated by the back side with polychromatic light [2].
The density of the excess minority carrier is obtained by solving the diffusion equation in the base (p) of the solar cell, provided with the boundary conditions at the junction surface (p+/p) and on the back surface (p+). These boundary conditions bring to the excess minority carriersrecombinationvelocity, respectively (Sf) at the junction and (Sb) on the rear [3] [4] [5] [6].
The photocurrent is calculated and obtained as a function of these recombination velocities (Sf, Sb) and the parameters (ϕp, kl) of the irradiation imposed on the solar cell of (H) thick base.
The study of the photocurrent as a function of the (Sf) recombination velocity at the junction, for each irradiation parameter yields to extract the expressions of the (Sb) recombination velocity on the rear face [7]. The analysis of these recombination velocityexpressions through their graphic representations as a function of the solar cell thickness (H) [8] yields to obtain the optimum thickness under each irradiation parameter and mathematically modeled.
The well-known Einstein's relation links the diffusion coefficient D(Kl, ϕp) [24] [25]to the lifetime (and the diffusion length(L), for given irradiation ϕp and intensity kl.
: represents the density of excess minority carrier in the base resulting from polychromatic illumination and under the influence of irradiation.

 
x G ar is therate of generation of excess minority carrier at depth x in the base under polychromatic illumination. Its expression is given by [26]: x : is the depth in the base of the solar cell.
is determined from the resolution of equation (1) and is given in the following form: The A ar and B ar coefficients are determined from the boundary conditions: At the junction (x=0) : Sf: is the excess minoritycarrier'srecombination velocity at the junction. It characterizes the operating point of the solar cell varying from short-circuit to open circuit [3] [4] [23].

Atthe rear face (x=H) :
Sb is the back surface recombination velocity of excess minority carrier [3], [25], [27], [28] resulting from the electric field created by the (p/p + ) high-lowjunction [11]. It characterizes the behavior of the excess minority carrierat the base back surface.

Influence of the irradiation on photocurrent density:
The photocurrent density is given by the following expression:    The resolution of this equation (10) thus gives respectively two expressions of the back surface recombination velocity as:    The decrease of (Hopt) optimum thickness of the base with irradiation energy is represented by a linear function. The obtained modelling relation is given as follow:     Optimum thickness (cm)

Damage coefficient (cm -2 /MeV)
The damages caused by the irradiation of a solar cell then lead to a reduction of the optimum thickness necessary for the production of an important photocurrent.
Knowing that the excess minority carrier recombination velocity depends on diffusion parameters (D, L) and optical parameters (monochromatic or polychromatic absorption coefficient of the material), results on the determination of optimum thickness were produced. These results take into account external factors that influence diffusion parameters (L, D).These include temperature [29], magnetic field [30], irradiation flow by charged particles [ 14], frequency of modulation [31] of optical or electrical signal, or combination of these factors [32], [33]. The conditions of manufacture of the semiconductor material through the doping rate also affect the diffusion coefficient [8].
The absorption coefficient (variable or constant) influences the recombination velocity in the rear face, also allows to produce results on the optimum thickness [34].
The different types of solar cells including the horizontal or vertical junction [35], [36] have been studied. Future investigations will take into account the 3D study model (grain boundary recombination velocity and grain size) and the combination of several external factors.

Conclusion:-
In this paper, we have proposed a method for determining the optimal thickness of the bifacial solar cell back surface illuminated and under irradiation. The expressions of the excess minority carrier in the base and the photocurrent density have been proposed. Calibration curves of the photocurrent density were plotted versus the junction recombination rate for different values of the irradiation energy (ϕp), the base thickness H and the damage coefficient (kl). The expressions of the excess minority carrier recombination velocity at the back surface, have been deduced and resolved graphically, to obtain the optimum thickness at intercept points of the curves. The correlation between the irradiation energy, the damage coefficient and the optimal thickness of the solar cell has been established.