4.8. Solar cells The solar spectrum
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1 4.8. Solr cell Solr cell re p-i-n oodiode, which re opered under forwrd bi. The inenion i o conver he incoing opicl power ino elecricl power wih xiu efficiency The olr pecru The olr pecru i hown in Figure The pecru een fro ellie i referred o he AM0 pecru (where AM nd for ir nd cloely fi he pecru of blck body 5800 K. The ol power deniy i 1353 W/ ower Deniy [W/u] hoon Energy [e] Figure The olr pecru under of AM1 condiion The olr pecru oberved on erh i odified due o borpion in he oere. For AM1 (norl incidence he power deniy i reduced o 95 W/c where for AM1.5 (45 bove he horizon he power deniy i 844 W/. The irregulriie in he pecru re due o borpion pecific oon energie. The correponding cuulive ourren i preened in Figure 4.8. funcion of he oon energy.
2 Cuulive hourren [A/c] hoon Energy [e] Figure 4.8. Cuulive hourren veru hoon Energy under AM1 condiion Clculion of xiu power The curren hrough he olr cell cn be obined fro: / = (e 1 (4.8.1 where i he urion curren of he diode nd i he oo curren (which i ued o be independen of he pplied volge. Thi expreion only include he idel diode curren of he diode, hereby ignoring recobinion in he depleion region. The hor circui curren, c, i he curren zero volge which eul c = -. The open circui volge eul: = ( = 0 = ln( + 1 ln (4.8. The ol power diipion i hen: / = = (e 1 (4.8.3 d The xiu power cur = 0. The volge nd curren correponding o he xil d power poin re nd.
3 d / = 0 = (e 1 + e / d (4.8.4 Thi euion cn be rewrien : + 1 = ln[ ] [ ln( ] (4.8.5 by uing euion (4.8. for he open circui volge. A ore ccure oluion i obined by olving hi rncendenl euion nd ubiuing ino euion (4.8.1 nd ( The xiu power cn be pproxied by: = (1 ( ln( 1+ (4.8.6 ( (4.8.7 or = E (4.8.8 where E = ( (4.8.9 The energy E i he energy of one oon, which i convered o elecricl energy he xiu power poin. The ol oo curren i clculed (for given bndgp E g nd he efficiency eul: J ( E ( g = E ( η = = in in
4 Converion efficiency for onhroic illuinion Thi fir order odel provide n nlyic pproxiion for he efficiency of olr cell under onhroic illuinion. We r wih he reul of ecion 4.8.: η = in = in ( (4.8.1 nd replce by he lrge poible open circui volge, E g, yielding: = ln(1 + kt ( nd η = in kt = [1 ln(1 + ] kt ( for GA olr cell 300K, E g = 55 o h he efficiency eul η = 85% Effec of diffuion nd recobinion in olr cell hoo curren veru volge The oo curren i obined by fir olving he coninuiy euion for elecron d n dn n 0 = D n + µ ne + g dx dx τ op ( well iilr euion for hole. The oo curren i obined fro A ( = ( φ i ( µ nn + µ d d 0 p p dx ( Once hi ourren i obined he ol curren i obined fro: / = (e 1 ( ( To obin he correponding xiu power one h o repe he derivion of ecion 5.3..
5 Specrl repone Becue of he wvelengh dependence of he borpion coefficien one expec he horer wvelengh o be borbed cloer o he urfce while he longer wvelengh re borbed deep in he bulk. Surfce recobinion will herefore be ore iporn for hor wvelengh while recobinion in he ui-neurl region i ore iporn for long wvelengh nfluence of he erie reince ex = + R ( / = (e 1 ( = ex (4.8.0 Repeing he derivion of ecion 4.8. one cn how h he xiu power condiion i given by he following e of rncendenl euion: = ln[ R + ] (4.8.1 / = (e 1 (4.8. while he xiu exernl power eul:,ex = ( + R
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