A.C. Recombination Velocity as Applied to Determine n+/p/p+ Silicon Solar Cell Base Optimum Thickness

Amadou Mar Ndiaye^{1},
Sega Gueye^{1},
Ousmane Sow^{2},
Gora Diop^{1},
Amadou Mamour Ba^{1},
Mamadou Lamine Ba^{1},
Ibrahima Diatta^{1},
Lemrabott Habiboullah^{3},
Gregoire Sissoko^{1}

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1. Introduction

Expressions of the recombination velocity of the minority carriers in the back (p/p^{+}) from the base of the n^{+}/p/p^{+} silicon solar cell [1] under constant monochromatic illumination [2] [3] were obtained through the study of the photocurrent versus the carrier’s recombination velocity at the junction [4]. These expressions are dependent on the minority carriers diffusion coefficient (D) [5] and diffusion length (L) [6] [7], as well as the monochromatic absorption coefficient α(λ) [8] in the silicon material.

Earlier theoretical and experimental works, on semiconductors or on solar cells, using a frequency modulation signal [9] - [15], have helped to determine:

1) phenomelogical parameters (lifetime, diffusion coefficient-mobility, surface recombination velocity) in different regions of the material taking into account the signal penetration depth [16], associated with the distribution of defects [17] [18] [19].

2) the parameters of the equivalent electrical model (conductance and capacitance) through Boode and Nyquist diagram technique [20] [21] [22] [23] [24].

This work is based on the ac technique, through new expressions of minority carrier recombination velocity (ac Sb) [25] [26] [27] [28] [29] at the back surface of the base under monochromatic illumination (α(λ)) in frequency modulation, depending on the complex parameters, such as D(ω) and L(ω) [11] [12] [13] [25] [26] [29].

The thickness of the different parts of the solar cell [30] [31] especially the base, has been the subject of theoretical and experimental investigations on samples of different thicknesses [32] [33] [34] [35] in order to optimize the efficiency of photo conversion [36], by the economy of material entering its industrial development.

The technique of determining the optimum thickness of the base is applied in this study to an n^{+}/p/p^{+} silicon solar cell [31] [34] [37] illuminated by the (n^{+}) surface, and leads to a new expression of Hopt according to the frequency.

2. Theoretical Model

The structure of the n^{+}-p-p^{+} silicon solar cell [1] under modulated monochromatic illumination on the (n^{+}) side is represented by Figure 1.

The excess minority carriers’ density $\delta \left(x,t\right)$ generated in the base of the solar cell obeying to the continuity equation under modulated monochromatic illumination, is then given by [38] [39]:

Figure 1. Structure of n^{+}/p/p^{+} silicon solar cell.

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

The expression of the excess minority carrier’s 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)

The modulated carrier generation rate $G\left(x,\alpha ,\omega ,t\right)$ is given by the relationship:

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

with the coordinate dependent generation rate:

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

where:

I_{0}(λ) is the incident monochromatic light intensity.

R and α are respectively the reflection coefficient and absorption coefficient for silicon material at wavelength (λ) [3] [7] [8].

$D\left(\omega \right)$ is the complex diffusion coefficient of excess minority carrier in the base. Its expression is given by the relationship [9] [11] [12] [13] [29]:

$D\left(\omega \right)={D}_{0}\times \left(\frac{1-j\cdot {\omega}^{2}\cdot {\tau}^{2}}{1+{\left(\omega \tau \right)}^{2}}\right)$ (5)

D_{0} is the excess minority carrier diffusion in the base under steady.

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

$\frac{{\partial}^{2}\delta \left(x,\omega \right)}{\partial {x}^{2}}-\frac{\delta \left(x,\omega \right)}{{L}^{2}\left(\omega \right)}=-\frac{g\left(x\right)}{D\left(\omega \right)}$ (8)

$L\left(\omega \right)$ is the complex diffusion length of excess minority carriers in the base given by:

$L\left(\omega \right)=\sqrt{\frac{D\left(\omega \right)\tau}{1+j\omega \tau}}$ (9)

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

The solution of Equation (8) is:

$\delta \left(x,\omega \right)=A\cdot \mathrm{cosh}\left[\frac{x}{L\left(\omega \right)}\right]+B\cdot \mathrm{sinh}\left[\frac{x}{L\left(\omega \right)}\right]+K\cdot {\text{e}}^{-\alpha \cdot x}$ (10)

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

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

Coefficients A and B are determined through the boundary conditions:

■ At the junction (x = 0)

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

■ On the back side in the base (x = H)

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

Sf and Sb are respectively the recombination velocities of the excess minority carriers at the junction and at the back surface. The recombination velocity Sf reflects the charge carrier velocity of passage at the junction, in order to participate in the photocurrent. It is then imposed by the external load which fixes the solar cell operating point [2] [29]. It has an intrinsic component which represents the carrier losses associated with the shunt resistor in the solar cell electrical equivalent model [39] [40]. The excess minority carrier recombination velocity Sb on the back surface is associated with the presence of the p^{+} layer which generates an electric field for throwing back the charge carrier toward the junction [2] [41].

3. Results and Discussions

3.1. Ac Excess Minority Carrier Density

Excess minority carrier density is plotted versus depth in the base, for given illumination modulated frequency (ω) with large wavelength (giving rise to weak α(λ) for silicon), while the solar cell is under short circuit condition (large Sf values) (Figure 2).

3.2. Photocurrent Density

From the density of minority carriers in the base, the ac photocurrent density at the junction is given by the following expression:

${J}_{ph}\left(Sf,Sb,\omega \right)=qD\left(\omega \right){\frac{\partial \delta \left(x,Sf,Sb,\omega \right)}{\partial x}|}_{x=0}$ (14)

where q is the elementary electron charge.

Figure 3 shows ac photocurrent versus the junction surface recombination velocity for different frequency. As junction’s recombination velocity indicates solar cell operating point, ac photocurrent is weak for low Sf values i.e. open circuit. And at large Sf values, the ac photocurrent reaches flat region assimilate to short circuit current which decrease decreases with frequency.

3.3. Back Surface Recombination Velocity

Photocurrent density versus minority carriers recombination velocity at the junction, shows a bearing sets up and corresponds to the short-circuit current density (Jphsc), for very large Sf. For this junction recombination velocity interval, it then comes [2] [27] [39] [41]:

Figure 2. Excess minority carrier density versus base depth for different frequencies (D_{0} = 35 cm; α = 6.2 cm^{−1}).

Figure 3. Module of photocurrent density versus recombination velocity for different frequency (D = 35 cm; α = 6.2 cm^{−1}).

${\frac{\partial {J}_{ph}\left(Sf,Sb,\omega ,T\right)}{\partial Sf}|}_{Sf\ge {10}^{5}\text{cm}\cdot {\text{s}}^{-1}}=0$ (15)

The solution of Equation (15) gives the ac recombination velocity expressions in the back surface through Equation (16) and Equation (17):

$Sb1\left(\omega \right)=-\frac{D\left(\omega \right)}{L\left(\omega \right)}\cdot \mathrm{tanh}\left(\frac{H}{L\left(\omega \right)}\right)$ (16)

$Sb2\left(\omega ,\lambda \right)=\frac{D\left(\omega \right)}{L\left(\omega \right)}\cdot \left[\frac{\alpha \left(\lambda \right)\cdot L\left(\omega \right)\cdot \left(\mathrm{exp}\left(-\alpha \left(\lambda \right)\cdot H\right)-\mathrm{cosh}\left(\frac{H}{L\left(\omega \right)}\right)+\mathrm{sinh}\left(\frac{H}{L\left(\omega \right)}\right)\right)}{\mathrm{exp}\left(-\alpha \left(\lambda \right)\cdot H\right)-\mathrm{cosh}\left(\frac{H}{L\left(\omega \right)}\right)+\alpha \left(\lambda \right)\cdot L\left(\omega \right)\cdot \mathrm{sinh}\left(\frac{H}{L\left(\omega \right)}\right)}\right]$ (17)

3.4. Optimum Thickness Determination Technique

This technique is based on the results of the calculation of the photocurrent through the two emitters of a parallel vertical junction silicon solar cell [42].

Figure 4 gives the representation of the two back surface recombination velocities versus thickness of the base of the solar cell for different frequency, in order to determine the optimum thickness of the base.

Figure 5 allows us to model the optimum thickness through the following mathematical expression, for a low value of α(λ):

${H}_{op}\left(\text{cm}\right)=-3\times {10}^{-13}\times {\omega}^{2}-2.9\times {10}^{-8}\times \omega \left(\text{rad}\cdot {\text{s}}^{-1}\right)+0.015$

For the large wavelengths of incident light, corresponding to the low values of the silicon absorption coefficient α(λ), minority carriers are generated in depth from the base [7] [8]. The optimum thickness (Hopt) obtained in static (low modulation frequency, i.e. $\omega \tau \ll \text{1}$ ) is therefore large. As the modulation frequency increases, the density of the generated carriers decreases and is folded back to the junction [27], the optimum thickness (Hopt) decreases (in dynamic state, i.e. $\omega \tau \gg \text{1}$ ). Figure 6 gives the optimum thickness of the base according to the diffusion coefficient D(ω) Equation (5) [9] [10] [11] [13]

The optimum thickness is a growing right according to the diffusion coefficient, modeled by the following relationship:

${H}_{op}\left(\text{cm}\right)=3.1\times {10}^{-4}\times D\left(\text{cm}\cdot {\text{s}}^{-2}\right)+0.004$ (19)

Several works have produced a relationship giving Hopt thickness, depending on the D coefficient, which in turn can be expressed according to external parameters. These are the works giving Hopt variations with:

table_table_table

Figure 4. Sb1 and Sb2 versus depth in the base for different frequency (D = 35 cm; α = 6.2 cm^{−1}).

Figure 5. Optimum thickness versus pulsation.

Figure 6. Optimum thickness versus diffusion coefficient.

- The base’s doping rate (Nb) [43].

- The magnetic field applied to vertical junction series silicon solar cell [44].

- The magnetic field applied to front illuminated (n^{+}-p-p^{+}) silicon solar cell [45].

- The magnetic field and temperature applied to front illuminated (n^{+}-p-p^{+}) silicon solar cell [46].

- The temperature [47].

- The flow of electrical charge particles irradiating the (n^{+}-p-p^{+}) silicon solar cell [48] [49].

- The monochromatic absorption coefficient of the material (Si) [50].

Each value of the diffusion coefficient must correspond to an elaborated silicon solar cell, with Hopt its base optimum thickness. The diffusion coefficient of the minority carriers then imposes the thickness to be chosen for the manufacture of a high-performance solar cell. Thus low diffusion coefficients require low thicknesses to produce an important photocurrent, therefore a better efficiency.

4. Conclusions

The ac recombination velocity at the back surface of the n^{+}/p/p^{+} silicon solar cell was used to determine the optimum thickness of the base for long wavelengths of modulated incident light.

The light penetration depth at low monochromatic absorption coefficient values reduced the relaxation effect of photogenerated carriers, resulting in a small decrease of Hopt with frequency, through the expression of its modeling.

References

[1] 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

[2] Sissoko, G., Museruka, C., Corréa, A., Gaye, I. and Ndiaye, A.L. (1996) Light Spectral Effect on Recombination Parameters of Silicon Solar Cell. Renewable Energy, 3, 1487-1490.

[3] Antilla O.J. and Hahn S.K. (1993) Study on Surface Photovoltage Measurement of Long Diffusion Length Silicon: Simulation Results. Journal of Applied Physics, 74, 558-569.

https://doi.org/10.1063/1.355343

[4] 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. 11th European Photovoltaic Solar Energy Conference and Exhibition, Montreux, 12-16 October 1992, 352-354.

[5] Gupta, S., Feroz, A. and Garg, S. (1988) A Method for the Determination of the Material Parameters τ, D, Lo, 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

[6] Stokes, E.D. and Chu, T.L. (1977) Diffusion Lengths in Solar Cells from Short-Circuit Current Measurements. Applied Physics Letters, 30, 425-426.

https://doi.org/10.1063/1.89433

[7] Saritas, M. and Mckell, H.D. (1988) Comparison of Minority Carrier Diffusion Length Measurements in Silicon by the Photoconductive Decay and Surface Photovoltage Methods. Journal of Applied Physics, 63, 4561-4567.

https://doi.org/10.1063/1.340155

[8] Rajkanan, K., Singh, R. and Schewchun, J. (1979) Absorption Coefficient of Silicon for Solar Cell Calculations. Solidstate Electronics, 22, 793-795.

https://doi.org/10.1016/0038-1101(79)90128-X

[9] Misiakos, K., Wang, C.H., Neugroschel, A. and Lindholm, F.A. (1990) Simultaneous Extraction of Minority-Carrier Parameters in Crystalline Semiconductors by Lateral Photocurrent. Journal of Applied Physics, 67, 321-333.

https://doi.org/10.1063/1.345256

[10] Wang, C.H. and Neugroschel, A. (1991) Minority Carrier Lifetime and Surface Recombination Velocity Measurement by Frequency Domain Photoluminescence. IEEE Transaction on Electron Devices, 38, 2169-2170.

https://doi.org/10.1109/16.83745

[11] Bousse, L., Mostarshed, S. and Hafeman, D. (1994) Investigation of Carrier Transport through Silicon Wafers by Photocurrent Measurements. Journal of Applied Physics, 75, 4000-4008.

https://doi.org/10.1063/1.356022

[12] Diao, A., Thiam, N., Zoungrana, M., Sahin, G., Ndiaye, M. and Sissoko, G. (2014) Diffusion Coefficient in Silicon Solar Cell with Applied Magnetic Field and under Frequency: Electric Equivalent Circuits. World Journal of Condensed Matter Physics, 4, 84-92.

https://doi.org/10.4236/wjcmp.2014.42013

[13] Ward, M.A.A. and Lee, K.T. (1989) Combined AC Photocurrent and Photothermal Reflectance Response Theory of Semiconducting p-n Junctions. Journal of Applied Physics, 66, 5572-5583.

https://doi.org/10.1063/1.343662

[14] Grauby, S., Forget, B.C., Hole, S. and Fournier, D. (1999) High Resolution Photothermal Imaging of High Frequency Phenomena Using a Visible Charge Coupled Device Camera Associated with a Multichannel Lock-In Scheme. Review of Scientific Instruments, 70, 3603-3608. https://doi.org/10.1063/1.1149966

[15] Bonham, D.B. and Orazem, M.E. (1988) A Mathematical Model for the AC Impedance of Semiconducting Electrodes. AIChE Journal, 34, 465-473.

https://doi.org/10.1002/aic.690340314

[16] Ritter, D., Weiser, K. and Zeldov, E. (1987) Steady-State Photocarrier Grating Technique for Diffusion-Length Measurement in Semiconductors: Theory and experimental Results for Amorphous Silicon and Semi-Insulating GaAs. Journal of Applied Physics, 62, 4563-4570.

https://doi.org/10.1063/1.339051

[17] Herberholz, R., Igalson, M. and Schock, H.W. (1998) Distinction between Bulk and Interface States in CuInSe2/CdS/ZnO by Space Charge Spectroscopy. Journal of Applied Physics, 83, 318-325.

https://doi.org/10.1063/1.366686

[18] Longeaud, C. and Kleider, J.P. (1996) Density of States and Capture Cross-Sections in Annealed and Light-Soaked Hydrogenated Amorphous Silicon Layers. Journal of Non-Crystalline Solids, 198, 355-358.

https://doi.org/10.1016/0022-3093(95)00707-5

[19] Carstensen, J., Popkirov, G., Bahr, J. and Föll, H. (2003) CELLO: An Advanced LBIC Measurement Technique for Solar Cell Local Characterization. Solar Energy Material and Solar Cells, 76, 599-611.

https://doi.org/10.1016/S0927-0248(02)00270-2

[20] Anil Kumar, R., Suresh, M.S. and Nagaraju, J. (2001) Measurement of AC Parameters of Gallium Arsenide (GaAs/Ge) Solar Cell by Impedance Spectroscopy. IEEE Transaction on Electron Devices, 48, 2177-2179.

https://doi.org/10.1109/16.944213

[21] Streever, R.L., Breslin, J.T. and Ahlstron, E.H. (1980) Surface States at the n-GaAs-SiO2 Interface from Conductance and Capacitance Measurements. Solid State Electronics, 23, 863-868.

https://doi.org/10.1016/0038-1101(80)90103-3

[22] Vanmaekelbergh, D. and Cardon, F. (1992) Recombination in Semiconductor Electrodes Investigation by the Electrical Impedance. Electrochimica Acta, 37, 837-846.

https://doi.org/10.1016/0013-4686(92)85036-K

[23] Yaron, G. and Frohman-Bentchrowsky, D. (1980) Capacitance Voltage Characterization of Poly Si-SiO2-Si Structures. Solid State Electronics, 23, 433-439.

https://doi.org/10.1016/0038-1101(80)90078-7

[24] Scofield, J.H. (1995) Effects of Series and Inductance on Solar Cell Admittance Measurements. Solar Energy and Solar Cells, 37, 217-233.

https://doi.org/10.1016/0927-0248(95)00016-X

[25] Gueye, M., Diallo, H.L., Moustapha, A.K.M., Traore, Y., Diatta, I. and Sissoko, G. (2018) Ac Recombination Velocity in a Lamella Silicon Solar Cell. World Journal of Condensed Matter Physics, 8, 185-196.

https://doi.org/10.4236/wjcmp.2018.84013

[26] Traore, Y., Thiam, N., Thiame, M., Thiam, A., Ba, M.L., Diouf, M.S., Diatta, I., Mballo, O., Sow, E.H., Wade, M. and Sissoko, G. (2019) AC Recombination Velocity in the Back Surface of a Lamella Silicon Solar Cell under Temperature. Journal of Modern Physics, 10, 1235-1246.

https://www.scirp.org/journal/jmp

https://doi.org/10.4236/jmp.2019.1010082

[27] Zerbo, I., Barro, F.I., Mbow, B., Diao, A., Madougou, S., Zougmore, F. 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.

[28] Thiam, N.D., Diao, A., Ndiaye, M., Dieng, A., Thiam, A., Sarr, M., Maiga, A.S. and Sissoko, G. (2012) Electric Equivalent Models of Intrinsic Recombination Velocities of a Bifacial Silicon Solar Cell under Frequency Modulation and Magnetic Field Effect. Research Journal of Applied Sciences, Engineering and Technology, 4, 4646-4655.

[29] 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

[30] Caleb Dhanasekaran, P. and Gopalam, B.S.V. (1981) Effect of Junction Depth on the Performance of a Diffused n+ p Silicon Solar Cell. Solids-State Electronics, 24, 1077-1080.

https://doi.org/10.1016/0038-1101(81)90172-6

[31] 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

[32] 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

[33] 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. In: Luque, A., Sala, G., Palz, W., Dos Santos, G. and Helm, P., Eds., Tenth E.C. Photovoltaic Solar Energy Conference, Springer, Dordrecht, 66-67.

https://doi.org/10.1007/978-94-011-3622-8_17

[34] Cuevas, A., Sinton, R.A. and King, R.R. (1991) A Technology-Based Comparison between Two-Sided and Back-Contact Silicon Solar Cells. The 10th European Photovoltaic Solar Energy Conference, Lisbon, 8-12 April 1991, 23-26.

[35] Diasse, O., Diao, A., Ibrahima, L.Y., 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

[36] Arab, A.B. (1995) Photovoltaic Properties and High Efficiency of Preferentially Doped Polysilicon Solar Cells. Solids-State Electronics, 38, 1441-1447.

https://doi.org/10.1016/0038-1101(94)00283-L

[37] Nam, L.Q., Rodot, M., Ghannam, M., Cppye, J. and De Schepper, P. and Nijs, 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

[38] Sze, S.M. (1981) Physics of Semiconductor Devices. Wiley, New York.

[39] Sissoko, G., Nanéma, E., Corréa, A., Biteye, P.M., Adj, M. and Ndiaye, A.L. (1998) Silicon Solar Cell Recombination Parameters Determination Using the Illuminated I-V Characteristic. Renewable Energy, 3, 1848-1851.

[40] 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

[41] Diallo, H.L., Seïdou, A., Maiga, 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

[42] Gover, A. and Stella, P. (1974) Vertical Multijunction Solar-Cell One-Dimensional Analysis. IEEE Transactions on Electron Devices, 21, 351-356.

https://doi.org/10.1109/T-ED.1974.17927

[43] Diop, M.S., Ba, H.Y., Thiam, N., Diatta, I., Traore, Y., Ba, M.L., Sow, E.H., 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://www.scirp.org/journal/wjcmp

https://doi.org/10.4236/wjcmp.2019.94008

[44] 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. ARPN Journal of Engineering and Applied Sciences, 14, 4078-4085.

[45] Thiaw, C., Ba, M.L., Ba, M.A., 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://www.scirp.org/journal/jemaa

https://doi.org/10.4236/jemaa.2020.127009

[46] Faye, D., Gueye, S., Ndiaye, M., Ba, M.L., Diatta, I., Traore, Y., Diop, M.S., Diop, G., Diao, A. and Sissoko, G. (2020) Lamella Silicon Solar Cell under Both Temperature and Magnetic Field: Width Optimum Determination. Journal of Electromagnetic Analysis and Applications, 12, 43-55

https://www.scirp.org/journal/paperinformation.aspx?paperid=99976

https://doi.org/10.4236/jemaa.2020.124005

[47] Ndiaye, F.M., Ba, M.L., Ba, M.A., Diop, G., Diatta, I., Sow, E.H., Mballo, O. and Sissoko, G. (2020) Lamella Silicon Optimum Width Determination under Temperature. International Journal of Advanced Research, 8, 1409-1419.

https://doi.org/10.21474/IJAR01/11228

[48] Dia, O., El Moujtaba, M.A.O., Gueye, S., Ba, M.L., Diatta, I., Diop, G., Diouf, M.S. and Sissoko, G. (2020) Optimum Thickness Determination Technique as Applied to a Series Vertical Junction Silicon Solar Cell under Polychromatic Illumination: Effect of Irradiation. International Journal of Advanced Research, 8, 616-626.

https://doi.org/10.21474/IJAR01/10967

[49] 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

[50] Dede, M.M.S., Ba, M.L., Ba, M.A., Ndiaye, M., Gueye, S., Sow, E. H., Diatta, I., Diop, M.S., 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://www.scirp.org/journal/epe

https://doi.org/10.4236/epe.2020.127027