n+-p-p+ Silicon Solar Cell Base Optimum Thickness Determination under Magnetic Field

DOI: 10.4236/jemaa.2020.127009   PDF   HTML   XML   163 Downloads   350 Views   Citations


Base optimum thickness is determined for a front illuminated bifacial silicon solar cell n+-p-p+ under magnetic field. From the magneto transport equation relative to excess minority carriers in the base, with specific boundary conditions, the photocurrent is obtained. From this result the expressions of the carrier’s recombination velocity at the back surface are deducted. These new expressions of recombination velocity are plotted according to the depth of the base, to deduce the optimum thickness, which will allow the production, of a high short-circuit photocurrent. Calibration relationships of optimum thickness versus magnetic field were presented according to study ranges. It is found that, applied magnetic field imposes a weak thickness material for solar cell manufacturing leading to high short-circuit current.

Share and Cite:

Thiaw, C. , Ba, M. , Amadou Ba, 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. doi: 10.4236/jemaa.2020.127009.

1. Introduction

One major problem of silicon solar cells is the small collection of minority charge carriers which may be due among others at short diffusion lengths and carrier’s mobility and surfaces recombination velocity issues. In order to improve its performance, several characterization techniques relating to minority carriers deflection under magnetic field, were presented [1] - [6]. Thus, the structure solar cell studied can be with:

1) horizontal junction (monofacial, bifacial or double side surface field) [7] [8] [9].

2) multiple vertical junction (series or parallel) [10] [11] [12].

The operating conditions are various regimes i.e.: static [13] [14] [15] and dynamic [16] [17] [18] [19]. The phenomenological parameters to be determined are, diffusion length (L), diffusion coefficient (D), lifetime (τ), surface recombination velocities respectively at the junction (Sf) and the rear (Sb) [20] [21] [22] [23] [24]. The imposed both, thickness (H) [25] and doping rate [26] are to be take into account. The applied external conditions such as, radiation flux and energy [27], temperature and magnetic field [28] [29] [30], influence the phenomenological parameters.

In this work, we present a method to determinate the optimum thickness (Hopt) of silicon solar cell under external conditions i.e. magnetic field (B) and polychromatic illumination.

2. Theoretical Study

2.1. Monofacial Solar Cell Presentation

Silicon solar cell type n+/p/p+ [5] subjected to multi spectral illumination and a constant magnetic field (perpendicular to Ox axis), is presented in Figure 1.

2.2. Magnetotransport Equation

The magnetic field influences the movement of minority charge carriers. In this condition the distribution equation relative to minority charge carriers in the base is given as follows [4] [6] [14] [31] [32].


G(x) is the minority carrier’s generation rate [33]


D(B) is the minority carrier’s diffusion coefficient depending on B [25] [28] [31] [34] and D0 is diffusion coefficient without magnetic field.

Figure 1. Front illuminated silicon solar cell structure type n+/p/p+.



L is the minority carrier’s diffusion length B depending and τ their lifetime.

2.3. Solution

The Magnetotransport equation solution is given by following expression for front illumination:


The previous relationship is fully defined, by determining the coefficients E and F, using base boundary conditions, what are junction (i.e. space charge region) and back side (p/p+ surface).

2.4. Boundary Conditions

­ At the junction x = 0:


Sf is excess minority carrier junction recombination velocity and describes the solar cell operating point [35] [36].

­ At back side x = H:


Sb is back surface recombination velocity induced by the back surface field for low high junction (p/p+) and thus minority carriers are pushed back to the junction. The space charge region’s (n+/p) electrical field allows them to be collected and to contribute to the photocurrent [37] [38] [39].

2.5. Photocurrent Density for Different Magnetic Field Values

The excess minority charge carriers collected through junction give photocurrent density obtained from the following Fick relation.


Figure 2 gives the plot of photocurrent density versus minority carrier’s recombination velocity at the junction (Sf).

Regardless of the magnetic field values, the photocurrent increases with the junction recombination (Sf). When junction recombination velocity is high, short circuit photocurrent is obtained, and then, magnetic field reduced by deflection the electric charges due to increased Lorentz force intensity. Thus two study intervals will be defined according to magnetic field B value.

Figure 2. Photocurrent density for large magnetic field values versus junction recombination velocity (in front side H = 200 µm, D = 35 cm2/s).

2.6. Back Surface Recombination Velocity and Optimum Thickness Determination

Otherwise, we note that at high values recombination velocity Sf, photocurrent remains constant and becomes short circuit current Jsc(B, H). So its derivative with respect to Sf, is therefore zero [39]. Solving such an equation gives the new back surface recombination velocity (Sb) expressions, of excess minority carriers, magnetic field dependent.


Equation (9) leads to two expressions of back surface recombination velocity of excess minority charge carriers in the base respectively, Sb1 and Sb2 [24] [39]:



Sb1 electronic parameters dependent (D and L), is designed as intrinsic back surface recombination, while Sb2 also depending of average (composite) absorption coefficient (bi) [33] is considered as extrinsic one.

2.7. The Base Optimum Thickness Determination

The optimum thickness determination technique, already used on solar cells maintained under other conditions [26] [29] [30] [40] [41] [42] [43] is applied here, according to two ranges of magnetic field values. Sb1 and Sb2 are plotted versus H base thickness, for given magnetic values.

1) Low range values:

Figure 3 gives the representation of Sb1 and Sb2 versus H, for given magnetic field values B as:.

For each magnetic field B value, the optimum base thickness (Hopt) is determined by projection on absciss-axis of the intercept point of velocity curves Sb1 and Sb2. Thus the different values are presented in Table 1, and represented on Figure 4, as Hopt versus B.

The correlation between optimum thickness and magnetic field is established below:


with: and

2) Large range values:

Figure 5 shows Sb1 and Sb2 versus thickness H, for the second range of magnetic field B values:.

The previous technique is used to determine the numerical optimum thickness (Hopt) value of the base. Thus the different values are presented in Table 2. Figure 6, gives the obtained Hopt values representation versus B.

Figure 3. Back surface recombination velocity versus solar cell base thickness for different magnetic field values.

Table 1. Optimum thickness (Hopt) for different magnetic field (B) values.

Table 2. Optimum thickness (Hopt) for different magnetic field (B) values.

Figure 4. Optimum thickness Hop of base versus magnetic field.

Figure 5. Back surface recombination velocity versus thickness base for different values magnetic field.

The correlation between optimum thickness and magnetic field is established below:

Figure 6. Optimum thickness Hop versus magnetic field B.


with: and

The results obtained by the application of the optimum thickness determination technique, show here, a thickness decrease with the magnetic field, for the two magnetic field ranges. This means that Lorentz’s strength increases with the magnetic field imposes lower thicknesses to recover minority carriers, for a maximum photocurrent delivered by the solar cell. Both lowest and highest magnetic field values give respectively 176 μm and 117 μm solar cell base optimum thickness. This appears as a compromise between the different physical mechanisms of generation-diffusion-recombination-deflection, which take place in the base of the solar cell. This allows us to conclude that a front illuminated silicon solar to operate under magnetic field requires less material for its manufacturing.

It should be noted that previous work, using the same technique or other [44], has produced very interesting results, maintaining the solar cell (horizontal or vertical junction [41] [45]) under variation of: absorption coefficient [45], doping rate (hence the lifetime, the diffusion coefficient) [26] and irradiation flux by nuclear particles [40].

Modelling studies by combination of two to two or three of the previous conditions [29] [30] [42] have revealed the important economy of matter in the manufacture of solar cell, for these specific uses. The mathematical relationships between the optimum thickness of the base of the solar cell and the parameters of these specific conditions have been established

It appears from the analysis of these results that the deflection of minority carriers due to the magnetic field, leads to lower optimum thicknesses than in other cases, such as thermal agitation (Umklap process), or the use of monochromatic absorption coefficient radiation (short wavelengths).

3. Conclusion

The calibrating silicon solar cell base thickness under polychromatic illumination operating and applied magnetic field, was realized. The optimal thickness (Hopt) decreases significantly with the external applied magnetic field. This yield makes a judicious and optimal choice of the thickness of the base solar cell during its manufacture for an application of this kind.

Conflicts of Interest

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


[1] Reynolds, J.H. and Meulenberg, A. (1974) Measurement of Diffusion Length in Solar Cells. Journal of Applied Physics, 45, 2582-2592.
[2] Oualid, J., Bonfils, M., Crest, J.P., Mathian, G., Amzil, H., Dugas, J., Zehaf, M. and Martinuzzi, S. (1982) Photocurrent and Diffusion Lengths at the Vicinity of Grain Boundaries (g.b.) in N and P-Type Polysilicon. Evaluation of the g.b. Recombination Velocity. Revue de Physique Appliquée, 17, 119-124.
[3] 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.
[4] Bester, Y., Ritter, D., Bahia, G., Cohen, S. and Sparkling, J. (1995) Method Measurement of the Minority Carrier Mobility in the Base of Heterojunction Bipolar Transistor Using a Magneto transport Method. Applied Physics Letters, 67, 1883-1884.
[5] Rugider, M., Puzzer, T., Schäffer, E., Warta, W., Glunz, S.W., Würfel, P. and Trupke, T. (2007) Diffusion Lengths of Silicon Solar Cells from Luminescence Images. Journal of Applied Physics, 101, Article ID: 123110.
[6] Diao, A., Thiam, N., Zoungrana, M., Ndiaye, M., Sahin, G. 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, 1-9.
[7] Luque, A., Ruiz, J.M., Cuevas, A., Eguren, J. and Agost, M.G. (1997) Double Side Solar Cells to Improve Static Concentrator. Proceeding of the European Photovoltaic Solar Energy Conference, Luxembourg, 269-277.
[8] Yadav, P., Pandey, K., Tripathi, B., Mauli Kumar, C., Srivatava, S.K., Singh, P.K. and Kumar, M. (2015) An Effective Way to Analyze the Performance Limiting Parameters of a Poly-Crystalline Silicon Solar Cell Fabricated in the Production Line. Solar Energy, 122, 1-10.
[9] Diao, A., Wade, M., Thiame, M. and Sissoko, G. (2017) Bifacial Silicon Solar Cell Steady Photoconductivity under Constant Magnetic Field and Junction Recombination Velocity Effects. Journal of Modern Physics, 8, 2200-2208.
[10] Wise, J.F. (1970) Vertical Junction Hardened Solar Cell. US Patent, 3, 690-953.
[11] 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.
[12] Ngom, M.I., Thiam, A., Sahin, G., El Moujtaba, M.A.O., Faye, K., Diouf, M.S. and Sissoko, G. (2015) Influence of Magnetic Field on the Capacitance of a Vertical Junction Parallel Solar Cell in Static Regime, under Multispectral Illumination. International Journal of Pure & Applied Sciences & Technology, 31, 65-75.
[13] Madougou, S., Made, F., Boukary, M.S. and Sissoko, G. (2007) Recombination Parameters Determination by Using Internal Quantum Efficiency Data of Bifacial Silicon Solar Cells. Advanced Materials Research, 18-19, 313-324.
[14] Zouma, B., Maiga, A. S., Dieng, M., Zougmore, F. and Sissoko, G. (2009) 3D Approach of Spectral Response for a Bifacial Silicon Solar Cell under a Constant Magnetic Field. Global Journal of Pure and Applied Sciences, 15, 117-124.
[15] Zoungrana, M., Thiame, M., Dioum, A., Raguilnaba, S. and Sissoko, G. (2007) 3D Study of a Bifacial Silicon Solar Cell under Intense Light Concentration and under External Constant Magnetic Field: Recombination and Electrical Parameters Determination. Proceedings of the 22nd European Photovoltaic Solar Energy Conference and Exhibition, Milano, 3-7 September 2007, 447-453.
[16] Kumar, S., Singh, P.K. and Chilana, G.S. (2009) Study of Silicon Solar Cell at Different Intensities of Illumination and Wavelengths Using Impedance Spectroscopy. Solar Energy Materials and Solar Cells, 93, 1881-1884.
[17] Diallo, M.M., Tamba, S., Seibou, B., Cheikh, M.L.O., Diatta, I., Ndiaye, E.H., Traore, Y., Sarr, C.T. and Sissoko, G. (2017) Impact of Irradiation on the Surface Recombination Velocity of a Back Side Monochromatic Illuminated Bifacial Silicon Solar Cell under Frequency Modulation. Journal of Scientific and Engineering Research, 4, 29-40.
[18] Selma, M.S., Diatta, I., Traore, Y., Diouf, M.S., Habiboulahh, L., Wade, M. and Sissoko, G. (2018) Diffusion Capacitance in a Silicon Solar Cell under Frequency Modulated Illumination: Magnetic Field and Temperature Effects. Journal of Scientific and Engineering Research, 5, 317-324.
[19] Diouf, S., Ndiaye, M., Thiam, N., Traore, Y., Lamine Ba, M., Diatta, I., Diouf, M.S., et al. (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.
[20] Jain, S.C. (1983) The Effective Lifetime in Semicrystalline Silicon. Solar Cells, 9, 345-352.
[21] 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.
[22] 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.
[23] Gupta, S., Ahmed, F. and Garg, S. (1988) A Method for the Determination of the Material Parameters τ, D, Lo, S and α from Measured AC. Short-Circuit Photocurrent. Solar Cells, 25, 61-72.
[24] 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.
[25] Kosso, A.M.M., Thiame, M., Traore, Y., et al. (2018) 3D Study of a Silicon Solar Cell under Constant Monochromatic Illumination: Influence of Both, Temperature and Magnetic Field. Journal of Scientific and Engineering Research, 5, 259-269.
[26] Diop, M.S., Ba, H.Y., Thiam, N., et al. (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.
[27] Ba, M.L., Diallo, H.L., Ba, H.Y., Traore, Y., Diatta, I., Diouf, M.S., et al. (2018) Irradiation Energy Effect on a Silicon Solar Cell: Maximum Power Point Determination. Journal of Modern Physics, 9, 2141-2155.
[28] 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.
[29] Mohamed, N.M.M.O., et al. (2019) Influence of Both Magnetic Field and Temperature on Silicon Solar Cell Base Optimum Thickness Determination. Journal of Modern Physics, 10, 1596-1605.
[30] Ely, M.M., et al. (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.
[31] 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.
[32] Mbodji, S., Zoungrana, M., Zerbo, I., Dieng, B. and Sissoko, G. (2015) Modelling Study of Magnetic Field’s Effects on Solar Cell’s Transient Decay. World Journal of Condensed Matter Physics, 5, 284-293.
[33] Furlan, J. and Amon, S. (1985) Approximation of the Carrier Generation Rate in Illuminated Silicon. Solid-State Electronics, 28, 1241-1243.
[34] Diouf, M.S., et al. (2016) Study of the Series Resistance of a Solar Cell Silicon under Magnetic Field from of Junction Surface Recombination Velocity of Minority Charge Carriers at the Junction Limiting the Open Circuit (Sfoc). Journal of Scientific and Engineering Research, 3, 289-297.
[35] 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, 352-354.
[36] Diallo, H.L., Maiga, S.A., 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.
[37] 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.
[38] Joardar, K., Dondero, R.C. and Schroda, D.K. (1989) Critical Analysis of the Small-Signal Voltage-Decay Technique for Minority-Carrier Lifetime Measurement in Solar Cells. Solid State Electronics, 32, 479-483.
[39] Sissoko, G., Museruka, C., Corréa, A., Gaye, I. and Ndiaye, A.L. (1996) Light Spectral Effect on Recombination Parameters of Silicon Solar Cell. World Renewable Energy Congress, Pergamon, Part III, 1487-1490.
[40] 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.
[41] Diop, G., et al. (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.
[42] Faye, D., Gueye, S., Ndiaye, M., et al. (2020) Lamella Silicon Solar Cell under Both Temperature and Magnetic Field: Width Optimum Determination. Journal of Electromagnetic Analysis and Applications, 12, 43-55.
[43] Dia, O., El Moujtaba, M.A.O., Gueye, S., et al. (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.
[44] Navruz, T.S. and Saritas, M. (2012) Determination of the Optimum Material Parameters for Intermediate Band Solar Cells Diffusion Model. Progress in Photovoltaics Research and Applications, 22, 593-602.
[45] Dede, M.M.S., Ndiaye, M., Gueye, S., et al. (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.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.