External Electric Field Influence on Charge Carriers and Electrical Parameters of Polycrystalline Silicon Solar Cell

Transcription

1 Research Joural of Appled ceces, Egeerg ad Techology 4(17: , 1 IN: Maxwell cetfc Orgazato, 1 ubmtted: ecember, 11 Accepted: Jauary 1, 1 Publshed: eptember 1, 1 Exteral Electrc Feld Ifluece o Charge Carrers ad Electrcal Parameters of Polycrystalle lco olar Cell 1 M Zougraa, B eg, OH Lemrabott, 1 F Toure, 1 MA Ould El Moujtaba, 1 ML ow ad 1 G ssoko 1 Faculty of cece ad Techology, Uversty Chekh Ata op, akar, eegal Uversty of Bambey, UFR ATIC, UBI, Physcs ecto, Bambey, eegal Hgher Multatoal chool of Telecommucatos, EMT, akar, eegal Abstract: Ths study deals wth exteral electrc feld fluece o polycrystalle slco solar cell behavor We study a -p-p solar cell uder electrc feld resultg from a polarzato ad uder costat multspectral llumato Takg to accout ths electrc feld, we establsh ews expressos of cotuty equato, photocurret desty ad back surface recombato velocty O the bass of these equatos, we studed electrc feld effect o charge carrer s dstrbuto the bulk of the base, o photocurret behavour ad o the charge carrer s recombato at the rear zoe of the base Keywords: Electrc feld, electrc polarzato, multspectral lght llumato, photocurret, polycrystalle slco, recombato velocty INTROUCTION May researches o solar cells are desged to mprove ther performace To do ths we try to fd maufacturg techology (Neame, or operatg codtos that mmze the effects lmtg the performace of solar cells, that s to say photogeerated morty carrer s recombato the bulk of the base (hockley-read-hall, Auger ad radatve (ze ad Kwok, 7; to ad waso, 197 ad surface, shadg effects ad resstve losses We preset ths study, a study of electrc polarzato effect o crystalle slco solar cell uder multspectral llumato ad statc codtos (Madougou et al, 7 Ths study deals wth exteral electrc feld effect o photogeerated carrer s behavour the base PREENTATION OF THE MOEL AN CONTINUITY EQUATION ETERMINATION We preset Fg 1 a -p-p (Le Quag et al, 199 olar cell uder multspectral llumato I order to study exteral electrc feld fluece o charge carrer s behavour the bulk of solar cell base, we polarze by applyg a potetal dfferece ad we study the theory of Quas Neutral Base (QNB (Furla ad Amo, 195 Exteral polarsato creates a teral electrc feld that flueces charge carrers total movemet Ths electrc feld s the sum of the exteral electrc feld resultg from polarzato ad of the solar cell teral r r r electrc feld ( E = Eext Et Uder these codtos the equato for the dstrbuto of charge carrers the bulk of the base s gve by Eq (1: d 1 t dx e J 1 e J = R x G x x x dx ( ( e s the elemetary charge, Gx = a e = 1 bx (1 s the carrer geerato rate at posto x (Mohammad, 197, a ad b are coeffcets deduced from modelg of the geerato rate cosdered for overall the solar radato spectrum whe AM=15 (ssoko et al, 1996, R(x = *(t / J represets morty carrer recombato rate at the posto x: *(x s the photogeerated morty carrers desty at the depth x the base ad t s the lfetme of these carrers The dstace dx s ftesmal, we ca do a developmet of J(x dx Taylor seres: J(x dx = j(x Mj(x / Mx dx Equato (1 becomes: 1 Jx = Gx Rx t e x ( J(x s the curret desty resultg of both coducto curret J c = *(xe : E ad dffuso curret J d = e M*(x / Mx alog (Ox axs, m s the electro moblty ad the dffuso coeffcet of electros photogeerated the base J x therefore expressed as: Correspodg Author: M Zougraa, Faculty of cece ad Techology, Uversty Chekh Ata op, akar, eegal 967

2 Res J App c Eg Techol, 4(17: , 1 Fg 1: -p-p slco solar cell uder exteral electrc feld Jx = Jc Jd = δ ( x e µ E e x By jectg ( (, we have: ( Let us L E = : EJ ad troduce electros dffuso legth ths expresso, we obta the followg expresso: L E = : E L / By replacg L E = : E L / Eq (6, we obta the Eq (7 follow: 1 = δ ( x e µ E e Gx Rx = t e x x L δ δ E x x Gx = L L (7 fally: E = µ E µδ ( x Gx Rx t (4 Equato (4 s the geeral cotuty equato of morty charge carrers the base of a semcoductor polarzed I the case of our study, the polarzato s costat, we have ME / Mx = Over the solar cell s also uder costat multspectral llumato statc codtos, we have M*(x / Mt = The cotuty equato for morty charge carrers the base of the solar cell uder such codtos ca be summarzed thus: δ ( x E Gx Rx µ = x (5 olvg the cotuty equato: Equato (5 s a dfferetal equato of secod order wth costat coeffcets ad secod member whch may be released as follows, after replacg R(x by ts expresso: µ δ δ x E x x Gx x τ = (6 The soluto of ths dfferetal equato wthout secod member s gve by: *(x e $x [Ach(" x B sh(" x] wth α = ( L E 4 L L 1 ad $ =!L E / L The geeral soluto of the dfferetal equato wth secod member s gve by the followg expresso: β δ x α α wth x = e [ A ch( x B sh( x] c e c = α L [ L b L b 1] E = 1 bx ( Coeffcets A ad B ca be determed through the boudary codtos gve by: C at the jucto (x = : ( x δ F = x = δ x (9 96

3 Res J App c Eg Techol, 4(17: , 1 Chage carrets des ty (cm Chage carrets des ty (cm :E = V/cm :E = V/cm :E = 5V/cm 5:E = 1V/cm 1 Base depth x (cm Fg : Carrers desty versus base depth for dfferet values of the electrc feld; (L: cm; B : 1 4 cm/s; F : 1 cm/s; H: cm; : 6 cm /s; :: 1 cm /Vs Electrc feld E (V/cm Fg : Jucto carrers desty profle versus electrc feld short crcut stuato: (L: cm; B : 1 4 cm/s; F : 1 cm/s; H: cm; : 6 cm /s; :: 1 cm /Vs C at the back surface (x = : ( ( x δ B = x= H δ x (1 Parameters F ad B represet respectvely the jucto recombato velocty ad the back surface recombato velocty (allo et al, ; Mbodj et al, 1 Expressos of coeffcets A ad B are gve by Eq (11 ad (1: A= = 1 H ( β b α b B e ( bf ( β B sh( α ( b F α ch( α α ( B F ch( α α ( β B ( β F sh( α (11 Chage carrets des ty (cm Base depth x (cm 1:E = V/cm :E = V/cm :E = 5V/cm 5:E = 1V/cm Fg 4: Carrer desty profle versus solar cell base depth x ope crcut stuato for dfferet values of the electrc feld: (L: cm; B : 1 4 cm/s; F : cm/s; H: cm; : 6 cm /s; :: 1 cm /Vs B= = 1 C α( b F sh( α ( b F ( β B ch( α ( b B H( β b ( F e β α ( B F ( α α ( β B sh( α ( β ch H F (1 Carrer desty profle the base: Fgure shows carrer desty varato versus depth x for fve values of exteral electrc feld O Fg we observe the jucto carrers depedece of the electrc feld short crcut stuato We observe o the curves Fg, a frst zoe where carrer s desty gradet s postve All carrers that part of the curve ca be retured to the jucto to partcpate photocurret We also ote that the dfferet curves peaks move toward the jucto whe electrc feld creases Ths pheomeo s terpreted as a base depth reducto (ssoko et al, 199 Ideed for a solar cell, t s the carrers located the frst rego (rego wth postve gradet that ca cross the jucto ad cotrbute to the photocurret The base depth appears to be lmted to the rego betwee the jucto ad the peak maxma for each value of the electrc feld A shft of peaks towards the jucto characterzes the reducg of the usable base depth Ths pheomeo s accetuated wth creasg electrc feld We also ote that wth the crease of electrc feld, carrer s desty maxma decrease but ther postve slopes crease The decrease of the carrer s desty maxma reflects a reducto of photogeerated carrers the bulk of the base The depleto eforcemet (Fg traduces a crease of the carrers retured to the jucto uder the fluece of the electrc feld; there s a creasg 969

4 Res J App c Eg Techol, 4(17: , 1 Photo curret des ty (A/cm :E = V/cm :E = V/cm :E = 5V/cm 5:E = 1V/cm Recombato velocty f (cm/s ELECTRIC FIEL EFFECT ON PHOTOCURRENT ENITY AN PHOTOVOLTAGE Electrc feld effect o photocurret desty: The geeral expresso of photocurret desty s gve by (to ad waso, 197: J = q E = µ δ ph x (1 Fg 5: Photocurret desty versus jucto recombato velocty for dfferet values of electrc feld: ( B : 41 4 cm/s; : 6 cm /s; L: cm; H: cm; :: 1 cm /Vs Photo curret des ty (A/cm Electrc feld E (V/cm Fg 6: Photocurret desty versus electrc feld short crcut stuato: (L: cm; B : 1 4 cm/s; F : 1 cm/s; H: cm; : 6 cm /s; :: 1 cm /Vs carrer cocetrato at the jucto wth electrc feld It s as f the electrc feld resultg from the exteral bas accelerates charge carrers so that they ca reach the jucto Fgure 4 below shows the morty carrer desty profle wth depth the base for dfferet values of the electrc feld a stuato of ope crcut It s oted here that the maxma of the carrer desty curves the rego ear the jucto decrease whe the electrc feld creases We observe also o ths fgure that all curves have egatve slopes Ths traduces the fact that at the ope crcut ay carrer ca cross the jucto to partcpate to the photocurret The decrease of the maxmum carrer destes wth the electrc feld both stuatos (short ad ope crcut characterzes a decrease of photogeerato ad crease of bulk recombato wth the electrc feld It meas also, a more dffuso of carrer through the jucto wth electrc feld applcato Ths also reflects a ope crcut voltage decrease wth the crease of electrc feld By jectg Eq (9 (1, we have Eq (14: J ph = q *( ( F : E (14 By replacg *( by ts value Eq (14, we obta the expresso of J ph : ( α H( β b α ( ch( α J q C b ch H e α B ph = = 1 B F α ( β B ( b β sh( α ( F µ E α ( β B ( β F sh( α (15 We ote here that whe we take to accout the coducto term, we obta a ew expresso photocurret desty Fgure 5 ad 6 below show respectvely, photocurret desty profles versus jucto recombato velocty ad versus exteral electrc feld I Fg 5, we otce that each curve presets three parts: the frst part where gradet s almost zero, a secod part where t s postve ad the thrd part where he s also zero Wthout electrc polarzato (E = we see that the photocurret desty s practcally zero at low F values (the carrers are blocked at the jucto, the solar cell operates ths case ope crcut codto The photocurret desty creases quckly wth F to fally stablze at large F values The photocurret s maxmum ad the solar cell therefore operates short crcut codto Whe we apply a polarzato, we fd that the curret at ope crcut ( F s ot zero, but rather s proportoal to the bas duced feld, as s the short crcut It therefore appears that the electrc feld has a great fluece o the photocurret ad hece the carrer dffuso across the jucto, as cofrmed also Fg 6 97

5 Res J App c Eg Techol, 4(17: , 1 Photo cvoltage (V 6 4 1:E = V/cm :E = V/cm :E = 5V/cm 5:E = 1V/cm Recombato velocty f (cm/s - Recombato velocty b (cm/s Electrc feld E (V/cm Fg 7: Photovoltage versus jucto recombato velocty for dfferet values of electrc feld: ( F : 41 4 cm/s; : 6 cm /s; L: cm; H: cm; :: 1 cm /Vs Fg 9: Back surface recombato velocty B versus electrc feld: (L: cm; H: cm; : 6 cm /s; :: 1 cm /Vs Photo voltage (V Electrc feld E (V/cm I addto, some electros the p rego ad a few holes the rego, drve by the duced electrc feld are able to cross the space charge rego eve ear the ope crcut ( F It s ths movemet whch explas photocurret presece for low values of jucto recombato velocty F Electrc feld effect o the photovoltage: The photovoltage expresso s gve the case of the approxmato by Boltzma: Fg : Ope crcut voltage versus electrc feld: ( B : 41 4 cm/s; F : 1 cm/s; : 6 cm /s; L: cm; H: cm; :: 1 cm /Vs V phm m = VT l δ 1 (16 The creasg of the photocurret obtaed ear the ope crcut wth electrcal bas could also be oe reaso for the decrease the carrer desty observed o Fg 4 Ideed, ths pheomeo reflects the fact that a part of photogeerated carrers the bulk of the base flows through the jucto Ths physcal pheomeo could be terpreted as follows: The solar cell was reverse based, the resultg electrc feld, oreted from to p as show Fg 1, wll provde addtoal eergy to the electro-hole pars of the base ad emtter so that morty carrers ca move toward the jucto more easly (ssoko et al, 199 These electros ad holes reforce some of the ozed layers of the space charge rego, whch s the source of the potetal barrer o there s a crease of the space charge rego s wdth ad subsequetly a crease of the barrer potetal ad the electrc feld at the jucto Gve that the feld at the jucto becomes more tese, the charge carrers set to ths zoe flow much faster, reducg the carrer s cocetrato the bulk of the base Ths could expla the curves Fg (decrease of the maxma ad shft to the jucto V T Thermal voltage V T = k T /q( V T = 6 mv at T = K Electros desty at thermodyamc equlbrum = /N B N B Electros trsc cocetrato for the slco The dopg desty at the base (N B = 1 16 cm! ad k s the Boltzma costat Fgure 7 ad show photovoltages varato versus jucto recombato velocty F for varous electrc feld We observe Fg 7 that large photovoltage values correspod to small values of F wth a zero gradet (ope crcut voltage ad ths gradet becomes egatve ad costat whatever electrc feld value before vashg for large F values We also ote thattheope crcut voltage (low values of F decreaseswth the electrc feldaccordg to ourprojectos paragraph(, as cofrmedalso Fg Electrc feld effect o back surface recombato velocty: We study ths secto the duced electrc feld effect o electro-hole par geerato or recombato to the solar cell uder optcal exctato 971

6 Res J App c Eg Techol, 4(17: , 1 By observg photocurret desty profles (Fg 5, we see that the gradet of photocurret s zero for large values of F I ths rego of F, we ca wrte: MJ ph / M F = (17 The soluto of Eq (17 gves two values of back surface recombato velocty B : Bo = µ E α ch α H α sh µ E β β ( α ch( α ( µ E β sh( α ( α (1 We ote here that B s a fucto of electrc feld ad the dffuso coeffcet, ad depedet of the carrer s geerato terms a, b, so t s a dffuso rate The secod value of B s: B = = 1 H( β b α b ( ch( α e [ α β( b β] sh α H H( β b α( ch( α e ( b β sh H ( α (19 Back surface recombato velocty B s a fucto of geerato terms a, b, electrc feld ad dffuso coeffcet Fgure 9 follow llustrates back surface recombato velocty behavor versus polarzato electrc feld We observe ths fgure back surface recombato decrease wth electrc feld crease We ca therefore say that solar cell electrc polarzato reduces carrer s recombato at the rear zoe of the base ad ehaces the BF (Back urface Feld effect (Umesh ad Jasprt, These results are perfect agreemet wth those of the precedg paragraphs: creases of photogeerated carrer s desty at the jucto, short-crcut ad ope crcut currets wth electrc feld crease We thus arrve atthe coclusothat solar cell electrc polarzato reducesthe pheomeo of bulk recombato the base ad ehacescarrer s mgratotothe juctofor a possblepartcpato thephotocurret CONCLUION I ths study, we establshed a cotuty equato that depeds o the electrc feld The resoluto of the cotuty equato drove us to ew expressos of excess morty carrers desty, photocurret ad back surface recombato velocty, all depedet o the electrc feld We studed electrc feld fluece o these parameters It appears from ths study that the solar cell polarzato decreases back surface recombato velocty ad bulk recombato, crease carrer s moblty to the jucto ad facltate ther crossgs of the jucto Ths pheomeo comes wth the wdeg of jucto space charge zoe, whch drve to short crcut curret crease wth polarzato electrc feld crease REFERENCE allo, HL, A Wereme, A Maïga ad G ssoko, New approach of both jucto ad back surface recombato veloctes a modellg study of a polycrystalle slco solar cell Eur Phys J Appl Phys, 4: -11 Furla, J ad Amo, 195 Approxmato of the carrer geerato rate llumated slco old tate Electro, : Le Quag, N, M Rodot, J Njs, M Ghaam ad J Coppye, 199 Répose spectrale de photoples de haut redemet au slcum multcrstall J Phys III Frace, : Madougou,, F Made, M Boukary ad G ssoko, 7 I-V Characterstcs for bfacal slco solar cell studed uder a magetc feld Adv Mat Res, 1-19: -1 Mbodj,, B Mbow, FI Barro ad G ssoko, 1 A d model for thckess ad dffuso capactace of emtter-base jucto a bfacal polycrystalle solar cell Global J Pure Appl c, 16(4: Mohammad, N, 197 A alteratve method for the performace aalyss of slco solar cells J Appl Phys, 61(: Neame, A, emcoductor Physcs ad evces Basc Prcple McGraw-Hll, New York to, RA ad PM waso, 197 A optmsato study of Pot Cotact Cocetrato 15th LEEE Photov pect Cof UA, pp: 17-1 ssoko, G, E Naéma, A Corréa, PM Bteye, M Adj ad AL Ndaye, 199 lco olar cell recombato parameters determato usg the llumated I-V characterstc Reew Eerg, : ssoko, G, C Museruka, A Corréa, I Gaye ad AL Ndaye, 1996 Lght spectral effect o recombato parameters of slco solar cell Reew Eerg, : ze, M ad KN Kwok, 7 Physcs of emcoductors evces Wley, New York Umesh, KM ad Jasprt, emcoductor evce Physcs ad esg prger 97