Quantitative Model of PV Cells The Illuminated Diode. G.R. Tynan UC San Diego MAE 119 Lecture Notes

Transcription

1 Quantitativ Modl of PV Clls T Illuminatd Diod G.R. Tynan UC San Digo MAE 119 ctur Nots

2 WE FOUND WHAT WE SEEK: JJ(V) Currnt Dnsity vs Voltag Across Diod: J total qdn p qd pn J + J kt ( xp( qv / ) 1) Total Currnt, I (Amps), Is Just Jtotal * Ara of Diod ( xp( qv / ) 1) I( V ) I0 kt qdn p qd p 0 n0 I 0 A +

3 I-V Caractristics of p-n diod

4 Basics of Solar PV Clls Ky Concpts Poton Enrgy Spctrum Carg Carrir Gnration Via Poton Absorption Carg Carrir oss Mcanisms Un-illuminatd p-n junction diod Illuminatd p-n junction diod: T Solar PV Cll Solar PV Cll s as an Elctricity Sourc

5 Calculating Effct of Illumination wit E > Egap Potons Assum - gnration rat G constant Corrsponds to Epoton ~ Egap Flux Earlir Assumptions Still Valid Quasinutral Rgion, Dpltion Rgion Drift Currnt Dnsity ~ Diffusiv Dnsity in Dpltion Rgion Small minority carrir population Diffusiv minority carrir transport in quasinutral rgion

6 Poton absorption in smiconductor For Poton Enrgy, E n > E gap Poton Is Adsorbd & Crats /ol pair At Adsorption Sit:

7 Poton absorption in smiconductor For Poton Enrgy, E n < E gap Poton May b Adsorbd BUT DOES NOT CREATE /ol pair Or (mor likly) it passs troug matrial:

8 Approximat /ol Gnration Rat Assum All Potons Hav Enoug Enrgy to Crat /ol Pairs Tn G Is G ( 1 R) αn xp( xα) Poton Flux vs Distanc into PV Cll N(x) Numbr of Potons/Unit Ara/Unit Tim PV Cll x

9 Approximat /ol Gnration Rat For Wak Adsorption Approximat Gnration Rat, G (units: /ol pairs/unit volum/unit tim) G ~ ( 1 R) αn R fraction of ligt rflctd from surfac (R~0.05 wit Anti-rflction coating) N numbr potons/unit ara/unit tim a poton intnsity -folding attnuation lngt Typically fw microns

10 Typical Adsorption Cofficint Data for Ga-As Typical Pnntration Dpt for E>Egap,: 1/a~1 micron Data for Silicon Not Too Diffrnt

11 Basics of Solar PV Clls Ky Concpts Poton Enrgy Spctrum Carg Carrir Gnration Via Poton Absorption Carg Carrir oss Mcanisms Un-illuminatd p-n junction diod Illuminatd p-n junction diod: T Solar PV Cll Solar PV Cll s as an Elctricity Sourc

12 Effct of Illumination on diod MINORITY CHARGE CARRIER DISTRIBUTION: Diffusion Eqn for ol population distribution d dx Gnral Solution p n Δp 2 Δp 2 Gτ Δp + C G 2 D x + D x Us Sam Boundary Conditions to find Particular Solution qv kt pn + G + [ pn ( 1] ( x) τ 0 0 x Similar Rsult for Elctrons Holds

13 Effct of Illumination on diod MINORITY CHARGE CARRIER CURRENT: Currnt is Diffusiv, I.. J ~ dp/dx, J ~dn/dx è J J ( x) ( x') qd qd p n n p 0 0 ( ( qv kt qv kt 1) 1) x x' qg qg x x' Nxt, nd currnt across junction

14 Nd Currnt Flow in Dpltion Rgion (aka Transition Rgion or Junction) Currnt continuity quation givs 1 q dj dx ( U G) 1 q dj dx Nglct osss in Junction & Intgrat across junction to find cang in currnt: 0 W δj δj q Gdx ~ qgw (sinc G ~ constant)

15 Distribution of carrirs wit Illumination

16 Diod Rspons w/ Illumination: Currnt Dnsity vs Voltag Across Diod: J total qd n p J J qd dj p n 0 ( xp( qv / kt ) 1) + qgw Total Currnt, I (Amps), Is Just Jtotal * Ara of Diod I I I 0 ( qv kt qag( 1) I + W + )

17 Illuminatd p-n diod V mp Powr, PI V Voltag, V

18 Caractrizing Solar PV Cll Prformanc Opn Circuit Voltag, Voc Sort-circuit Currnt, Maximum Powr Point (Vmp,Imp) Fill Factor, V FF V MP OC V oc kt q I ln( I 0 + 1) I I qag( + W + ) I I SC MP SC Typically FF~ Efficincy η V I P MP in MP V I P OC in SC ~

19 Solar Poton Flux Spctrum & Maximum Sort-Circuit Currnt

20 Solar Cll Efficincy imits On Poton > On -ol pair + Trmal Enrgy Rcombination osss (Surfacs, Dfcts, Impuritis) Rflctions & Scattring

21 Basics of Solar PV Clls Ky Concpts Poton Enrgy Spctrum Carg Carrir Gnration Via Poton Absorption Carg Carrir oss Mcanisms Un-illuminatd p-n junction diod Illuminatd p-n junction diod: T Solar PV Cll Solar PV Cll s as an Elctricity Sourc