Determination of the Base Optimum Thickness of Back Illuminated (n^{+}/p/p^{+}) Bifacial Silicon Solar Cell, by Help of Diffusion Coefficient at Resonance Frequency ()

Mohamed Yaya Teya^{1,2}, Ousmane Sow^{1,3}, Khady Loum^{1}, Ibrahima Diatta^{1}, Gora Diop^{1,3}, Youssou Traore^{1,3}, Mamadou Wade^{1,2}, Gregoire Sissoko^{1}

^{1}International Research Group in Renewable Energy (GIRER), Dakar, Senegal.

^{2}Ecole Polytechnique de Thiès, Thiès, Senegal.

^{3}Institut Universitaire de Technologie, Université Iba Der THIAM, Thiès, Senegal.

**DOI: **10.4236/jemaa.2023.152002
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The bifacial silicon solar cell subjected to a magnetic field, is illuminated by the back side by a monochromatic light in frequency modulation, with high absorption, At minority carriers diffusion coefficient resonance frequency, a graphical study of the expressions of recombination velocity on the rear side is carried out. The optimum thickness of the base of the bifacial solar cell is deduced for each resonance frequency.

Keywords

Bifacial Silicon Solar Cell, Frequency, Magnetic Field, Wavelength-Recombination Velocity, Base Thickness

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Teya, M. , Sow, O. , Loum, K. , Diatta, I. , Diop, G. , Traore, Y. , Wade, M. and Sissoko, G. (2023) Determination of the Base Optimum Thickness of Back Illuminated (n^{+}/p/p^{+}) Bifacial Silicon Solar Cell, by Help of Diffusion Coefficient at Resonance Frequency. *Journal of Electromagnetic Analysis and Applications*, **15**, 13-24. doi: 10.4236/jemaa.2023.152002.

1. Introduction

The realization of a junction (p/p^{+}) (low-high junction or BSF) [1] [2] [3] on the (p) base of the (n^{+}/p/p^{+}) solar cell [4] [5] [6] improves the photoconversion efficiency. However, the depth (H) at which this junction must be made in the base is often evaluated after the complete elaboration of the solar cell with wafers of different thicknesses which are cut [7] [8] [9] [10] . Recent works on the location of this junction (p/p^{+}) [11] [12] [13] [14] [15] , based on the study of mathematical expressions of the recombination velocity (*Sb*) of minority carriers on this rear surface [16] - [21] , has made it possible to obtain the optimum thickness (Hopt) of the base of the solar cell under various operating conditions [22] [23] [24] . These expressions [21] [25] [26] are dependent on the diffusion coefficient (*D*), the diffusion length (*L*) of the minority carriers, the thickness (*H*) and the absorption coefficient of the material (Si).

This work is based on the expressions of the diffusion coefficient expressed by the Einstein relation and influenced by parameters of many conditions:

1) External which are: temperature [27] [28] [29] , electromagnetic field [30] [31] [32] [33] [34] , irradiation flux by charged particles [35] [36] [37] , the frequency [38] - [43] of modulation of incident light.

2) Intrinsic, linked to manufacturing through doping rates [44] [45] [46] .

The possibility of combining the different conditions [47] [48] [49] [50] [51] allows us to propose this present work, which considers the silicon solar cell (n^{+}/p/p^{+}) under the influence of the magnetic field, and illuminated by the back side, by a monochromatic light in frequency modulation. The optimum thickness (*H _{opt}*) of the base, is obtained by studying the expressions of the recombination velocity (

2. Theory

The structure of (n^{+}-p-p^{+}) bifacial silicon solar cell [52] - [57] under back monochromatic illumination, in frequency modulation, is given in Figure 1.

The excess minority carriers’ density $\delta \left(x,t\right)$ generated by illumination in frequency modulation, in the base of the solar cell obeying the continuity magneto-resistance equation, is given by [31] [32] [39] [40] [41] :

$D\left(\omega ,B\right)\times \frac{{\partial}^{2}\delta \left(x,t\right)}{\partial {x}^{2}}-\frac{\delta \left(x,t\right)}{\tau}=-G\left(x,\omega ,t\right)+\frac{\partial \delta \left(x,t\right)}{\partial t}$ (1)

The expression of the excess minority carriers’ density is written, according to the space coordinates (*x*) and the time *t*, as:

$\delta \left(x,t\right)=\delta \left(x\right)\cdot {\text{e}}^{-j\omega t}$ (2)

2.1. Generation Rate

AC carrier generation rate $G\left(x,t\right)$ is given by the relationship [39] [40] [41] [53] as:

$G\left(x,t\right)=g\left(x\right)\cdot {\text{e}}^{-j\omega t}$ (3)

Figure 1. Structure of back illuminated bifacial silicon solar cell under magnetic field.

With *g*(*x*) the spatial component:

$g\left(x\right)=\alpha \left(\lambda \right)\cdot {I}_{0}\left(\lambda \right)\cdot \left(1-R\left(\lambda \right)\right)\cdot {\text{e}}^{-\alpha \left(\lambda \right)\cdot \left(H-x\right)}$ (4)

The monochromatic optical parameters [58] [59] of the (Si) material at wavelength (*λ*) are respectively, incident flux (*I*_{0}(*λ*)), absorption coefficient (*α*(*λ*)) and reflection coefficient *R*(*λ*). Base depth is represented by (*H*).

2.2. AC Diffusion Coefficient

The expression of complex diffusion coefficient of excess minority carrier in the base under magnetic field and frequency modulation
$D\left(\omega ,B\right)$ is given by the following relationship [38] [48] [49] whose representation as a function of (*ω*), reveals peaks at given (*B*), which correspond to the resonance:* *

$D\left(\omega ,B\right)=D\left(B\right)\cdot \left[\frac{1+{\tau}^{2}\cdot \left({\omega}_{c}^{2}+{\omega}^{2}\right)}{4\cdot {\omega}^{2}\cdot {\tau}^{2}+{\left[1+{\tau}^{2}\left({\omega}_{c}^{2}-{\omega}^{2}\right)\right]}^{2}}-\frac{j\cdot \omega \cdot {\tau}^{2}\left(1-{\tau}^{2}{\left({\omega}_{c}^{2}-\omega \right)}^{2}\right)}{4\cdot {\omega}^{2}\cdot {\tau}^{2}+{\left[1+{\tau}^{2}\left({\omega}_{c}^{2}-{\omega}^{2}\right)\right]}^{2}}\right]$ (5)

With

${\omega}_{c}=\frac{q\cdot B}{{m}_{e}^{\ast}}$ (6)

The electron has a circle as trajectory, for given cyclotron frequency, leading to decreasing minonority carriers diffusion coefficient. The elementary charge is (*q*) while
${m}_{e}^{\ast}$ is the effectice mass.

2.3. Boundary Conditions and Solution

By replacing Equations (2) and (3) in Equation (1), the continuity equation for the excess minority carriers’ density in the base is reduced to the following relationship:

$\frac{{\partial}^{2}\delta \left(x,\omega \right)}{\partial {x}^{2}}-\frac{\delta \left(x,\omega \right)}{{L}^{2}\left(\omega ,B\right)}=-\frac{g\left(x\right)}{D\left(\omega ,B\right)}$ (7)

$L\left(\omega ,B\right)$ is the complex diffusion length, under magnetic field and frequency modulation, of excess minority carriers in the base, given by:

$L\left(\omega ,B\right)=\sqrt{\frac{D\left(\omega ,B\right)\tau}{1+j\omega \tau}}$ (8)

$\tau $ is the excess minority carriers lifetime in the base.

The solution of Equation (7) is given as:

$\delta \left(x,\omega ,B,\lambda \right)=A\cdot \mathrm{cosh}\left[\frac{x}{L\left(\omega ,B\right)}\right]+B\cdot \mathrm{sinh}\left[\frac{x}{L\left(\omega ,B\right)}\right]+K\cdot {\text{e}}^{-\alpha \cdot \left(H-x\right)}$ (9)

With

$K=\frac{\alpha \left(\lambda \right)\cdot {I}_{0}\cdot \left(1-R\left(\lambda \right)\right)\cdot {\left[L\left(\omega ,B\right)\right]}^{2}}{D\left(\omega ,B\right)\left[L{\left(\omega ,B\right)}^{2}\cdot \alpha {\left(\lambda \right)}^{2}-1\right]}$ (10)

and

$L{\left(\omega ,B\right)}^{2}\cdot \alpha {\left(\lambda \right)}^{2}\ne 1$ (11)

Coefficients *A* and *B* are determined through the boundary conditions:

• At the (n^{+}/p) junction (*x* = 0)

${\frac{\partial \delta \left(x,\omega ,B,\lambda \right)}{\partial x}|}_{x=0}=Sf\cdot {\frac{\delta \left(x,\omega ,B,\lambda \right)}{D\left(\omega ,B\right)}|}_{x=0}$ (12)

• On the back side (p/p^{+}) in the base (*x* = *H*)

${\frac{\partial \delta \left(x,\omega ,B,\lambda \right)}{\partial x}|}_{x=H}=-Sb\cdot {\frac{\delta \left(x,\omega ,B,\lambda \right)}{D\left(\omega ,B\right)}|}_{x=H}$ (13)

Boundary conditions are characterize by the recombination velocity [16] - [22] [35] [60] [61] [62] [63] respectively, (*Sf*) at the junction (p/p^{+}) and *Sb* at the rear (p/p^{+}) of the base.

3. Results and Discussions

3.1. AC Back Surface Recombination and Optimum Base Thickness Determination at Ringing Frequency

The representation of AC photocurrent density according to the junction recombination velocity of minority carriers [21] [22] [64] shows that, for very large *Sf*, the AC short-circuit current density (*J _{phsc}*) prevails as constant. So, in this junction recombination velocity interval, the derivative of AC photocurrent density with respect to (

${\frac{\partial {J}_{ph}\left(Sf,Sb,\omega ,B,\alpha \left(\lambda \right),H\right)}{\partial Sf}|}_{Sf\ge {10}^{5}\text{\hspace{0.17em}}\text{cm}\cdot {\text{s}}^{-1}}=0$ (14)

The solution of Equation (14) leads to the expressions of AC recombination velocity in the rear surface [16] [17] [18] [19] [20] given by Equations (15) and (16):

$S{b}_{1}\left(\omega ,B\right)=-\frac{D\left(\omega ,B\right)}{L\left(\omega ,B\right)}\cdot \mathrm{tanh}\left(\frac{H}{L\left(\omega ,B\right)}\right)$ (15)

$\begin{array}{l}S{b}_{2}\left(H,\alpha \left(\lambda \right),\omega ,B\right)\\ =\frac{D\left(\omega ,B\right)}{L\left(\omega ,B\right)}\cdot \frac{L\left(\omega ,B\right)\cdot \alpha \left(\lambda \right)-\left(L\left(\omega ,B\right)\cdot \alpha \left(\lambda \right)\cdot ch\left(\frac{H}{L\left(\omega ,B\right)}\right)+sh\left(\frac{H}{L\left(\omega ,B\right)}\right)\right){\text{e}}^{-\alpha \left(\lambda \right)\cdot H}}{\left(ch\left(\frac{H}{L\left(\omega ,B\right)}\right)+L\left(\omega ,B\right)\cdot \alpha \left(\lambda \right)\cdot sh\left(\frac{H}{L\left(\omega ,B\right)}\right)\right){\text{e}}^{-\alpha \left(\lambda \right)\cdot H}-1}\end{array}$ (16)

Figure 2, gives the profile of the two expression of AC back surface recombination velocity for different ringing frequencies inducing Dmax values, versus thickness of the base of the solar cell, under short wavelength (*α*(*λ*) = 21,000 cm^{−1}). The technique [11] [12] [13] [15] [23] [24] [50] [51] of the intercept point of the curves, produces the optimum thickness of the base, and allow the establishment of Table 1 data.

Figure 2. *Sb*_{1} and *Sb*_{2} versus depth in the base for different magnetic field values (*D*_{0} = 35 cm/s; *α* = 21,000 cm^{−1}).

Table 1. Ringing frequencies, maximum diffusion coefficient and diffusion length for given magnetic field.

From Figure 3, the relationship obtained is expressed as:

${H}_{op}\left(\text{cm}\right)=5.6\times {10}^{-4}\times {D}_{\mathrm{max}}\left({\text{cm}}^{\text{2}}/\text{s}\right)-0.0028$ (17)

From obtained Table 1, base optimum thickness versus *L*_{max}, is represented in Figure 4.

The representation is also an increase strait line, expresses as:

${H}_{op}\left(\text{cm}\right)=1.2\times {L}_{\mathrm{max}}\left(\text{cm}\right)-0.0094$ (18)

3.2. Discussion

The results obtained from (*H _{opt}*) show the decay with the resonance frequency, consequently with the magnetic field (Table 1). The physical phenomena to be taken into account are:

- The absorption-generation of minority carriers in low penetration therefore close to the incident rear surface (p/p^{+}) [12] [16] [21] [57] [65] .

- The modulation frequency, which at the resonance point of Dmax, causes the decay of both, *D*_{max} and *L*_{max} (in Table 1) for a given magnetic field (*B*), reflects the degradation of the electronic properties of the material and the difficulties of movement of minority carriers.

Figure 3. *D*_{max} versus base optimum thickness.

Figure 4. Optimum thickness of the base versus *L*_{max}.

At resonance, the study of *D *(*ω*, *B*) [15] [38] [48] [49] shows an opposition of capacitive and inductive phenomena to the detriment of the resistive phenomenon, which favors the diffusion of minority charge carriers. The increase in frequency and magnetic field, leads to deflection of minority charge carriers.

Thus when the electronic properties of the material are degraded (under the reversible action of the two parameters that are the magnetic field and the modulation frequency, Equations (5) and (8)), then the optimum thickness is low (Figure 3 and Figure 4), to allow the collection of minority carriers in thin base. For high electronic quality material, large optimum thickness can be used.

Previous results have shown the decrease in the optimum thickness of the base:

- For low penetration of incident light (strong *α*(*λ*)), regardless of the illuminated face [11] [12] [65] front or rear.

- With the increase in the frequency of incident light.

- With the increase of the applied magnetic field.

- With the increase in applied temperature.

- The combination [23] [24] [50] [51] [57] [65] of these physical phenomena leads to a decrease in the optimum thickness of the base.

This study on the solar cell in the one-dimensional model can be reinforced by the three-dimensional study [26] [49] , taking into account the effects of both, recombination velocity at grain boundaries and grain size.

4. Conclusions

This study used the phenomenon of resonance of the diffusion coefficient of minority carriers, to determine the optimum thickness of the base of the bifacial silicon solar cell. The latter is placed under magnetic field and illuminated from the back side by a monochromatic light of low penetration. Thus the optimum thickness of the base delimited by the junction (p/p^{+}), is low because of:

- Strong absorption of incident light near the rear surface;

- Decay with the frequency of the diffusion coefficient of the excess minority carriers, near the rear surface and their deflection with the applied magnetic field.

The optimum thickness decreases as the diffusion coefficient decreases (poor quality material). In this situation, the low thicknesses of the base of the bifacial silicon solar cell illuminated by the back side are better suited for improving photoconversion efficiency.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

[1] |
Nam, L.Q., Rodot, M., Ghannam, M., Cppye, J. and de Schepper, P.J. (1992) Solar Cells with 15.6% Efficiency on Multicristalline Silicone, Using Impurity Gettering, back Surface Field and Emitter Passivation. International Journal of Solar Energy, 11, 273-279. https://doi.org/10.1080/01425919208909745 |

[2] |
Fossum, J.G. (1977) Physical Operation of Back-Surface-Field Silicon Solar Cells. IEEE Transactions on Electron Devices, 24, 322-325. https://doi.org/10.1109/T-ED.1977.18735 |

[3] |
Wu, C.Y. (1980) The Open-Circuit Voltage of Back-Surface-Field (BSF) p-n Junction Solar Cells in Concentrated Sunlight. Solid-State Electronics, 23, 209-216. https://doi.org/10.1016/0038-1101(80)90004-0 |

[4] |
Bertrand, D., Manuel, S., Pirot, M., Kaminski-Cachopo, A. and Veschetti, Y. (2017) Modelling of Edge Losses in Al-BSF Silicon Solar Cells. IEEE Journal of Photovoltaics, 7, 78-84. https://doi.org/10.1109/JPHOTOV.2016.2618603 |

[5] |
Del Alamo, J., Eguren, J. and Luque, A. (1980) Operating Limits of Al-Alloyed High-Low Junction for BSF Solar Cells. Solid-States Electronics, 24, 415-420. https://doi.org/10.1016/0038-1101(81)90038-1 |

[6] |
Martin, A.G. (2013) High-Efficiency Silicon Solar Cell Concepts. In: McEvoy, A., Castañer, L. and Markvart, T., Eds., Solar Cells: Materials, Manufacture and Operation, Elsevier Ltd., Amsterdam, 87-113. https://doi.org/10.1016/B978-0-12-386964-7.00005-6 |

[7] |
Van Steenwinkel, R., Carotta, M.C., Martinelli, G., Mercli, M., Passari, L. and Palmeri, D. (1990) Lifetime Measurement in Solar Cell of Various Thickness and Related Silicon Wafer. Solar Cells, 28, 287-292. https://doi.org/10.1016/0379-6787(90)90063-B |

[8] |
Demesmaeker, E., Symons, J., Nijs, J. and Mertens, R. (1991) The Influence of Surface Recombination on the Limiting Efficiency and Optimum Thickness of Silicon Solar Cells. Proceedings of 10th European Photovoltaic Solar Energy Conference, Lisbon, 8-12 April 1991, 66-67. https://doi.org/10.1007/978-94-011-3622-8_17 |

[9] |
Giesecke, J.A., Schubert, M.C., Michl, B., Schindler, F. and Warta, W. (2011) Minority Carrier Lifetime Imaging of Silicon Wafers Calibrated by Quasi-Steady-State Photoluminescence. Solar Energy Materials and Solar Cells, 95, 1011-1018. https://doi.org/10.1016/j.solmat.2010.12.016 |

[10] |
Hameiri, Z. and Chaturvedi, P. (2013) Spatially Resolved Electrical Parameters of Silicon Wafers and Solar Cells by Contactless Photoluminescence Imaging. Applied Physics Letters, 102, Article ID: 073502. https://doi.org/10.1063/1.4792348 |

[11] |
Dede, S.M., Ba, M.L., Ba, M.A., Ndiaye, M., Gueye, S., Sow, E., Diatta, I., Diop, M., Wade, M. and Sissoko, G. (2020) Back Surface Recombination Velocity Dependent of Absorption Coefficient as Applied to Determine Base Optimum Thickness of an n+/p/p+ Silicon Solar Cell. Energy and Power Engineering, 12, 445-458. https://doi.org/10.4236/epe.2020.127027 |

[12] |
Sall, M., Diarisso, D., Fall, M.F.M., Diop, G., Ndiaye, M., Loum, K. and Sissoko, G. (2021) Back Illuminated N/P/P+ Bifacial Silicon Solar Cell under Modulated Short-Wavelength: Determination of Base Optimum Thickness. Energy and Power Engineering, 13, 207-220. https://doi.org/10.4236/epe.2021.135014 |

[13] |
Ndiaye, A., Gueye, S., Sow, O., Diop, G., Ba, A., Ba, M., Diatta, I., Habiboullah, L. and Sissoko, G. (2020) AC Recombination Velocity as Applied to Determine n+/p/p+ Silicon Solar Cell Base Optimum Thickness. Energy and Power Engineering, 12, 543-554. https://doi.org/10.4236/epe.2020.1210033 |

[14] |
Ndiaye, M., Sow, O., Diatta, I., Diop, G., Faye, D., Loum, K., Traore, Y., Thiame, M., Wade, M. and Sissoko, G. (2022) Optimization of the Thickness of the Doping Rate Base (Nb) of the (n+/p/p+) Silicon Solar Cell with Vertical Multi-Junction Connected in Series and Placed under Monochromatic Illumination in Frequency Modulation. Journal of Chemical, Biological and Physical Sciences, 12, 251-265. https://doi.org/10.24214/jcbps.C.12.4.25165 |

[15] |
Ndiaye, A., Gueye, S., Fall, M.M., Diop, G., Ba, A., Ba, M., Diatta, I., Habiboullah, L. and Sissoko, G. (2020) Diffusion Coefficient at Resonance Frequency as Applied to n+/p/p+ Silicon Solar Cell Optimum Base Thickness Determination. Journal of Electromagnetic Analysis and Applications, 12, 145-158. https://doi.org/10.4236/jemaa.2020.1210012 |

[16] |
Fall, M., Gaye, I., Diarisso, D., Diop, G., Loum, K., Diop, N., Sy, K., Ndiaye, M. and Sissoko, G. (2021) AC Back Surface Recombination Velocity in n+-p-p+ Silicon Solar Cell under Monochromatic Light and Temperature. Journal of Electromagnetic Analysis and Applications, 13, 67-81. https://doi.org/10.4236/jemaa.2021.135005 |

[17] | Ly, I., Zerbo, I., Wade, M., Ndiaye, M., Dieng, A., Diao, A., Thiam, N., Thiam, A., Dione, M.M., Barro, F.I., Maiga, A.S. and Sissoko, G. (2011) Bifacial Silicon Solar Cell under Frequency Modulation and Monochromatic Illumination: Recombination Velocities and Associated Equivalent Electrical Circuits. Proceedings of 26th European Photovoltaic Solar Energy Conference and Exhibition, Hamburg, 5-9 September 2011, 298-301. |

[18] | Zerbo,I., Barro, F.I., Mbow, B., Diao, A., Madougou, S., François, Z. and Sissoko, G. (2004) Theoretical Study of Bifacial Silicon Solar Cell under Frequency Modulate white Light: Determination of Recombination Parameters. Proceedings of the 19th European Photovoltaic Solar Energy Conference, Paris, 7-11 June 2004, 258-261. |

[19] | Ly Diallo, H., Wade, M., Ly, I., Diaye, M.N., Dieng, B., Lemrabott, O.H., Amadou, S.M. and Sissoko, G. (2012) 1D Modeling of a Bifacial Solar Cell Silicon under Monochromatic Illumination Frequency Modulation: Determination of the Equivalent Electrical Circuit Related to the Recombination Area Velocity. Research Journal of Applied Sciences, Engineering and Technology, 4, 1672-1676. |

[20] |
Denise, K., Ba, L.M., Ba, A.M., Diop, G., El Hadj, S., Oulimata, M. and Gregoire, S. (2020) AC Back Surface Recombination in n+-p-p+ Silicon Solar Cell: Effect of Temperature. International Journal of advanced Research (IJAR), 8, 140-151. https://doi.org/10.21474/IJAR01/11273 |

[21] | Sissoko, G., Museruka, C., Corréa, A., Gaye, I. and Ndiaye, A.L. (1996) Light Spectral Effect on Recombination Parameters of Silicon Solar Cell. Proceedings of World Renewable Energy Congress, Pergamon, 15-21 June 1996, 1487-1490. |

[22] |
Ndiaye, E.H., Sahin, G., Dieng, M., Thiam, A., Diallo, H.L., Ndiaye, M. and Sissoko, G. (2015) Study of the Intrinsic Recombination Velocity at the Junction of Silicon Solar under Frequency Modulation and Irradiation. Journal of Applied Mathematics and Physics, 3, 1522-1535. https://doi.org/10.4236/jamp.2015.311177 |

[23] |
Diop, G., Sow, O., Thiame, M., Mane, R., Diatta, I., Loum, K., Gueye, S., Wade, M. and Sissoko, G. (2022) Diffusion Coefficient at Double Resonances in Frequency and Temperature, Applied to (n+/p/p+) Silicon Solar Cell Base Thickness Optimization under Long Wavelength Illumination. Journal of Electromagnetic Analysis and Applications, 14, 89-103. https://doi.org/10.4236/jemaa.2022.148008 |

[24] |
Sow, O., Gueye, S., Mane, R., Diop, G., Diatta, I., Loum, K., Thiame, M., Wade, M. and Sissoko, G. (2022) n+/p/p+ Silicon Solar Cell Base Thickness under Modulated Short Wavelength Illumination, at Resonances in both Frequency and Temperature of Minority Carriers’ Diffusion Coefficient. International Journal of Engineering Research Updates, 3, 40-52. https://doi.org/10.53430/ijeru.2022.3.2.0059 |

[25] |
Diasse, O., Diao, A., Ly, I., Diouf, M.S., Diatta, I., Mane, R., Traore, Y. and Sissoko, G. (2018) Back Surface Recombination Velocity Modeling in White Biased Silicon Solar Cell under Steady State. Journal of Modern Physics, 9, 189-201. https://doi.org/10.4236/jmp.2018.92012 |

[26] |
Diallo, H.L., Maiga, A.S., Wereme, A. and Sissoko, G. (2008) New Approach of both Junction and Back Surface Recombination Velocities in a 3D Modelling Study of a Polycrystalline Silicon Solar Cell. The European Physical Journal Applied Physics, 42, 203-211. https://doi.org/10.1051/epjap:2008085 |

[27] |
Misiakos, K. and Tsamakis, D. (1994) Electron and Hole Mobilities in Lightly Doped Silicon. Applied Physics Letters, 64, 2007-2009. https://doi.org/10.1063/1.111721 |

[28] |
Arora, N.D., Hauser, J.R. and Roulston, D.J. (1982) Electron and Hole Mobilities in Silicon as a Function of Concentration and Temperature. IEEE Transactions on Electron Devices, 29, 292-295. https://doi.org/10.1109/T-ED.1982.20698 |

[29] |
Dorkel, J.M. and Leturcq, P. (1981) Carrier Mobilities in Silicon Solar Semi-Empirically Related Temperature, Doping and Injection Level. Solid-State Electron, 24, 821-825. https://doi.org/10.1016/0038-1101(81)90097-6 |

[30] | Vardanyan, R., Kerst, U., Tierock, B. and Wagemann, H.G. (1997) Measurement of Recombination Parameters of Solar Cell in a Magnetic Field. Proceeding of the 14th European Photovoltaic Solar Energy Conference, Barcelona, 30 June-4 July 1997, 2367-2369. |

[31] |
Bester, Y., Ritter, D., Bahia, G., Cohen, S. and Sparkling, J. (1995) Measurement of the Minority Carrier Mobility in the Base of Heterojunction Bipolar Transistor Using a Magneto Transport Method. Applied Physics Letters, 67, 1883-1884. https://doi.org/10.1063/1.114364 |

[32] |
Thiaw, C., Ba, M., Ba, A.M., Diop, G., Diatta, I., Ndiaye, M. and Sissoko, G. (2020) n+-p-p+ Silicon Solar Cell Base Optimum Thickness Determination under Magnetic Field. Journal of Electromagnetic Analysis and Applications, 12, 103-113. https://doi.org/10.4236/jemaa.2020.127009 |

[33] | Diop, G., Ba, H.Y., Thiam, N., Traore, Y., Dione, B., Ba, M.A., Diop, P., Diop, M.S., Mballo, O. and Sissoko, G. (2019) Base Thickness Optimization of a Vertical Series Junction Silicon Solar Cell under Magnetic Field by the Concept of Back Surface Recombination Velocity of Minority Carrier. Journal of Engineering and Applied Sciences, 14, 4078-4085. |

[34] |
Flohr, T. and Helbig, R. (1989) Determination of Minority-Carrier Lifetime and Surface Recombination Velocity by Optical Beam Induced Current Measurements at Different Light Wavelengths. Journal of Applied Physics, 66, 3060-3065. https://doi.org/10.1063/1.344161 |

[35] |
Rosenzweig, W. (1962) Diffusion Length Measurement by Mean of Ionization Radiation. The Bell System Technical Journal, 41, 1573-1588. https://doi.org/10.1002/j.1538-7305.1962.tb03995.x |

[36] |
Rose, B.H. and Weaver, H.T. (1983) Determination of Effective Surface Recombination Velocity and Minority-Carrier Lifetime in High-Efficiency Si Solar Cells. Journal of Applied Physics, 54, 238-247. https://doi.org/10.1063/1.331693 |

[37] |
Ba, M.L., Thiam, N., Thiame, M., Traore, Y., Diop, M.S., Ba, M., Sarr, C.T., Wade, M. and Sissoko, G. (2019) Base Thickness Optimization of a (n+-p-p+) Silicon Solar Cell in Static Mode under Irradiation of Charged Particles. Journal of Electromagnetic Analysis and Applications, 11, 173-185. https://doi.org/10.4236/jemaa.2019.1110012 |

[38] |
Cardona, M. (1969) Modulation Spectroscopy of Semiconductors. Advances in Solid State Physics, 10, 125-173. https://doi.org/10.1016/B978-1-4831-2427-8.50007-3 |

[39] |
Luc, B., Shahriar, M., Dean, H., Marco, S., Manuela, A. and Claudio, N. (1994) Investigation of Carrier Transport through Silicon Wafers by Photocurrent Measurement. Journal of Applied Physics, 75, 4000-4008. https://doi.org/10.1063/1.356022 |

[40] |
Sudha, G., Feroz, A. and Suresh, G. (1988) A Method for the Determination of the Material parameters τ, D, L0, S and α from Measured A.C. Short-Circuit Photocurrent. Solar Cells, 25, 61-72. https://doi.org/10.1016/0379-6787(88)90058-0 |

[41] |
Wang, C.H. and Neugroschel, A. (1991).Minority-Carrier Lifetime and Surface Recombination Velocity Measurement by Frequency-Domain Photoluminescence. IEEE transactions on Electron Devices, 38, 2169-2180. https://doi.org/10.1109/16.83745 |

[42] |
Honma, N. and Munakata, C. (1987) Sample Thickness Dependence of Minority Carrier Lifetimes Measured Using an ac Photovoltaic Method. Japanese Journal of Applied Physics, 26, 2033-2036. https://doi.org/10.1143/JJAP.26.2033 |

[43] |
Chenvidhya, D., Kirtikara, K. and Jivacate, C. (2003) A New Characterization Method for Solar Cell Dynamic Impedance. Solar Energy Materials & Solar Cells, 80, 459-464. https://doi.org/10.1016/j.solmat.2003.06.011 |

[44] |
Fossum, J.G. and Lee, D.S. (1952) A Physical Model for the Dependence of Carrier Lifetime on Doping Density in Non-Degenerate Silicon. Solid-State Electronics, 15, 741-747. https://doi.org/10.1016/0038-1101(82)90203-9 |

[45] |
Diop, M., Ba, H., Thiam, N., Diatta, I., Traore, Y., Ba, M., Sow, E., Mballo, O. and Sissoko, G. (2019) Surface Recombination Concept as Applied to Determinate Silicon Solar Cell Base Optimum Thickness with Doping Level Effect. World Journal of Condensed Matter Physics, 9, 102-111. https://doi.org/10.4236/wjcmp.2019.94008 |

[46] |
Lemine, M., Cheikh, O., Seibou, B., Abderrahim, M., Moujtaba, O.E., Faye, K., Wade, M. and Sissoko, G. (2015) Study of Base Doping Rate Effect on Parallel Vertical Junction Silicon Solar Cell under Magnetic Field. International Journal of Engineering Trends and Technology, 19, 44-55. http://www.ijettjournal.org https://doi.org/10.14445/22315381/IJETT-V19P210 |

[47] |
Richard, M., Ibrahima, L., Mamadou, W., Ibrahima, D., Marcel, S.D., Youssou, T., Mor, N., Seni, T. and Grégoire, S. (2017) Minority Carrier Diffusion Coefficient D*(B, T): Study in Temperature on a Silicon Solar Cell under Magnetic Field. Energy and Power Engineering, 9, 1-10. http://www.scirp.org/journal/epe |

[48] |
Seydina, D., Mor, N., Ndeye, T., Youssou, T., Mamadou, L.B., Ibrahima, D., Marcel, S.D., Oulimata, M., Amary, T. and Grégoire, S. (2019) Influence of Temperature and Frequency on Minority Carrier Diffusion Coefficient in a Silicon Solar Cell Under Magnetic Field. Energy and Power Engineering, 11, 355-361. https://doi.org/10.4236/epe.2019.1110023 |

[49] |
Dieng, A., Zerbo, I., Wade, M., Maiga, A.S. and Sissoko, G. (2011) Three-Dimensional Study of a Polycrystalline Silicon Solar Cell: The Influence of the Applied Magnetic Field on the Electrical Parameters. Semiconductor Science and Technology, 26, Article ID: 095023. https://doi.org/10.1088/0268-1242/26/9/095023 |

[50] |
Loum, K., Sow, O., Diop, G., Mane, R., Diatta, I., Ndiaye, M., Gueye, S., Thiame, M., Wade, M. and Sissoko, G. (2023) AC Back Surface Recombination Velocity as Applied to Optimize the Base Thickness under Temperature of an (n+-p-p+) Bifacial Silicon Solar Cell, Back Illuminated by a Light with Long Wavelength. World Journal of Condensed Matter Physics, 13, 40-56. https://doi.org/10.4236/wjcmp.2023.131003 |

[51] | Diop, G., Mane, R., Diatta, I., Loum, K., Gueye, S., Thiame, M., Sow, O., Wade, M. and Sissoko, G. (2022) Optimization of the Base Thickness of an (n+/p/p+) Bifacial Silicon Solar Cell Illuminated from the Back Side, Using Short-Wavelength Light: Resonance Effect on the Diffusion Coefficient in Temperature under Applied Magnetic Field. Journal of Chemical, Biological and Physical Sciences, 13, 38-52. |

[52] |
Cuevas, A., Sinton, R.A. and King, R.R. (1991) A Technology-Based Comparison between Two-Sided and Back-Contact Silicon Solar Cells. Proceedings of the 10th European Photovoltaic Solar Energy Conference, Lisbon, 8-12 April 1991, 23-26. https://doi.org/10.1007/978-94-011-3622-8_6 |

[53] |
Meier, D.L., Hwang, J.-M. and Campbell, R.B. (1988) The Effect of Doping Density and Injection Level on Minority Carrier Lifetime as Applied to Bifacial Dendritic Web Silicon Solar Cells. IEEE Transactions on Electron Devices, 35, 70-79. https://doi.org/10.1109/16.2417 |

[54] |
Jain, G.C., Singh, S.N. and Kotnala, R.K. (1983) Diffusion Length Determination in n+-p+-p+ Structure Based Silicon Solar Cells from the Intensity Dependence of the Short-Circuit Current for Illumination from the p+ Side. Solar Cells, 8, 239-248. https://doi.org/10.1016/0379-6787(83)90063-7 |

[55] |
Uematsu, T., Tsutsui, K., Yazawa, Y., Warabisako, T., Araki, I., Eguchi, Y. and Joge, T. (2003) Development of Bifacial PV Modules for New Applications of Flat-Plate Modules. Solar Energy Materials and Solar Cells, 75, 557-566. https://doi.org/10.1016/S0927-0248(02)00197-6 |

[56] |
Zhou, C.Z., Verlinden, P.J., Crane, R.A., Swanson, R.M. and Sinton, R.A. (1997) 21.9% Efficient Silicon Bifacial Solar Cells. Conference Record of the Twenty Sixth IEEE Photovoltaic Specialists Conference-1997, Anaheim, 29 September-3 October 1997, 287-290. https://doi.org/10.1109/PVSC.1997.654085 |

[57] |
Dione, G.N., Hamet, Y.B.A., Diop, G., Ndiaye, M., Diatta, I., Loum, K., Traore, Y., Thiame, M., Sow, O., Wade, M. and Gregoire, S. (2022) Bifacial (n+-p-p+) Silicon Solar Cell Base Thickness Optimization, While Illuminated by the Rear Face with Monochromatic Light of Short Wavelenths. International Journal of advanced Research (IJAR), 10, 409-418. https://doi.org/10.21474/IJAR01/15372 |

[58] |
Green, M.A. and Keevers, M. (1995) Optical Properties of Intrinsic Silicon at 300K. Progress in Photovoltaics, 3, 189-192. https://doi.org/10.21474/IJAR01/15372 |

[59] |
Rajman, K., Singh, R. and Shewchun, J. (1979) Absorption Coefficient for Solar Cell Calculations. Solid-State Electronics, 22, 793-795. https://doi.org/10.1016/0038-1101(79)90128-X |

[60] | Sissoko, G., Sivoththanam, S., Rodot, M. and Mialhe, P. (1992) Constant Illumination-Induced Open Circuit Voltage Decay (CIOCVD) Method, as Applied to High Efficiency Si Solar Cells for Bulk and Back Surface Characterization. Proceedings of 11th European Photovoltaic Solar Energy Conference and Exhibition, Montreux, 12-16 October 1992, 352-354. |

[61] | Diasse, O., Sam, R.S., Diallo, H.L., Ndiaye, M., Thiam, N., Mbodji, S. and Sissoko, G. (2012) Solar Cell’s Classification by the Determination of the Specific Values of the Back Surface Recombination Velocities in Open Circuit and Short-Circuit Operating Conditions. International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), 1, 18-23. |

[62] |
Joardar, K., Dondero, R.C. and Schroda, D.K. (1989) A Critical Analysis of the Small-Signal Voltage-Decay Technique for Minority-Carrier Lifetime Measurement in Solar Cells. Solid State Electronics, 32, 479-483. https://doi.org/10.1016/0038-1101(89)90030-0 |

[63] |
Sylla, B.D.D., Ly, I., Sow, O., Dione, B., Traore, Y. and Sissoko, G. (2018) Junction Surface Recombination Concept as Applied to Silicon Solar Cell Maximum Power Point Determination Using Matlab/Simulink: Effect of Temperature. Journal of Modern Physics, 9, 172-188. http://www.scirp.org/journal/jmp https://doi.org/10.4236/jmp.2018.92011 |

[64] |
Ly, I., Ndiaye, M., Wade, M., Thiam, N., Sega, G. and Siaaoko, G. (2013) Sissoko Concept of Recombination Velocity Sfcc at the Junction of a Bifacial Silicon Solar Cell, in Steady State, Initiating the Short-Circuit Condition. Journal of Applied Sciences, Engineering and Technology, 5, 203-208. https://doi.org/10.19026/rjaset.5.5105 |

[65] | Loum, K., Diop, G., Diatta, I., Mane, R., Ndiaye, M., Traore, Y., Gueye, S., Thiame, M., Sow, O., Wade, M. and Sissoko. G. (2023) Derivative of AC Back Surface Recombination Velocity as Applied to (n+-p-p+) Silicon Solar Cell Optimum Base Thickness Determination: Effect of both Temperature and Frequency. Journal of Chemical, Biological and Physical Sciences, 13, 139-151. |

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