A method to determine the transient capacitance of the bifacial solar cell considering the cylindrica grain and the dynamic junction velocity (Sf)

In this paper, we present a new technic based on t transient diffusion capacitance of the bifacial solar cell back surface recombination velocity (Sb) and the grain boundary recombination velocity (Sgb), we resolved the continuity equation in the base of the solar cell under monochro diffusion capacitance profile which decreases with the dynamic junction velocity (Sf), the back surface recombination velocity (Sb), the grain boundary recombination velocity (Sgb) and the high wave transient diffusion capacitance increases with the grains size (R).


Introduction
The choice of a model constitutes the basis of any modeling study leading to simulations and therefore to the results which enable to the physicist to make his scientific reading.For the characterization of solar cells, the one dimension (1D) [1,2] and the columnar grains [3 The choice of a model constitutes the basis of any modeling study leading to simulations and therefore to the results which enable to the physicist to make his scientific reading.For the characterization of solar cells, the one dimension he columnar grains [3-4-5] models are widely used.Hence, combined to the dynamic junction velocity (SF), some methods are proposed to determine the diffusion length and the lifetime of the excess minority carriers in the base of the solar cell [6].These permit also to calculate the excess minority carriers density, the photocurrent I [5], the photot cell's power (P), the I-V and P intrinsic junction recombination velocity (Sf0) [1,2], the real .This is an open access article distributed under the terms of the Creative ), which permits unlimited use, distribution and widely used.Hence, combined to the dynamic junction velocity (SF), some methods are proposed to determine the diffusion length and the lifetime of the excess minority carriers in the base of the solar cell [6].These two models permit also to calculate the excess minority carriers density, the photocurrent I [5], the phototension V [5], the solar V and P-V characteristics [5], the intrinsic junction recombination velocity (Sf0) [1,2], the real

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S. N. Leye, A. Diouf, S. Mbodji and G. Sissoko back side recombination velocity (Sb) [1,2], the series and shunt resistances [5] and the diffusion capacitance solar cell's efficiency.Considering these two dimensions, effects of magnetic and electric fields and the irradiation on the electrical solar cell parameters are also studied [7,8].In [3], authors used the columnar grains model and concluded that the solar cell's junction could be considered as a plane capacitor with two identical plane electrodes separated by an extension region width which de the dynamic junction velocity (SF), the grain size, the grain boundary recombination velocity and the wavelength.In this study, the primary role of Sf which related to the operating point of the solar cell is demonstrated.However, the columnar approach of the grains of the solar cell which gives good results is not the only method to allow the characterization and must be improved.The cylindrical orientation can also be considered in order to better refine the control of the parameters of the solar cells.
That is why, this paper aims at presenting the behavior of the transient diffusion capacitance of an N solar cell.The capacitance is studied using the cylindrical orientation of the grains of the solar cell.We take into account of the dynamic junction velocity Sf [9], the grain radius (R) and the grain boundary recombination velocity (Sgb).

Theory
We present in figure 1 an isolated cylindrical grain of the bifacial silicon solar cell under monochromatic illumination.

Figure 1. Isolated cylindrical grain
The bifacial solar cell is assumed to have four zones: the emitter doped N + , the base doped P, the junction N is setted between the emitter and the base, and the back contact where another junction is created by a thin film Sissoko ack side recombination velocity (Sb) [1,2], the series and shunt resistances [5] and the diffusion capacitance solar cell's efficiency.Considering these two dimensions, effects of magnetic and electric fields and the irradiation on the ell parameters are also studied [7,8].In [3], authors used the columnar grains model and concluded that the solar cell's junction could be considered as a plane capacitor with two identical plane electrodes separated by an extension region width which depends on the dynamic junction velocity (SF), the grain size, the grain boundary recombination velocity and the wavelength.In this study, the primary role of Sf which related to the operating pproach of the grains of the solar cell which gives good results is not the only method to allow the characterization and must be improved.The cylindrical orientation can also be considered in order to better refine lar cells.
That is why, this paper aims at presenting the behavior of the transient diffusion capacitance of an N + P-P + bifacial solar cell.The capacitance is studied using the cylindrical orientation of the grains of the solar cell.We take into of the dynamic junction velocity Sf [9], the grain radius (R) and the grain boundary recombination velocity We present in figure 1 an isolated cylindrical grain of the bifacial silicon solar cell under monochromatic illumination.
The bifacial solar cell is assumed to have four zones: the , the base doped P, the junction N + P which between the emitter and the base, and the back contact where another junction is created by a thin film strongly doped P + .This second junction is the seat of the very intense electric field which returns the minority carriers towards the base [3][4][5].This recombination at the back side of this type of solar cell which are more efficient than the conventional solar cell [3 5].
According to [10], the transfer phenomenas in the base of the solar cell are modeled by the equation of cylindrical coordinates: As, we have an azimuthal symmetry, the angle θ is not processed.Therefore the continuity equation becomes: (r;z) : minority carrier's density; D: electron diffusion coefficient in the base (D = 26 cm s −1 ); L: electron diffusion length in the base; G(z): minority carriers generation rate at position z in the base [3] While proceeding by the separation method of the variables used by [10], we put: The solution of the equation is given by: K are obtain boundaries conditions of the solar cell:  At the junction (z=0) [3,5]:

Capacitance
The bifacial solar cell's transient diffusion is given by [5]: . This second junction is the seat of the very intense electric field which returns the minority carriers 5].This electrical field limits the recombination at the back side of this type of solar cell which are more efficient than the conventional solar cell [3-According to [10], the transfer phenomenas in the base of the solar cell are modeled by the equation of continuity in δ(r,θ,z)  (1) As, we have an azimuthal symmetry, the angle θ is not processed.Therefore the continuity equation becomes: ensity; electron diffusion coefficient in the base (D = 26 cm 2 .

: electron diffusion length in the base;
: minority carriers generation rate at position z in the While proceeding by the separation method of the variables (3) The solution of the equation is given by: k u are obtained from the tions of the solar cell: At the junction (z=0) [3,5]: (5) At the grain boundary (r=R) : (6) The bifacial solar cell's transient diffusion is given by [5]:

Results and Discussions
In figures 2, 3 and 4, we plotted the transient diffusion capacitance versus the junction recombination velocity.Figure 2 shows effects of grain boundary recombination velocity.As for the influence of the grain size and wavelength (), we considered various radius (R) and wavelength () in figures 4 and 5, respectively. the open circuit transient diffusion capacitance is very brief.It can be seen here that there is a difference between the considered model and that of the cubic grains where the range of operating points of the open circuits is sufficiently long [4]. the short circuit operating points zone is very important and there, the transient diffusion capacitance stretches toward zero ;  a transient diffusion capacitance, depending on operating point which is related to SF, appears between the open circuit operating to the shortcircuit operating points.The increase of SF corresponds to an increase of the extension region width and hence to the increase of solar cell's photocurrent as shown by [3].We also noted that the transient diffusion capacitance decreases with Sgb; meaning that increasing of Sgb leads to high recombination in the grain boundary of the solar.In figure 3, we noticed that the variation of the solar cell grain radius (R) leads to increase the transient diffusion capacitances.
Figure 4 shows that when the wavelength () increases in the considered range between 980 to 1020 nm, the transient diffusion capacitance decreases.When the wavelength increases, the energy of incoming photons decreases and less excess minority carriers are extracted in the base of the solar cell.
In figure 5 we represented the solar cell's transient diffusion capacitance versus the dynamic junction velocity (SF) and the solar cell grain radius (R).Indeed, the solar cell's capacitance increases according to the grain radius (R) and decreases with the junction recombination velocity.acitance of the bifacial solar cell considering the cylindrical model of the grain and In figure 6, we showed the variation of the capacitance according to Sgb and the wavelength (λ).These figures represent the bifacial solar cells transient diffusion capacitance for a fixed solar cell grain radius (R) and for various grain boundary recombination velocities (Sgb) and wavelengths (λ).Effects of these two parameters on the transient diffusion capacitance are the same as for the results of [3].

Conclusion
In this paper, we determined the transient diffusion capacitance using the cylindrical orientation of solar cell's grains.We have shown that, as for the columnar isolated grain model, the diffusion transient diffusion capacitance increases with solar cell grain radius (R) and with wave length.It decreases with the grain boundary recombination velocity and the dynamic junction velocity (SF).The approach confirms that best solar cells correspond to high grain radiuses (R) which lead to low grain boundary recombination velocity (Sgb).
Research Article A method to determine the transient capacitance of the l model of the grain and the dynamic junction velocity (Sf) Laboratory of Semiconductors and Solar Energy, Department of Physics, Faculty of Science and Technology, Cheikh Anta s, Faculty of Science a Laboratory of Semiconductors and Solar Energy, Department of Physics, Faculty of Science a ductors and Solar Energy, Department of Physics, Faculty of Science a ersity of Bambey, Bambey, tion velocity (Sf) concept for the evaluation of the considering cylindrical model of the grains.Associating (Sf), the back surface recombination velocity (Sb) and the grain boundary recombination velocity (Sgb), we resolved the continuity ion.We calculated and plotted the solar cell's transient diffusion capacitance profile which decreases with the dynamic junction velocity (Sf), the back surface recombination length.The study shows also that the Grain Size, Grain Boundary Recombination Velocity, Polycrystalline, Solar Cell, Junction Recombination Velocity,

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7) the electron's charge.EAI Endorsed Transactions on Collaborative Computing 12 2016 -06 2017 | Volume 3 | Issue 11 | e5 method to determine the transient capacitance of the bifacial solar cell considering the cylindrical model of the grain and the dynamic junction velocity (Sf)

Figure 2 .
Figure 2. Capacitance of the illuminated solar cell versus SF for various Sgb: R= 0.01 cm.

Figure 3 .Figure 4 .
Figure 3. Capacitance of the illuminated solar cell by the front surface versus SF for various radius (R): L = 0.01 cm