Silicon solar cell under electromagnetic wave in steady state: effect of the telecommunication source's power of radiation

Transcription

1 IOP Coferece Seres: Materals Scece ad Egeerg Slco solar cell uder electromagetc wave steady state: effect of the telecommucato source's power of radato To cte ths artcle: I Zerbo et al 1 IOP Cof. Ser.: Mater. Sc. Eg Related cotet - 3D modellg of magetc feld ad lght cocetrato effects o a bfacal slco solar cell llumated by ts rear sde M Zougraa, I Zerbo, F Ouédraogo et al. - 3D determato of the morty carrer lfetme ad the p- jucto recombato velocty of a polycrystalle slco solar cell R Sam, B Zouma, F Zougmoré et al. - Three-dmesoal study of a polycrystalle slco solar cell A Deg, I Zerbo, M Wade et al. Vew the artcle ole for updates ad ehacemets. Ths cotet was dowloaded from IP address o 9/1/18 at 15:18

2 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 Slco solar cell uder electromagetc wave steady state: effect of the telecommucato source s power of radato I Zerbo 1, M Zougraa 1, A D Seré, F Zougmoré 1 1 aboratore de Matéraux et Evroemet, Départemet de Physque, UFR-SEA, Uversté de Ouagadougou, BURKINA FASO. Départemet de Physque, Isttut des Sceces Exactes et Applquées, Uversté Polytechque de Bobo Doulasso, BURKINA FASO E-mal : zerbo@uv-ouaga.bf Abstract. The charactersato of morty carrers recombato parameters s mportat to desg ay optoelectroc compoet, sce they play a mportat role the devce performace. May dagostc techques, steady state, quas-steady state, traset ad modulato methods for both the expermetal ad theoretcal measuremet have bee developed for the determato of sgle or several recombato parameters. May studes o recombato ad electrcal parameters of solar cells uder costat magetc feld ad / or electrc feld the bulk due to carrer cocetrato have bee proposed wth oe or three dmesoal approach. I prevous works, we study the effects of electromagetc waves o slco solar cell recombato parameters by chagg the dstace betwee the MW power of radato AM atea ad the solar cell. Ths work presets a oe dmesoal study of the fluece of telecommucato source s power of radato o a slco solar cell llumated by a whte lght steady state. The telecommucato sources whch ca be a AM rado atea or a FM rado atea radate electromagetc waves. Electrc feld testy depeds o the power of radato ad the dstace betwee the electrc feld testy measuremet pot ad the atea. The mageto trasport equatos of excess morty carrers are solved wth ew boudary codtos. New aalytcal expressos of morty carrers desty, photocurret desty, back surface recombato velocty, trsc jucto recombato velocty ad photo voltage depedg o electromagetc feld testy are establshed. The effects of electromagetc feld o photo-curret desty, back surface recombato velocty, trsc jucto recombato velocty ad photo- voltage by makg vary the atea power of radato are the aalysed. We aalyze also the effects of electromagetc feld o the electrc power delvered by the solar cell to a exteral charge. Thus, usg the maxmum of electrc power delvered by the solar cell to a exteral charge, we deduce the solar cell coverso effcecy. The aalyss of electromagetc feld effects o the slco solar cell put out the fluece of AM rado atea or FM rado atea o recombato parameters. 1. Itroducto I prevous work we have studed the fluece of electromagetc waves, produced by a rado atea fuctog ampltude modulato AM, o slco solar cell recombato parameters [1]. I the preset artcle we study the fluece of a telecommucato atea s power of radato o the same parameter. Ths telecommucato atea ca be ether a rado atea fuctog frequecy modulato FM or a rado atea fuctog ampltude modulato AM. Ths rado Publshed uder lcece by IOP Publshg td 1

3 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 stato atea s the source of producto of progressve moochromatc plae electromagetc waves learly polarzed whose electrc feld testy measured at a dstace r from the source s depedat o the power radated by the source ad the dstace r. Therefore we wll study the fluece of electromagetc feld o photo-curret desty, back surface recombato velocty, trsc jucto recombato velocty ad photo- voltage by varyg the atea power of radato. We wll study the fluece of the atea power of radato o the electrc power delvered by the solar cell to a exteral load crcut ad the solar cell coverso effcecy. Fally we wll dscuss the fluece of each type of atea o the solar cell recombato parameters.. Theory.1. Excess morty carrers desty We cosder a polycrystalle back surface feld slco solar cell wth + -p-p + structure []. Sce the base has a greater cotrbuto to photo coverso tha the emtter [3-5], the oe-dmesoal aalyss wll be developed oly o ths rego usg the Quas-Neutral Base assumpto. Moreover we are located the quas eutral bass hypothess (Q.N.B) whle eglectg the crystalle feld that exsts wth the solar cell. Fgure 1. Slco solar cell llumated by whte lght ad uder electromagetc waves fluece We suppose that the solar cell represeted o fgure 1 above s submtted to the acto of a progressve moochromatc plae wave learly polarzed, polarzed Ox drecto ad propagatg the sese of the creasg z. s the ut vector of the electromagetc wave drecto of propagato as the trhedral E,B, s drect. The complex expresso of the electrc feld s: E = E e (1.a) expj ω t k z x ether real otato E = E e cos ωt k z x (1.b) The magetc feld of a progressve plae wave s obtaed by the relato: ()

4 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 ez E B = c B = B e y expj ω t k z ether real otato B = B e cos ω t k y z (.a) (.b) We choose as org of space ad tme the momet whe the electromagetc wave meets the solar cell. At t =, z = so E = E e ad B = B ey x E ad B are respectvely the ampltudes of electrc ad magetc feld. I telecommucato, the level of recepto a gve place of the sgal radated by a trasmtter s measured through the testy of electrc feld E of ths wave. For a sotropc atea radatg a power P r (W) free space, the electrc feld testy E (V /m) depedg o the dstace r (m) s gve by the formula [6]: E 1 = r P Z r π r beg the dstace that separates the source of radato at the measuremet pot of electrc feld testy E ad Z s the characterstc mpedace free space. Whe the solar cell s llumated wth a mult-spectral whte lght ad submtted to the acto of a electromagetc feld, the cotuty equato relatve to excess morty carrers (electros) desty photo geerated the base rego ca be wrtte as []: (x) E x (x) G(x) (4) x x D I ths expresso the solar cell base, E E s a coeffcet that accouts for the mgrato pheomea wth D μ s the electros moblty, E s the electrc feld testy, (3)? the electros dffuso legth, the electros dffuso legth presece of magetc feld. (x) ad G(x) represet respectvely carrers desty ad the optc geerato rate. E x The term of the prevous equato beg a frst dervatve relato wth posto x, s x smlar to a term of dampg. The electros-holes par s optc geerato rate for a mult-spectral cdet lght s gve by [7] 3 b x G x = a e (5) =1 Parameters a ad b are coeffcets deduced from modellg of the geerato rate cosdered for over all the solar radato spectrum uder Ar Mass 1, 5 stadard codtos [8]. The excess morty carrers (electros) desty, soluto of equato (9) s gve by expresso: 3 αx b x δ x = e A ch β x + B sh β x K e (6) =1 3

5 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 wth K D b a 1 E b E, et E 4 Costats A ad B are determed usg the two boudary codtos below: - At the jucto emtter-base (x = ) δx δ ) x= = Sf x D 1 - At the rear sde of the solar cell (x = H) δx δh ) x=h = Sb (7.b) x D Sf s the sum of two cotrbutos: Sf whch s the trsc jucto recombato velocty duced by the shut resstace ad Sf j whch traslates the curret flow mposed by a exteral load ad defes the operatg pot of the cell [9]: (8) Sf = Sf + Sf j Sb s the effectve back surface recombato velocty. Table 1 gves formato cocerg the power of radato of AM ad FM rado ateas [6]. Table 1. Power of radato of AM ad FM rado ateas Type of atea FM atea AM atea Power of radato 5 W 5 kw 5 W MW The results of the prevous work [] showed that the solar cell coverso effcecy s much better as the dstace that separates the solar cell of the atea s weak. Cosequetly we wll carry out the smulato by supposg that the solar cell s placed at 1 m from the electromagetc waves trasmttg atea. The table below gves formato cocerg the atea power of radato ad the electrc ad magetc felds testy used the umerc smulato for a dstace solar cell-atea r =1 m. Alphabetc letter Table. Electrc ad magetc felds testy versus power of radato Power of radato (W) E (V/m) a B (T) b c d e B 1 (7.a).. Photo-curret desty Whle applyg Fck s law at the solar cell jucto, we get photocurret desty expresso presece of electromagetc feld: 4

6 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 δ(x) μ E Jph = q D ) + δ (9) x= x 1+ μ B where q s the electroc charge. The photo-curret desty curves versus jucto recombato velocty are plotted o fgure for dfferet values of electromagetc feld testy or for dfferet values of the power radated by the atea. Fgure. Photo-curret desty versus jucto recombato velocty for dfferet values of power of radato (=. cm; H=.3 cm; D=6 cm /s; μ =135 cm /V.s) Curves of fgure show that the short crcut photo-curret ad the leak curret or dode curret are creasg fuctos of the atea power of radato. Oe also otes that the ope crcut photocurret or dode curret s proportoal to the atea power of radato ad stretches toward the value of short crcut photo-curret for large values of the atea power of radato. Curves (a) ad (b) are practcally cofused short crcut stuato whle they are dfferet oe from the other ope crcut. Curve (b) represets the maxmum power radated by a FM rado atea. We deduce that photo-curret produced by the solar uder the fluece of AM rado waves s more mportat tha the oe produced by the FM rado waves. O fgure 3 below we plot photo-curret desty curves versus solar cell back surface recombato velocty for dfferet values of electromagetc feld testy or for dfferet values of the power radated by the atea. We otce o fgure 3, that for low values of back surface recombato velocty (Sb 1 cm.s -1 ), the photo-curret desty s maxmal whatever the power of radato. The, t decreases wth crease of back surface recombato velocty to reach a asymptotc mmal value for Sb 1 4 cm.s -1. Whatever s the part of the curves; photo-curret desty s a creasg fucto of the power of radato. 5

7 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 Fgure 3. Photo-curret desty versus back surface recombato velocty for dfferet radato powers (=. cm; H=.3 cm; D=6 cm /s; μ =135 cm /V.s).3. Recombato veloctes Photo-curret desty curves versus jucto recombato velocty (fgure ) are asymptotc for large values of Sf (Sf 1 6 cm.s -1 ); ther dervatve wth respect of Sf equals zero ad leads to the back surface recombato velocty [3-5] from equato (1) below: Jph = (1) Sf Solvg the equato (1) eables us to obta back surface recombato velocty expresso: Sb = D 3 =1 β b ch β ch +α H +α H β H e b + α b + α β shβ H β H e b α + b shβ H Photo-curret desty curves versus back surface recombato velocty (fgure 3) are also asymptotc for large values of Sb (Sb 1 4 cm.s -1 ); ther dervatve wth respect of Sb equals zero ad leads to the trsc jucto recombato velocty [3-5] from equato (1) below: Jph = Sb (1) Resoluto of equato (1) permts to obta also trsc jucto recombato velocty expresso: Sf = D 3 =1 e b +αh β α shβ H+ b β chβ H α shβ H β e b +αh β chβ H+ b + αshβ H β b (11) (13) 6

8 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 O fgure 4 below, we plot back surface recombato velocty curves versus carrers dffuso legth for dfferet values of the atea power of radato. We otce that solar cell back surface recombato velocty s a decreasg fucto of the dffuso legth ad the atea power of radato. Fgure 4. Back surface recombato velocty versus dffuso legth for dfferet values of power of radato (H=.3 cm; D=6 cm /s; μ =135 cm /V.s) Electrc feld testy beg also a creasg fucto of the atea power of radato ad cosderg the prevous work results [], the electrc feld tesfes carrers mgrato toward the solar cell jucto. It has for cosequece the decrease of back surface recombato velocty so a reducto of the losses of carrers ths solar cell zoe ad a mprovemet of the Back Surface Feld effect. The tesfcato of carrers mgrato toward the solar cell jucto s also at the org of short crcut curret crease whereas ope crcut stuato t s at the org of the ope crcut curret observed o the curves of fgure. Thus, solar cell back surface recombato velocty s weaker whe the cdet wave s a AM rado wave. We plot o fgure 5 below, solar cell trsc jucto recombato velocty curves versus carrers dffuso legth for dfferet values of the atea power of radato. 7

9 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 Fgure 5. Itrsc jucto recombato velocty versus dffuso legth for dfferet values of power of radato (H=.3 cm; D=6 cm /s; μ =135 cm /V.s) The shape of the dfferet curves shows that solar cell trsc jucto recombato velocty s a decreasg fucto of dffuso legth ad a creasg fucto of the atea power of radato. Ideed, the trsc jucto recombato velocty s a mcroscopc parameter that accouts for the losses of carrers at the solar cell jucto. These losses of carrers costtute the leak curret at the solar cell jucto. Thus, the hgher the trsc jucto recombato velocty, the more the losses of carrers or eve the leak curret at the solar cell jucto s eormous. Ths s agreemet wth the curves of fgure where we observed a leak curret ope crcut, whch curret s strogly trbutary of the atea power of radato. It s fally evdet from the aalyss of the dfferet curves that the trsc jucto recombato velocty duced by the AM rado waves s more mportat tha the oe duced by the FM rado waves..4. Jucto photo-voltage The photo-voltage across the jucto s expressed by meas of excess morty carrers desty at the jucto (x = ) accordg to Boltzma s relato: k B T δ Vph = l +1 (14) q Wth N ad V = k T / q B T B where s the trsc carrer s desty at thermal equlbrum, N B the dopg desty of the base ad V T the thermal voltage. We plot o fgure 6 photo-voltage curves versus jucto recombato velocty for dfferet values of the atea power of radato 8

10 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 Fgure 6. Photo-voltage versus jucto recombato velocty for dfferet values of power of radato (=. cm; H=.3 cm; D=6 cm /s; μ =135 cm /V.s) Curves of fgure 6 show that ope crcut voltage s a decreasg fucto of the power of radato. Ideed, we have observed o the curves of fgure the exstece of a curret ope crcut amed leak curret due to the passage of some carrers through the solar cell jucto Thus, a decrease of the ope crcut voltage traslated a decrease of the carrers stocked at the jucto. I fact, some carrers havg crossed the jucto produce a leak curret that s quatfed, from a mcroscopc vew pot, by the trsc jucto recombato velocty. A decrease of the ope crcut voltage traslates so a crease of the losses of carrers at the jucto or eve a crease of the trsc jucto recombato velocty at the solar cell jucto. The aalyss of the dfferet curves permts to say that the theoretcal ope crcut voltage produced by the solar cell uder the fluece of FM rado waves s more mportat tha the oe produced by the AM rado waves..5. Solar cell electrc power ad coverso effcecy The electrc power delvered by the solar cell base to a exteral load crcut s expressed usg the equato (14) below: PSf = VphSf JphSf T (15) Wth JphSf = q Sf δ T j Jph(Sf) T s the photo-curret that crosses the exteral load resstace. Electrc power varatos versus jucto recombato velocty for dfferet values of the electromagetc waves trasmttg atea power of radato are plotted o fgure 7. 9

11 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 Fgure 7. Electrc power delvered by the solar cell versus jucto recombato velocty for dfferet values of power of radato (=. cm; H=.3 cm; D=6 cm /s; μ =135 cm /V.s) The aalyss of the dfferet curves shows that the electrc power delvered by the solar cell base s ull ear the ope crcut ad the short crcut. It passes by a maxmum that s located a termedate operatg pot. Ths operatg pot for whch the electrc power s maxmal moves toward the short crcut (large values of Sf) whe the electromagetc feld testy creases or whe the atea power of radato creases. The maxmum electrc power delvered by the solar cell to a exteral crcut permts to calculate the solar cell coverso effcecy. Thus, ths coverso effcecy s the report of the maxmum electrc power delvered by the solar cell to a exteral crcut ad the power of cdet lght flux receved by the solar cell. P η = el Sf P c max P c s the power of the cdet lght flux ad P c = 1 mw/cm Ar Mass 1.5 stadard codtos. We determed the values of maxmum electrc power delvered by the solar cell to a exteral crcut ad the values of jucto recombato velocty correspodg, ad the we calculated the solar cell coverso effcecy. These results are cosged the table 3. The maxmum electrc power delvered by the solar cell base to a exteral crcut creases wth electromagetc feld testy that s to say wth the atea power of radato. The aalyss of the results cosged table 3 permts to say that the FM rado ateas that produce weak values of electromagetc feld have less fluece o the solar cell tha AM rado ateas. Besdes, the solar cell coverso effcecy ad the maxmum electrc power delvered by the solar cell to a exteral crcut evolve the same sese. (16) 1

12 1st Iteratoal Symposum o Electrcal Arc ad Thermal Plasmas Afrca (ISAPA) IOP Publshg IOP Cof. Seres: Materals Scece ad Egeerg 9 (1) 119 do:1.188/ x/9/1/119 Table 3. Maxmum electrc power delvered by the solar cell, correspodg jucto recombato velocty ad solar cell coverso effcecy for dfferet power of radato Alphabetc letter Power of radato (W) E (V/m) B (T) Sf (cm/s) Pel max (W/cm ) Effcecy η ( ) a, ,17 17, (absece atea) b 5 38,7 1, ,36.1 4, ,167 c 5 1,4 4, ,19.1 4, ,486 d 5 387,1 1, ,47.1 5, ,854 e 774,3, ,95.1 5, , Cocluso A theoretcal study of electromagetc waves power of radato fluece o slco solar cell recombato parameters s preseted. The study of photo curret desty shows that the short crcut photo-curret ad the ope crcut photo-curret (leak curret or dode curret) are creasg fuctos of the atea power of radato. The study of back surface recombato velocty shows that the electrc feld whch s a creasg fucto of the atea power of radato tesfes carrers mgrato toward the solar cell jucto. The cosequece of ths mgrato pheomeo s the decrease of back surface recombato velocty, whch meas a reducto of the losses of carrers at the solar cell jucto ad a mprovemet of the Back Surface Feld effect. The same mgrato pheomeo explas the exstece of the ope crcut curret. As for the trsc jucto recombato velocty whch s a mcroscopc parameter that accouts for the losses of carrers at the solar cell jucto, t s a creasg fucto of the atea power of radato. The decrease of the ope crcut voltage, decreasg fucto of the power of radato, traslates a crease of the losses of carrers at the solar cell jucto or eve a crease of the trsc jucto recombato velocty at the same jucto. Accordg to the aalyss above, the short crcut curret, the ope crcut curret ad the trsc jucto recombato velocty of the solar cell uder the fluece of AM rado waves are more mportat tha that of the same solar cell uder the fluece of FM rado waves. The same aalyss also put evdece a decrease of solar cell ope crcut voltage ad a back surface recombato velocty wth the crease of the atea power of radato. The umerc calculatos put evdece a crease of the maxmum electrc power ad the solar cell coverso effcecy wth the crease of the atea power of radato. These results permt to coclude that the fluece of FM rado waves o the solar cell s lesser tha that of AM rado waves. Refereces [1] Zerbo I, Zougraa M ad Zougmoré F 11 4 th IUPAP It. Cof. of Wome I Physcs ICWIP Stellebosch South Afrca [] e Quag N, Rodot M, Njs J, Ghaam M ad Coppye J 199 Joural de Physque III (7) [3] Barro F I, Naema E, Wereme A, Zougmore F ad Sssoko G 1 Joural des Sceces 1 (1) 76-8 [4] Barro F I, Naema E, Zougmore F, Wereme A, Ndaye A ad Sssoko G 3 Joural des Sceces 3 (1)1-14 [5] Zerbo I, Koalaga Z, Barro F I, Zougmore F, Ndaye A, Dao A ad Sssoko G 4 Joural des Sceces 4 () 4-46 [6] Ulrch Freyer 1994 Nachrchte-Uebertragugstechk (Much Carl Haser) [7] Furla J ad Amo S 1985 Sold State Electrocs 8(1) [8] Mohammad S N 1987 J. Appl. Phys. 61() [9] Dallo H, Maga A S, Wereme A. ad Sssoko G 8 Europea Phy. J.: Appl. Phys