IJISET International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 1, January

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1 IJISET Iteratioal Joural of Iovative Sciece, Egieerig & Techology, Vol. Issue 1, Jauary 015. ISSN Thermal behavior of a parallel vertical juctio Silico photocell i static regime by study of the series ad shut resistaces uder the effect of temperature. 1 Nfally DIEME, Boureima SEIBOU, 1 Mohamed Abderrahim Ould El Moujtaba, 1 Idrissa GAYE, 1 Grégoire SISSOKO (1) Laboratory of Semicoductors ad Solar Eergy, Physics Departmet, Faculty of Sciece ad Techology, Uiversity Cheikh Ata Diop, Dakar, Seegal () Mies, Idustry ad Geology School of Niamey- Niger Abstract This work presets a theoretical study of a vertical parallel juctio solar cell uder multispectral illumiatio i steady state. Based o the diffusio equatio, the excess miority carrier s desity is expressed ad the characteristic curret-voltage, series resistace at shuts resistace are determied. For all these parameters we showed the effect of exteral temperature. Keywords: Vertical juctio - temperature series resistace- shuts resistace. I Itroductio The aim of this work is to ivestigate the ifluece of temperature o electrical parameters such as: series resistace ad shut resistace. These two parasitic parameters eable us to come out with the performace of a photovoltaic cell. From the diffusio-recombiatio equatio the excess miority carrier s desity, the photocurret desity ad the photovoltage will be determied. Based o these parameters characteristic curretvoltage, shuts resistace ad series resistace are deduced. I the last part of this work we preset our simulatio results. II. Theory This study is based o a vertical parallel juctio silico solar cell [1]-[]-[3] preseted o figure 1. The solar cell is illumiated alog the z axis i steady state. Figure 1: Vertical parallel juctio solar cell H =0,0cm; W =0,03cm We assume that the followig hypotheses are satisfied. The cotributio of the emitter is eglected. Illumiatio is made with polychromatic light, ad is cosidered to be uiform o the z = 0 plae. There is o electric field without space charge regios. II.1 Desity of miority charge carriers Whe the solar cell is illumiated, there are simultaeously three major pheomea that happe: geeratio diffusio ad recombiatio. These pheomea are described by the diffusiorecombiatio equatio give by [3]-[4]-[5]-[6]. ( ( G (1) x L D D is the diffusio costat ad is related to the operatig temperature through the relatio [7]. 433

2 IJISET Iteratioal Joural of Iovative Sciece, Egieerig & Techology, Vol. Issue 1, Jauary 015. K D.. T () q with q the elemetary charge, k the Boltzma costat ad T the temperature. G= g(z)+gth is the carrier geeratio rate. g(z) is the carrier geeratio rate at the depth z i the base ad ca be writte as [1] g z a e biz ( ) i (3) a i ad b i are obtaied from the tabulated values of AM1.5 solar illumiatio spectrum ad the depedece of the absorptio coefficiet of silico with illumiatio wavelegth. gth is the carrier thermal geeratio rate. It is give by: g c (4) th with. i 3. Eg i A T.exp( ) (5) KT i refers to the itrisic cocetratio of miority carriers i the base [7], A is a specific costat of the material (A =3.87x10 16 for silico) ad N b is the base dopig cocetratio i impurity atoms. Ad 1 (6) C.Nb (, L,, ad μ are respectively the excess miority carriers desity, diffusio legth, lifetime ad mobility ad C is the proportioality coefficiet. The solutio of equatio (1) is: x x ( Asih( ) Bcosh( ) L L (7) ai biz L 3 Eg L e C. A. T.exp( ) D D KT Coefficiets A ad B are determied through the followig boudary coditios []-[3]-[5] at the juctio (x=0): ISSN ( x ) S f ( 0 ) (8) x x 0 D This boudary coditio itroduces a parameter S f which is called recombiatio velocity at the juctio. Sf determies the charge carriers flow through the juctio ad is directly related to the operatig poit of the solar cell []-[3]-[5]. The higher Sf is, the higher the curret desity will be. - i the middle of the base (x=w/) : ( x ) x x w 0 (9) Equatio 6 traduces the fact that excess carrier cocetratio reaches its maximum value i the middle of the base due to the presece of juctio o both sides of the base alog x axis (figure 1). II. Photocurret desity The photocurret Jph is obtaied from the followig relatio give that there is o drift curret []-[8]. J ph ( x ) qd x x 0 (10) II.3 Photovoltage The photovoltage derives from the Boltzma relatio []-[8]. (0) V k. T l Nb. 1 (11) ph q i II.4 Characteristic curret-voltage La characteristic curret voltage is represeted by the followig curve: 434

3 IJISET Iteratioal Joural of Iovative Sciece, Egieerig & Techology, Vol. Issue 1, Jauary 015. Figure : Curret versus voltage This characteristic presets two areas very importat [9]: Area1 is has a curret geerator Jsc of admittace that ca be modeled par : 1 Rsh The correspodig electrical circuit is: Figure 3: Electric equivalet circuit of the photocell operatio by short-circuitig Jsc : short circuit curret desité, Rsh : shut resistace per uit area Jph et Vph: desity curret et photovoltage. Rch : Load resistace The law of mesh applied to the circuit of figure (area1) gives: Vph Rsh ( Isc Jph ) (1) This relatioship; It draws the Rsh expressio that is writte i the form : ISSN Vph Rsh (13) Isc Jph Area is similar to a geerator voltage Voc of equivalet resistace iteral impedace Rs series The model of equivalet electrical circuit of a photocell operatig i ope circuit is represeted by the followig figure: Figure 4: Electric equivalet circuit of the photocell i ope circuit operatio Vco : ope circuit voltage, Rs : Résistace série par uité de surface Vph : voltage Applyig the law of mesh to the circuit of figure (area), we get V ph V oc R s. (14) I ph We the deduce the series resistace expressio as V oc V ph (15) R s I ph III. Results ad discussio The two resistors model iteral losses [9] : - Series Resistace Rs: models the ohmic losses i the material. - Shuts Resistace Rsh: models the parasitic currets traversig the cell We preset here some simulatio results obtaied from the previously described model. 435

4 IJISET Iteratioal Joural of Iovative Sciece, Egieerig & Techology, Vol. Issue 1, Jauary 015. Figure 5: Séries Résistace versus temperature Sf=10 cm.s -1, z=10 - cm Figure 6 : Résistace versus temperature Sf=10 6 cm.s -1, z=10 - cm Series Resistace: Figure4 shows that the series Resistace icreases the temperature of. I fact it icreases temperature creates a followed warmig of a dilatio of metals. This pheomeo icreases the ability of materials to resist the passage of electric curret. Thus there for a positive temperature gradiet is a icrease i resistivity of semicoductor material, the costituet metal cotacts the electrodes ad the grid of the miority carrier collectio. ISSN Figure 5 represets the profile of the series resistace depedig o the speed of recombiatio for differet temperature values. This figure shows the series resistace believes o the basis of the recombiatio velocity at the juctio. This icrease of Rs is all the more importat that the temperature rises. Ideed whe the recombiatio velocity icreases, the diode characterizig the juctio behaves as a resistace ad opposes the passage of electric curret [10]. Shuts Fig.5: resistace: Séries Résistace versus juctio recombiatio velocity The figure for various 6 shows temperatures that the shut z=10 - resistace cm decreases with temperature. I fact the charge carriers photogeeses uder the effect of temperature are equipped with great kietic eergy ad put themselves i a chaotic movemet [11]. This radom motio causig much collusio betwee the carriers ad the leakage curret. Thus the diode curret greatly icreases. As a result the shut resistace decreases with temperature. The figure7 represets the profile of the Shut Resistace (Rsh) based o the recombiatio velocity at the juctio for differet values of the Fig.7: Shut Résistace versus juctio recombiatio temperature. velocity for various temperatures z=10 - cm This figure shows that the shut Resistace believes based o the recombiatio velocity at the juctio. This icrease of Rsh is all the more importat that the temperature is low. Ideed whe the recombiatio velocity icreases, may carriers arrive at the juctio. They thus cross the juctio to participate i electric power. Thus the leakage curret is reduced: it is said that the shut resistace is high. 436

5 IJISET Iteratioal Joural of Iovative Sciece, Egieerig & Techology, Vol. Issue 1, Jauary 015. ISSN Coclusio: I this simulatio study, we foud that the resistace series icreases the temperature both drive the shut resistace decreases. The series resistace that characterizes the ohmic characterizes the leakage curret is greater that the photocell is of good quality. It ca be cocluded that the icrease i temperature i the material cotributes sigificatly to the weakeig of the performace of the photocell losses is smaller that the photocell is of good quality. The shut resistace (Rsh) that REFERENCES [1] Furla, J. ad S. Amo, Approximatio of the carrier geeratio rate i illumiated silico. Solid State Electro., 8(1): [] Nfally Dieme, Martial Zougraa, Seghae Mbodji, Hawa Ly Diallo, Mor Ndiaye, Fabé Idrissa Barro ad Grégoire Sissoko, Ifluece of Temperature o the Electrical Parameters of a Vertical Parallel Juctio Silico Solar Cell uder Polychromatic Illumiatio i Steady State, Res.J. App. Sci, Eg. ad Techology, vol. 7(1), pp: , (014) [3] Ly Diallo, H., A. Wereme, A.S. Maïga ad G. Sissoko, 008. New approach of both juctio Ad back surface re recombiatio velocities i a 3D modelig study of a polycrystallie silico solar cell. Eur. Phys. J. Appl. Phys., 4: [4] Mbodji, S., B. Mbow, F.I. Barro ad G. Sissoko, 011. A 3D model for thickess ad diffusio capacitace of emitter-base juctio determiatio i a bifacial polycrystallie solar cell uder real operatig coditio.turk J. Phys., 35: [7] Fracis Levy, Traité des matériaux 18, Physique et techologie des semi-coducteurs. Presses Polytechiques et Uiversitaires Romades. [8] Madougou, S., F. Made, M.S. Boukary ad G. Sissoko, 007. Characteristics for bifacial silico solar cell studied uder a magetic field. Adv. Mater. Res., 18-19: [9] Samer Said, Ahmed Massoud, Mohieddie Beammar ad Shehab Ahmed. A Matlab/Simulik-Based Photovoltaic Array Model Employig SimPowerSystems Toolbox Joural of Eergy ad Power Egieerig 6 (01) [10] I. Sari-Ali, B. Beyoucef, B. Chikh-Bled, Etude de la joctio PN d u semi-coducteur à l équilibre thermodyamique, Joural of Electro Devices, Vol. 5,, pp (007) [11] Sze, S.M. ad K.K. Ng, 007. Physics of Semicoductor Devices. 3rd Ed., Joh Wiley ad Sos, New York. [5] Wafaa ABD EL-BASIT, Ashraf Mosleh ABD El MAKSOOD ad Fouad Abd El-Moiem Saad SOLIMAN. Mathematical Model for Photovoltaic Cells. Leoardo Joural of Scieces. Issue 3, July-December 013 p [6] Ly Diallo, H., B. Dieg, I. Ly, M.M. Dioe, A. Wereme, M. Ndiaye ad G. Sissoko, 01. Determiatio of the recombiatio ad electrical parameters of a vertical multijuctio silico solar cell. Res. J. Appl. Sci. Eg. Techol., 4(16):