Influence of Incident Illumination Angle on Capacitance of a Silicon Solar Cell under Frequency Modulation

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1 Research Jurnal f Appled Scences Engneerng and Technlgy 5(4): -8 0 ISSN: ; e-issn: Mawell Scenfc Organzan 0 Sumed: May 06 0 Acceped: June 08 0 Pulshed: Feruary 0 0 Influence f Incden Illumnan Angle n Capacance f a Slcn Slar Cell under Frequency Mdulan A. Tham M. Zungrana. y all A a N. Tham S. Gueye M.M. eme M. Sarr and G. Sssk arary f Semcnducrs and Slar Energy Physcs eparmen Faculy f Scence and Technlgy Unversy Chekh Ana p akar Senegal UFR-SET Unversy f Thes Senegal Asrac: The am f hs sudy s presen a herecal sudy f a slcn slar cell under frequency mdulan. Slvng he cnnuy equan lead he analycal epressns f he mnry carrers densy he phcurren and he ph vlage. The phcurren and he ph vlage are pled versus he mdulan frequency n a sem-lgarhmc scale fr varus ncdence angles; he dynamc mpedance f he slar cell s hen derved. The Nyqus dagram f he mpedance s pled fr varus ncdence angles leadng he deermnan f he seres and parallel ressances. The deermnan f he dffusn capacance s als made ased n he Bde dagram f he slar cell mpedance. The nfluence f he mdulan frequency and he ncdence angle n he dffusn capacance and he seres and parallel ressances s hen ehed. Keywrds: Elecrcal parameers frequency mdulan ncdence angle slar cell INTROUCTION In he pas many sudes were made n he n + -p-p + slcn slar cell (Meer e al. 988) n rder mprve he cell effcency. In addn such a leraure knwledge and undersandng he nrnsc and ernsc prperes f he slar cells are fundamenal n cnrllng he prcess f farcan and reamen f semcnducrs. In hs sudy we cnsder a facal slcn slar cell under varus ncdence angles f mulspecral llumnan (eme e al. 00) n frequency mdulan. We sudy he ehavr f sme elecrcal parameers f he facal slar cell dependng n he angle f ncdence f a plychrmac llumnan. Afer slvng he cnnuy equan an epressn f he ecess mnry carrers densy s aned; such a sep leads he esalshmen and deducn f he slar cell phcurren and ph vlage. These epressns lead he deermnan f he slar cell mpedance whch s hen suded versus mdulan frequency fr varus ncdence angles rugh Nyqus dagrams (Pannalal ; eng e al. 0). The seres and parallel ressances are deermned fr varus ncdence angles. The slar cell capacance s aned y usng he Bde dagram (Chenvdhya e al. 00; y all e al. 0) als fr varus ncdence angles and mdulan frequences. METOOOGY We presen n Fg. he slcn slar cell under varus llumnan ncdence angles. e and are respecvely he emer and he ase wdhs s he llumnan ncdence angle and s he deph n he ase. Cnnuy equan: The cnnuy equan s epressed as fllws: ² ² G () : The dffusn ceffcen δ( θ ) : The mnry carrers densy G( θ ) : The generan rae dependng n h me and spaal crdnaes and θ he ncden llumnan angle (eme e al. 00; Meer 988) The mnry carrers densy and he generan rae can e epressed respecvely as elw: ep( j) G G ep( j) () () Crrespndng Auhr: A. Tham arary f Semcnducrs and Slar Energy Physcs eparmen Faculy f Scence and Technlgy Unversy Chekh Ana p akar Senegal

2 Res. J. Appl. Sc. Eng. Technl. 5(4): Fg. : Slcn slar cell where () s he mnry carrers densy fr a gven deph n he ase and G(θ) he generan rae a quany dependng h n spaal crdnae and n θ he ncden llumnan angle. Cmnng and nserng he Eq. () and () n he Eq. () resul he fllwng dfferenal equan: g (4) s he cmple dffusn lengh. The slun f Eq. (4) s gven y he fllwng epressn: j a n Bsh Ach ep ep cs (5) where ceffcens A and B are derved frm he undary cndns a he juncn and a he ack surface. Bundary cndns: A he juncn ( = 0) j a n Bsh Ach ep ep cs (6) A he ack surface ( = ) S (7) where Sf & S : The juncn and ack surface recmnan velces : The ase deph ω : The mdulan frequency RESUTS AN ISCUSSION Shr crcu phcurren densy: The shr crcu phcurren s aned hrugh he mnry carrers dffusn a he juncn when Sf>0 4 cm/s and s epressn s as fllws: snh ep csh snh. csh.. cs S S S e a n sc J (8) wh: e he elemenary charge Fg. we presen he shr crcu phcurren versus mdulan frequency (sem-lgarhmc scale) fr varus ncdence angles. In Fg. a he frs sep fr lwer frequency values he shr crcu phcurren s relavely cnsan efre decreasng fr hgh frequency values. A he same me he shr crcu phcurren ncreases fllwng he lwer angle f ncdence values; he hghes curren s aned fr he drec nrmal ncdence (Sssk e al. 99; Madugu e al. 007). Open crcu ph vlage: The pen crcu ph vlage s aned when he juncn recmnan

3 Res. J. Appl. Sc. Eng. Technl. 5(4): -8 0 Shr crcu curren densy (A/cm ) Fg. : Shr crcu phcurren densy versus mdulan frequency (sem-lgarhmc scale) fr varus ncdence angles 0 : 6 cm /s; : 0.0 µm; : s; 0 : 0.0 cm Fg. : Open crcu ph vlage versus mdulan frequency (sem-lgarhmc scale) fr varus ncdence angles 0 : 6 cm /s; : 0.0 µm; : s; 0 : 0.0 cm velcy Sf s very lw; fr an deal cell Sf shuld e zer (Sf = 0) and n a real case wuld e he nrnsc juncn recmnan Sf 0 (all e al. 008). In ur case (Sf = 0) s epressn s gven y: V c Open crcu vlage (v) = 0 = 0 = 0 = g = 0 = 0 = 0 = g N n cs a n 0 S csh snh V ln T S snh S csh ep (9) The Fg. shws a pl f he pen crcu ph vlage versus mdulan frequency n sem lgarhmc scale. Slar cell mpedance: The dynamc mpedance f he slar cell can e epressed as: Imagnary par f he mpedance Fg. 4: Imagnary par versus real par f he slar cell mpedance fr dfferen ncdence angles Sf:.0 cm/s; 0 : 6 cm /s; : 0.0 µm; : s; 0 : 0.0 cm Z Sf V Sf J Sf (0) The NYQUIST dagram (magnary par versus real par) f slar cell dynamc mpedance Z (nma and Munakaa 987; Perera e al. 006) s pled (Fg. 4) fr varus ncdence angles. The Nyqus pl f mpedance s a sem-crcle. These curves shw ha he lcus f he sem-crcle ncreases wh ncreasng ncdence angle. Seres and parallel ressances Rs and Rp are deduced frm he ave Nyqus dagram (nma and Munakaa 987; Perera e al. 006; Buzd e al. 007) gven ha he w nerceps f he mpedance lcus n he real as are apprmaely Rs and Rs + Rp (Bashahu and ayarmana 995; El-Adaw 00). Frm Fg. 5 seres and parallel ressances are eraced fr varus ncdence angles and presened n Tale. Tale shw ha he seres and parallel ressances ncrease wh he ncdence angle. Once hese parameers are deermned we can use he Bde dagram access he cu-ff angular frequency and fnally he capacance. Slar cell dffusn capacance: The dffusn capacance C asscaed he mnry carrers cllecn regn s relaed he cu-ff angular frequency c y: R p C c Real par f he mpedance () Bde dagram: ere Bde dagram (Pannalal ) s used access he cu-ff frequency; we presen n he Fg. 4 he Bde dagram f he slar cell mpedance fr varus ncdence angles. 5

4 Res. J. Appl. Sc. Eng. Technl. 5(4): -8 0 (a) θ = 0 () θ = 0 (c) θ = 0 (d) θ = 0 Fg. 5: Nyqus dagram f he dynamc mpedance fr varus ncdence angles Sf:.0 cm/s; 0 : 6 cm /s; : 0.0 µm; : s; 0 : 0.0 cm Tale : Seres and parallel ressances fr varus ncdence angles θ ( ) Rs (Ω.cm ) Rp (Ω.cm ) Tale : Capacance values fr varus ncdence angles θ ( ) θ ( ) Z (.cm ) = 0 = 0 = 0 = g Fg. 6: Bde dagram f he mpedance fr varus ncdence angles Sf:.0 cm/s; 0 : 6 cm /s; : 0.0 µm; : s; 0 : 0.0 cm Fr angular frequences n he nerval 0<< c he mpedance s ndependen f he frequency: ha s we are sll n a quas-seady sae. Fr he values f he pulsan such as > c he mpedance ncreases wh he angular frequency. Effecvely fr frequency ave c mnry carrers are slwed dwn raducng he fac ha he dynamc mpedance ncreases. 6 Z (.cm ) g c Fg. 7: Bde dagram f he mpedance Sf:.0 cm/s; 0 : 6 cm /s; : 0.0 µm; : s; 0 : 0.0 cm We als ne ha all he curves n Fg. 6 presen a knee a apprmaely he same angular frequency ha s he angular cu-ff frequency d n depend n he ncdence angle. Snce he curves n Fg. 6 lead he same cu-ff angular frequency fr any ncdence angle we fnally cnsder Fg. 7 (θ = 0 ) fr he deermnan f c. Fgure 7 shws he deermnan f he angular cu-ff frequency. Apprmaely we have:.0 / () Snce he parallel ressance has een already deermned ased n he angular cu-ff frequency ave we can deduce he capacance value fr varus ncdence angles; he resuls are presened n Tale. 7

5 Res. J. Appl. Sc. Eng. Technl. 5(4): -8 0 C F/cm ) frequency s deermned y use f Bde dagram f he dynamc mpedance and he capacance s deduced ased n h parallel ressance and angular cu-ff frequency; he capacance deermned y hs way decreases wh ncreasng ncdence angle. Ths ehavur f he capacance s cnfrmed y usng an analycal epressn f he slar cell capacance. REFERENCES g Fg. 8: Bde dagram f he capacance fr varus ncdence angles Sf:.0 cm/s; 0 : 6 cm /s; : 0.0 µm : s; 0 : 0.0 cm Ths ale shws ha he capacance decreases wh ncreasng ncdence angle. T cnfrm such a resul le us epress he capacance as fllw: e n 0 C 0 K T N () Based n hs epressn we nw pl n Fg. 8 he capacance f he cell versus mdulan frequency n sem-lgarhmc scale (Bde dagram). Ths fgure shws ha he capacance ncreases wh ncreasng mdulan frequency fr a gven ncdence angle; ha s when mdulan frequency ncreases mnry carrers are sred mre and mre n he ase ecause hey cann crss he juncn; hs lead an ncrease n he capacance f he cell. We als ne ha he capacance decreases wh ncreasng ncdence angle as prevusly ned n Tale. Effecvely when he ncdence angle ncreases here s less and fewer carrers generaed n he ase leadng a decrease f he ne charge n he ase and hus a decrease n he capacance asscaed he cell. CONCUSION A herecal sudy s made n a slcn slar cell under he frequency mdulan fr varus ncdence llumnan angles. The phcurren and he ph vlage are suded and he nfluence f he mdulan frequency and ncdence angle are presened. The slar cell dynamc mpedance s presened and leads he deermnan f he seres and parallel ressances hrugh Nyqus dagrams. The angular cu-ff Bashahu M. and A. ayarmana 995. Revew and es f mehds fr deermnan f he slar cell seres ressance. Renew. Energ. 6(): 7-8. Buzd K. M. Chegaar and A. Buhemadu 007. Slar cells parameers evaluan cnsderng he seres and shun ressance. Slar Energ. Maer. Slar Cells 9: Chenvdhya. K. Krkara and C. Jvacae 00. A new characerzan mehd fr slar cell dynamc mpedance. Slar Energ. Maer. Slar Cells 80(4): eme M.M. S. Mdj S. Ndye A. Tham A. eng and G. Sssk 00. Influence f llumnan ncdence angle gran sze and gran undary recmnan velcy n he facal slar cell dffusn capacance. Revues des Energ. Renuvela. (): 09-. all.. A.S. Maga A. Wereme and G. Sssk 008. New apprach f h juncn and ack surface recmnan velces n a mdelng sudy f a plycrysallne slcn slar cell. Eur. Phys. J. Appl. Phys. 4: 9-. eng A. N. Tham A. Tham A.S. Maga and G. Sssk 0. Magnec feld effec n he elecrcal parameers f a plycrysallne slcn slar cell. Res. J. Appl. Sc. Eng. Technl. (7): El-Adaw M.K. and I.A. Al-Nuam 00. A mehd deermne he slar cell seres ressances frm a sngle I-V characersc curve cnsderng s shun ressance-new apprach. Vaccum. 64: -6. nma N. and C. Munakaa 987. Sample hckness dependence f mnry carrer lfemes measured usng an ac phvlac mehd. Japanese J. Appl. Phys. 6(): y all. M. Wade I. y M. aye B. eng O.. emra A.S. Maïga and G. Sssk 0. mdelng f a facal slcn slar cell under frequency mdulan mnchrmac llumnan: eermnan f he equvalen elecrcal crcu relaed he surface recmnan velcy. Res. J. Appl. Sc. Eng. Technl. 4():

6 Res. J. Appl. Sc. Eng. Technl. 5(4): -8 0 Meer.. J.M. wang and R.B. Camell 998. The effec f dpng densy and njecn level n mnry-carrer lfeme as appled facal dendrc we slcn slar cells. IEEE Trans. Elecr. ev. 5(): Madugu S. F. Made M.S. Bukary and G. Sssk 007. Recmnan parameers y usng Inernal Quanum Effcency (IQE) daa f facal slar cell. Adv. Maer. Res. 8-9: -4. Pannalal. and B. Sgnals Sysems and Cnrls. Ine Educanal Pulsher New Yrk. Perera.. Raner P. Barqunha E. Fruna and Marns 006. Impedance sudy f he elecrcal prperes f ply-s hn flm ranssrs. J. Nn- Crys. Slds 5(9-0): Sssk G. S. Svhhanam M. Rd and P. Malhe 99. Cnsan Illumnan-Induced Open Crcu Vlage ecay (CIOCV) mehd as appled hgh effcency S Slar cells fr ulk and ack surface characerzan. h Eurpean Phvlac Slar Energy Cnference and Ehn pser B -6 pp: