Université Cheikh Anta Diop, Dakar, Sénégal 2 Ecole Polytechnique de Thiès, Thiès, Sénégal

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1 International Journal o Emerging Research in Management &echnology Research Article January 017 Series Resistance Both emperature and Wavelength Dependent in Silicon Solar Cell under Steady State Ibrahima DIAA 1, Ibrahima LY, Mamadou WADE, Marcel Sitor DIOUF 1, Youssou RAORE 1, Mor NDIAYE 1, Senghane MBODJI 3 and Grégoire SISSOKO 1 1 Laboratoire des Semi-conducteurs et d Energie Solaire, Faculté des Sciences et echniques, Université Cheikh Anta Diop, Dakar, Sénégal Ecole Polytechnique de hiès, hiès, Sénégal 3 Université Alioune DIOP de Bambey-Sénégal DOI: /ijermt/V6N1/101 Abstract: he excess minority carrier junction recombination velocity limiting the open circuit Soc and the experimental series resistance o an exposed solar cell to temperature under monochromatic illumination in static regime were determined. It is determined by the photovoltage dierence and the open circuit photovoltage Voc. Expression o junction recombination velocity limiting the open circuit has determined the experimental series resistance values. Expressions o photocurrent density and photovoltage are obtained rom excess minority carrier density. Keywords: solar cell - junction recombination velocity - open circuit wavelength - series resistance - temperature. I. INRODUCION he series resistance is caused by electrons movement through the emitter and the solar cell base, the contact resistance between the silicon and the metal grids resistance at ront and back side [1-3]. In this paper, we study inluence o both temperature and wavelength on series resistance o silicon solar cell in static regime under monochromatic illumination. his resistance and Soc are determined rom the I-V characteristic. he experimental series resistance values are also determined rom the series resistance curves calibration versus minority carrier junction recombination velocity S. II. HEORY he studied silicon solar cell is an n+pp+ BSF type. It is represented by the ollowing igure: Figure 1 : Silicon solar cell n + pp + type When the solar cell is illuminated, there is electron-hole pairs generation in the base. he excess minority carrier density in the base is modeled by the ollowing continuity equation: x x g x x² L² D (1) With δ (x) is the minority carrier density at the depth x in the base g(x) is the carrier generation rate at the depth x in the base, it is expressed as: 1 g x R e x () Where α(λ) and R(λ) represent respectively absorption and relection coeicient o the material or a given wavelength ; 017, IJERM All Rights Reserved Page 1

2 DIAA et al., International Journal o Emerging Research in Management &echnology () Is the incident photons lux. he minority carrier diusion length in the base material is temperature dependent; it is expressed by the ollowing equation. L ² D (3) τ is the minority carrier lietime. is the diusion coeicient, it s temperature dependent. can be expressed by Einstein relationship: b D k q (4) 1,43.10 cm² V s (5) 9,4 1 1 μ is minority carriers mobility [11], Solution o equation (1) is given by the ollowing terms: ²1 x x L R e x,, Acosh Bsinh L L D L ² ² 1 he constants A and B are determined rom the boundary conditions: - At the junction surace, x = 0 : δ(x,,t) x X 0 - At the back side surace, x = H : δ(x,,t) x x H S δ(0,,t) Sb δ(h,,t) x S is the minority carrier junction recombination velocity, expresses with two components which describe the solar cell operating point and the looses induced by shunt resistance[1,13]. Sb is the minority carrier surace recombination velocity [13], induced by a back surace ied. III. DENSIE DE PHOOCOURAN he photocurrent density results rom the minority carrier diusion at the junction and it is given by: ( S,, J ph( S,, q x x0 IV. PHOOENSION he solar cell photovoltage is given by the Boltzmann relation. b V,, ln 0,S,, 1 ph S V N n i Where V is the thermal voltage, it is deined as: k b V (11) q Nb is the doping level and ni, the intrinsic minority carrier density [14] expressed as ollows: 3 E g ni ( A. exp. k b. Eg is the energy gap, it s corresponds to the dierence between the conduction and valence band energy expressed as: Eg = Ec - Ev. Eg = 1,1*1, J A is a constant. A = 3, cm -3-3 / K V. I-V CHARACERISIC V.1 Eect o temperature on I-V characteristic he igure represents the I(S)-V(S) characteristic o the solar cell under illumination or dierent temperature values[14]. 017, IJERM All Rights Reserved Page (7) (8) (9) (10) (1) (6)

3 Series resistance (Ω.cm ) Photocurrent density (A.cm - ) DIAA et al., International Journal o Emerging Research in Management &echnology Photovoltage (Volt) Figure 1: I-V characteristic or dierent temperature values We observe that photocurrent density is maximum and constant or low value photovoltage. he maximum photocurrent density is called short-circuit photocurrent density Jphsc (,. he maximum photovoltage is called open circuit photovoltage Vphoc (,. For increasing temperature Jphsc (, and Vphoc(, decreases, slightly or the ormer and very sensitive or the second one. V. Résistance série We note in the I-V characteristic that near the open circuit, the voltage across the solar cell is independent o output current. he solar cell is considered as equivalent to a real voltage generator [15, 16]. We have presence o internal resistance called series resistance Rs. R L is the external load resistance. he electrical equivalent circuit in open circuit situation is then represented [1, 17]: R ( S,, s Figure 3: Electrical equivalent circuit in open circuit situation. By applying the Kirchho laws or the previous equivalent circuit, we deduce Rs expression. V (, V ( S,, phco ph (13) J ( S,, ph V..1 emperature eect on series resistance Figure 4 shows series resistance versus minority carrier junction recombination velocity S or dierent temperature values. Minority carrier junction recombination velocity (cm.s -1 ) Figure 4: Series resistance versus minority carrier junction recombination velocity S or dierent temperature values. 017, IJERM All Rights Reserved Page 3

4 Series resistance (Ω.cm ) Series resistance (Ω.cm ) DIAA et al., International Journal o Emerging Research in Management &echnology We observe a bearing series resistance or low S values. he series resistance increases exponentially with S. And or increasing temperature, the series resistance increases either. V.. Wavelength eect on series resistance Figure 5 shows series resistance versus minority carrier junction recombination velocity S or dierent wavelength values. Minority carrier junction recombination velocity (cm.s -1 ) Figure 5: series resistance versus S or dierent wavelength values. We note that at open circuit situation, series resistance increases gradually with minority carrier junction recombination velocity. We also observe an increase o the series resistance with wavelength: It is explained by the material increasing resistivity. Figure 6 shows series resistance versus temperature or dierent wavelength values. emperature (K) Figure 6: series resistance versus temperature or dierent high wavelength values (S= 10 cm/s) For increasing temperature, the series resistance increases. It is more important or increasing wavelength values. Figure 6 allows us to obtain the equation 14 who expressed series resistance versus temperature. Rs ( = With, isthe slope and is the intercept and considered as resistance. and values are presented or high wavelength by table 1 able1: and or high wavelength m) cm.k -1 ) cm ) 0,84, ,10 0,88 3, ,160 0,9 4, ,47 0,9 4, ,38 V.3 Experimental determination o series resistance Using the technique o the limiting recombination velocity at the junction Soc [18], the expression is derived rom the equation 15, at S = Soc. 017, IJERM All Rights Reserved Page 4

5 DIAA et al., International Journal o Emerging Research in Management &echnology Vph(S, Vphoc( Ater solving equation 15 we obtain Soc expression given as: H L( (, K(, ( ) cos (, L( K(, ( ) L( (16) S oc, H H L( K (, (, cos L( K (, L( (, sinh L( L( Sco depend on both wavelength and temperature. With, ( ) ( ) L( 1 R( ) And K(, L( ( ) 1 Vco(, ) ni ( V( (, e 1 K(, Nb K(λ, and β(λ, are coeicients, dependent o both wavelength and temperature. Dierent temperature values introduced in Soc expression yield corresponding values.he calibration series resistance curve (Figure 4) at Soc values gives either the experimental Rs values who are given by able able : Soc and experimental Rs Values with their respective temperature or a given wavelength 0,94 m. (K) Soc(cm/s) Rs exp (cm²) 330 6, , , , , , ,4 We note in table that or a given wavelength value, Soc decreases increasing temperature, the experimental series resistance increases. or increasing temperature. And or VI. CONCLUSION In this study based on temperature eect, we ended up with some results: For a given wavelength value, temperature increases causes a reduction o photocurrent density and photovoltage. heorical and experimental series resistance increases with increasing temperature and or these conditions the Junction surace recombination velocity limiting the open circuit decreases. he series resistance increases either with increasing wavelength. REFERENCES [1] M. Bashahu and A. Habyarimana, Review and test o methods or determination o the solar cell series resistance, Renewable Energy 6() (1995) [] M.K. El- Adawi and I.A. Al-Nuaim, A method to determine the solar cell series resistance rom a single I- V characteristic curve considering its shunt resistance-new approach, Vacuum 64 (00) [3] K. Bouzidi, M. Chegaar and A. Bouhemadou, Solar cells parameters evaluation considering the series and shunt resistance, Solar Energ. Mater. Solar Cells 91 (007) [4] S. Mbodji, I. Ly, H. L. Diallo, M.M. Dione, O. Diassé and G. Sissoko Modeling Study o N + /P Solar Cell Resistances rom Single I-V Characteristic Curve Considering the Junction Recombination Velocity (S) Research Journal o Applied Sciences, Engineering and echnology 4(1) (01) 1-7. [5] D.. Cotas, P.A. Cotas, S. Kaplanis, Methods to determine the dc parameters o solar cells: A critical review, Renewable and Sustainable Energy Reviews 8 (013) [6] E. Radziemska, Dark I U measurements o single crystalline silicon solar cells, Energy Conversion and Management 46 (005) [7] J. Lauwaert, K. Decock, S. Khelii, M. Burgelman A simple correction method or series resistance and inductance on solar cell admittance spectroscopy, Solar Energy Materials & Solar Cells 94 (010) [8] S. Kumar, P.K. Singh, G.S. Chilana, Study o silicon solar cell at dierent intensities o illumination and wavelengths using impedance spectroscopy, Solar Energy Materials & Solar Cells 93 (009) [9] P. Yadav, K. Pandey, B. ripathi, C. M. Kumar, S. K. Srivastava, P.K. Singh, M. Kumar, An eective way to analyse the perormance limiting parameters o poly-crystalline silicon solar cell abricated in the production line, Solar Energy 1 (015) , IJERM All Rights Reserved Page 5

6 DIAA et al., International Journal o Emerging Research in Management &echnology [10] G.Sissoko, C. Museruka, A. Corréa, I. GAYE, A. L. Ndiaye, Light spectral eect on recombination parameters o silicon solar cell, World Renewable Energy Congress 3, 15-1 June Denver-USA (1996) [11] M. Kunst and A. Sanders, ransport o excess carriers in silicon waers, Semicond. Sci. echnol. 7 (199) in the UK. [1] G. Sissoko, E. Nanema, Y. L. B. Bocandé, A. L. Ndiaye, M. Adj, Minority Carrier Diusion Length Measurement in Silicon Solar Cell Under Constant White Bias Light, World Renewable Energy Congress (1996) [13] H.L. Diallo, A. Seïdou. Maiga, A. Wereme, and G.Sissoko, New approach o both junction and back surace recombination velocities in a 3D modelling study o a polycrystalline silicon solar cell, Eur. Phys. J. Appl. Phys. 4 (008) [14] Babou Dione, Ousmane Sow, Mamadou Wade, L. Y. Ibrahima, Senghane Mbodji, Gregoire Sissoko, Experimental Processus or Acquisition Automatic Features o I-V Properties and emperature o thesolar Panel by Changing the Operating Point, Scientic Research Publishing -Circuits and Systems, 016, 7, [15] G.Sissoko, C. Museruka, A. Corréa, I. GAYE, A. L. Ndiaye, Light spectral eect on recombination parameters o silicon solar cell, World Renewable Energy Congress (1996) [16] G.Sissoko, E.Nanéma, A.Corréa, P.M.Bitéye, M.Adj, A.L. Ndiaye, Silicon Solar cell recombination parameters determination using the illuminated I-V characteristic, World Renewable Energy Congress 3 (1998) [17] h. Flohr and R. Helbig, Determination o minority- measurements at dierent light wavelengths, J. Appl. Phys. 66 (7) (1989) carrier lietime and surace recombination velocity by Optical-Beam-Induced- Current. [18] M.M. Dione, H. L. Diallo, M. Wade, I. Ly, M. hiame, F.oure, A. G. Camara, N. Dieme, Z. N. Bako, S. Mbodji, F.I. Barro and G. Sissoko, Determination o the Shunt and Series Resistances o a Vertical Multijunction Solar Cell under Constant Multispectral Light, Proceedings o the 6 th European Photovoltaic Solar Energy Conerence (011) 50-54, DOI: 10.49/6thEUPVSEC0111CV.3.6, Retrieved rom: http: // proceedings.com. 017, IJERM All Rights Reserved Page 6