The modelling and determination of the geometric parameters of a solar cell are important data, which influence the evaluation of its performance under specific operating conditions, as well as its industrial development for a low cost. In this work, an n+/p/p+ crystalline silicon solar cell is studied under monochromatic illumination in modulation and placed in a constant magnetic field. The minority carriers’ diffusion coefficient (D(ω, B), in the (p) base leads to maximum values (Dmax) at resonance frequencies (ωr). These values are used in expressions of AC minority carriers recombination velocity (Sb(Dmax, H)) in the rear of the base, to extract the optimum thickness while solar cell is subjected to these specific conditions. Optimum thickness modelling relationships, depending respectively on Dmax, ωr and B, are then established, and will be data for industrial development of low-cost solar cells for specific use.
References
[1]
Rosling, M., Bleichner, H., Mundqvist, M. and Nordlander, E. (1992) A Novel Technique for the Simultaneous Measurement of Ambipolar Carrier Lifetime and Diffusion Coefficient in Silicon. Solid-State Electronics, 35, 1223-1227. https://doi.org/10.1016/0038-1101(92)90153-4
[2]
Dhariwal, S.R. and Vasu, N.K. (1981) A Generalized Approach to Lifetime Measurement in pn Junction Solar Cells. Solid-State Electronics, 24, 915-927. https://doi.org/10.1016/0038-1101(81)90112-X
[3]
Vardanyan, R.R., Kerst, U., Wawer, P., Nell, M.E. and Wagemann, H.G. (1998) Method for Measurement of All Recombination Parameters in the Base Region of Solar Cells. 2nd World Conference and Exhibition on Photovoltaic Solar Energy Conversion, Vienna, 191-193.
[4]
Zondervan, A., Verhoef, L.A. and Lindholm, F.A. (1988) Measurement Circuits for Silicon-Diode and Solar Cells Lifetime and Surface Recombination Velocity by Electrical Short-Circuit Current Delay. IEEE Transactions on Electron Devices, 35, 85-88. https://doi.org/10.1109/16.2419
[5]
Lindholm, F.A., Liou, J.J., Neugroschel, A. and Jung, T.W. (1987) Determination of Lifetime and Surface Recombination Velocity of p-n Junction Solar Cells and Diodes by Observing Transients. IEEE Transactions on Electron Devices, 34, 277-283. https://doi.org/10.1109/T-ED.1987.22919
[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]
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
[8]
Sissoko, G., Nanema, E., Correa, A., Adj, M., Ndiaye, A.L. and Diarra, M.N. (1998) Recombination Parameters Measurement in Double Sided Surface Field Solar Cell. Proceedings of World Renewable Energy Conference, Florence, 1856-1859.
[9]
Sharma, S.K., Singh, S.N., Chakravarty, B.C. and Das, B.K. (1986) Determination of Minority-Carrier Diffusion Length in a p-Silicon Wafer by Photocurrent Generation Method. Journal of Applied Physics, 60, 3550-3552. https://doi.org/10.1063/1.337610
[10]
Betser, Y., Ritter, D., Bahir, G., Cohen, S. and Serling, J. (1995) Measurement of the Minority Carrier Mobility in the Base of Heterojunction Bipolar Transistors Using a Magneto Transport Method. Applied Physics Letters, 67, 1883-1884. https://doi.org/10.1063/1.114364
[11]
Patrick De Visschere Comment on G. J. REES (1986) Surface Recombination Velocity—A Useful Concept? Solid-State Electronics, 29, 1161-1165. https://doi.org/10.1016/0038-1101(86)90059-6
[12]
Jain, S.C., Agarwal, S.K. and Harsh (1983) Importance of Emitter Recombination in Interpretation of Reverse Recovery Experiments at High Injections. Journal of Applied Physics, 54, 3618-3619. https://doi.org/10.1063/1.332400
[13]
Ray, U.C. and Agarwal, S.K. (1988) Wavelength Dependence of Short-Circuit Current Decay in Solar Cells. Journal of Applied Physics, 63, 547-549. https://doi.org/10.1063/1.340084
[14]
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
[15]
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.
[16]
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.
[17]
Joardar, K., Dondero, R.C. and Schroder, 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
[18]
Fossum, J.G. (1977) Physical Operation of Back-Surface-Field Silicon Solar Cells. IEEE Transactions on Electron Devices, 2, 322-325. https://doi.org/10.1109/T-ED.1977.18735
[19]
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
[20]
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
[21]
Dugas, J. (1994) 3D Modelling of a Reverse Cell Made with Improved Multicrystalline Silicon Wafers. Solar Energy Materials and Solar Cells, 32, 71-88. https://doi.org/10.1016/0927-0248(94)90257-7
[22]
Donalato, C. (1994) Reciprocity Theorem for Charge Collection by a Surface with Finite Collection Velocity: Application to Grain Boundaries. Journal of Applied Physics, 76, 959-966. https://doi.org/10.1063/1.357774
[23]
Van Steenwinkel, R., Carotta, M.C., Martinelli, G., Merli, M., Passari, L. and Palmeri, D. (1990) Lifetime Measurement in Solar Cells of Various Thicknesses and the Related Silicon Wafers. Solar Cells, 28, 287-292. https://doi.org/10.1016/0379-6787(90)90063-B
[24]
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
[25]
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. 10th European Photovoltaic Solar Energy Conference, Lisbon, 8-12 April 1991, 66-67. https://doi.org/10.1007/978-94-011-3622-8_17
[26]
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
[27]
Traore, Y., Thiam, N., Thiame, M., Thiam, A., Lamine Ba, M., 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
[28]
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
[29]
Dieng, M., Seibou, B., Ibrahima, L.Y., Diouf, M.S., Wade, M. and Sissoko, G. (2017) Silicon Solar Cell Emitter Extended Space Charge Region Determination under Modulated Monochromatic Illumination by Using Gauss’s Law. International Journal of Innovative Technology and Exploring Engineering, 6, 17-20.
[30]
Terheiden, B., Terheiden, G., Hahn, P., et al. (2000) The Lamella Silicon Solar Cell. Proc. 16th European Photovoltaic Solar Energy Conference, Glasgow, 1-5 May 2000, 1377-1380.
[31]
Gaubas, E. and Vanhellemont, J. (1996) A Simple Technique for the Separation of Bulk and Surface Recombination Parameters in Silicon. Journal of Applied Physics, 80, 6293-6974. https://doi.org/10.1063/1.363705
[32]
Bordin, N., Kreinin, L. and Eisenberg, N. (2001) Determination of Recombination Parameters of Bifacial Silicon Cells with a Two Layer Step-Liked Effect Distribution in the Base Region. Proc. 17th European PVSEC, Munich, 1495-1498.
[33]
Jung, T.-W., Lindholm, F.A. and Neugroschel, A. (1984) Unifying View of Transient Responses for Determining Lifetime and Surface Recombination Velocity in Silicon Diodes and Back-Surface-Field Solar Cells, with Application to Experimental Short-Circuit-Current Decay. IEEE Transactions on Electron Devices, 31, 588-595. https://doi.org/10.1109/T-ED.1984.21573
[34]
Gupta, S., Ahmed, F. and Garg, S. (1988) A Method for the Determination of the Material Parameters D, Lo, S and from Measured A.C. Short-Circuit Photocurrent. Solar Cells, 25, 61-72. https://doi.org/10.1016/0379-6787(88)90058-0
[35]
Flohr, Th. 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
[36]
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
[37]
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
[38]
Ly Diallo, H., Wade, M., Ly, I., et al. (2012). 1D Modeling of a Bifacial Silicon Solar Cell under Frequency Modulation, Monochromatic Illumination: Determination of the Equivalent Electrical Circuit Related to the Surface Recombination Velocity. Research Journal of Applied Sciences, Engineering and Technology, 4, 1672-1676. http://www.maxwell.org
[39]
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
[40]
Cardona, M. (1969) Solid State Physics. Supplement 11, Modulation Spectroscopy. Academic Press, New York.
[41]
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
[42]
Diouf, S., Ndiaye, M., Thiam, N., Traore, Y., Lamine Ba, M., Diatta, I., Diouf, M.S., Mballo, O., Thiam, A., Ly, I. and Sissoko, G. (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://www.scirp.org/journal/epe https://doi.org/10.4236/epe.2019.1110023
[43]
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
[44]
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.
[45]
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, 298-301.
[46]
Thiam, Nd., 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. https://doi.org/10.19026/rjaset.5.4825
[47]
Ndiaye, A., Gueye, S., Sow, O., Diop, G., Ba, A., Ba, M., Diatta, I., Habiboullah, L. and Sissoko, G. (2020) A.C. Recombination Velocity as Applied to Determine n+/p/p+ Silicon Solar Cell Base Optimum Thickness. Energy and Power Engineering, 12, 543-554.
[48]
Diop, G., Gueye, S., Sow, O., Mamour, A., Lamine, M., Diatta, I. and Sissoko, G. (2020) Ac Composite Back Surface Recombination Velocity as Applied to n+/p/p+ Silicon Solar Cell Optimum Thickness Base Determination. International Journal of Advanced Research, 8, 580-587. https://doi.org/10.21474/IJAR01/11695
[49]
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
[50]
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://doi.org/10.4236/jemaa.2020.124005 https://www.scirp.org/journal/paperinformation.aspx?paperid=99976
[51]
Nam, L.Q., Rodot, M., Ghannam, M., Cppye, J., 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
[52]
Kunst, M., Muller, G., Schmidt, R. and Wetzel, H. (1988) Surface and Volume Decay Processes in Semiconductors Studied by Contactless Transient Photoconductivity Measurements. Applied Physics, 46, 77-85. https://doi.org/10.1007/BF00615912
[53]
Kraner, H.W. (1983) Radiation in Silicon Detectors. 2nd Pisa Meeting in Advanced Detectors, Grosseto, 3-7 June 1983, 1-8.
[54]
Mane, R., Ly, I., Wade, M., Datta, I., Douf, M.S., Traore, Y., Ndiaye, M., Tamba, S. and Sissoko, G. (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 https://doi.org/10.4236/epe.2017.91001
[55]
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 Cell under Frequency Modulation and Radiation. Journal of Applied Mathematics and Physics, 3, 1522-1535. http://www.scirp.org/journal/jamp https://doi.org/10.4236/jamp.2015.311177
[56]
Dede, M.M.S., Ndiaye, M., Gueye, S., Ba, M.L., Diatta, I., Diouf, M.S., Sow, E.H., Ba, A.M., Diop, M. and Sissoko, G. (2020) Optimum Base Thickness Determination Technique as Applied to n/p/p+ Silicon Solar Cell under Short Wavelengths Monochromatic Illumination. International Journal of Innovation and Applied Studies, 29, 576-586. http://www.ijias.issr-journals.org
[57]
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.
[58]
Mohamed, N.M.M.O., Sow, O., Gueye, S., Traore, Y., Diatta, I., Thiam, A., Ba, M.A., Mane, R., Ly, I. and Sissoko, G. (2019) Influence of Both Magnetic Field and Temperature on Silicon Solar Cell Base Optimum Thickness Determination. Journal of Modern Physics, 10, 1596-1605. https://www.scirp.org/journal/jmp https://doi.org/10.4236/jmp.2019.1013105
[59]
Ely, M.M., Thiam, N., Ndiaye, M., Traore, Y., Mane, R., Sow, E., Mballo, O., Dieng, M.S., Sarr, C.T., Ly, I. and Sissoko, G. (2020) Surface Recombination Velocity Concept as Applied to Determinate Back Surface Illuminated Silicon Solar Cell Base Optimum Thickness, under Temperature and External Magnetic Field Effects Journal of Scientific and Engineering Research, 7, 69-77.
[60]
Diop, M.S., Ba, H.Y., Thiam, N., Diatta, I., Traore, Y., Lamine Ba, M., 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://doi.org/10.4236/wjcmp.2019.94008
[61]
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
[62]
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
[63]
Mballo, O., Seibou, B., Wade, M., Diouf, M.S., Ly, I., Tamba, S. and Sissoko, G. (2016) Influence of the Depth Base on the Electrical Parameters of a Parallel Vertical Junction Silicon Solar Cell under Polychromatic Illumination. International Journal of Electrical Engineering, 4, 6-16.
[64]
Diallo, M.M., Seibou, B., Ba, H.Y., Zerbo, I. and Sissoko, G. (2014) One-Dimensional Study of a Bifacial Silicon Solar Cell Illuminated from the Front Surface by a Monochromatic Light under Frequency Modulation: Influence of Irradiation and Damage Coefficient. Current Trends in Technology and Sciences, 3, 416-421.
[65]
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
