Quantitativ Modl of Unilluminatd Diod part II G.R. Tynan UC San Digo MAE 119 Lctur Nots
Minority Carrir Dnsity at dg of quasinutral rgion incrass EXPONENTIALLY forward bias p nb n pa = p n0 xp qv a kt = n p0 xp qv a kt
Wat appns to ts cargs onc ty gt into t quasi-nutral rgion? Dpltion Rgion Is Surroundd by two QUASINEUTRAL Rgions wr E=0 Currnt Transport Occurs Via Diffusion in Tis Rgion J J ~ qd ~ qd dn dx dp dx
Summary so far: Can divid p-n junction diod into two rgions Quasinutral & Dpltion Rgions Minority Carrir Concntration at Dpltion Edg Dpnds Exponntially on Ext. Voltag In Quasi-nutral Rgion Carg Carrirs Mov by Diffusion Solution to Diffusion Eqn è Carg & Currnt in Quasi-nut. rgions
Considr n-sid of diod: Currnt Diffusion: J ~ qd dp dx Hol Consrvation Law (similar to Fluid continuity qn) 1 q dj dx = ( U G) HOW TO TREAT U AND G TERMS?
Basic Equations of Smiconductors W Nd Exprssions for U and for G G ~ Gnration Rat/Unit Volum of /ol pairs via poton adsorption U ~ Loss Rat/Unit Volum of /ol pairs via rlvant mcanisms è Must Examin Poton Adsorption Procss & /ol Loss Procsss
Basics of Solar PV Clls Ky Concpts Poton Enrgy Spctrum Carg Carrir Gnration Via Poton Absorption Carg Carrir Loss Mcanisms Un-illuminatd p-n junction diod Illuminatd p-n junction diod: T Solar PV Cll Solar PV Cll s as an Elctricity Sourc
Carg Carrir Loss Mcanisms Radiativ Rcombination Augr Rcombination Rcombination at Traps Bulk Dfcts & Impuritis Crystal Surfacs/Boundaris
I: Radiativ Rcombination REVERSE of Poton Adsorption Procss:
I: Radiativ Rcombination Wat is t Rat, U R, of tis procss (#/unit volum/unit tim)? A. In Trmal Equilibrium U R =0 (by dfinition) B. Rat Proportional to -dnsity (n) and to Hol dnsity (p) C. Infr Tat Away from Equilibrium, Rat Is U = B( np n 2 R i ) Wr B is a rat constant tat dpnds upon t matrial (for Silicon B~2x10-15 cm 3 /sc)
II: Augr Rcombination Enrgy - - ol Conduction Band Valnc Band Enrgtic Elctron Rcombins wit Hol MUST Gt Rid of Excss Enrgy Transfrs to Scond Elctron Tis Scond Elctron Cascads Back to Lowr Enrgy Enrgy is Transfrrd to Matrial (as HEAT)
II: Augr Rcombination Elctron Augr Liftim: 1 = Cnp + Dn τ 2 Hol Augr Liftim 1 = Cnp + Dp τ 2 U=Dn/t =Dp/t Usually An Important Loss Procss
III. Dfct & Crystallin Surfac Rcombination Dfcts Can Induc /ol rcombination Dfcts Consist of Unwantd Impurity Atoms Bulk Crystal Dfcts (I.. missing atoms, missing rows, tc ) Surfacs Can Also Induc /ol rcombination Adjacnt microcrystal surfacs Solid-Air Intrfac
III. Dfct & Crystallin Surfac Implication Rcombination è WANT TO KEEP UNWANTED IMPURITIES OUT OF PV CELL è WANT TO MINIMIZE NUMBER OF MICROCRYSTALS (I.E. MAKE OUT OF A SINGLE CRYSTAL) BOTH EFFECTS IMPACT MANUFACTURING TECHNIQUES AND COSTS
Modl ts losss w/ Carrir Liftim Carrir liftims: τ = n n o U τ & τ = Δn U ; n o ~ quilibrium valu of n τ = p p o U = Δp quilibrium valu of U ; p o ~ For Radiation Rcombination wit τ = Bn 2 i n o ( n o p o + p o ) B Δn = Δp ~ 2 10 sc p 3 15 cm
Carrir Liftim Concpt (cont d) Carrir liftims, : τ & τ Non-quilibrium Carrir Dnsity Can Tn Dcay: Δ n; Δp τ or τ 1/ tim
Considr n-sid of diod: Minority Carrir (ols) Diffusion: J ~ qd dp dx Hol Consrvation Law (similar to Fluid continuity qn) 1 dj q dx = ( U G) But w ad U=(p n p 0 )/τ = Δp/τ è FIND A DIFFUSION EQUATION W/ SOURCE TERM: d 2 dx Δp 2 = Δp L G 2 D L = D τ
Basics of Solar PV Clls Ky Concpts Poton Enrgy Spctrum Carg Carrir Gnration Via Poton Absorption Carg Carrir Loss Mcanisms Un-illuminatd p-n junction diod Illuminatd p-n junction diod: T Solar PV Cll Solar PV Cll s as an Elctricity Sourc
Un-illuminatd ( DARK ) p-n Diod Rspons 2 p n 0 St G=0; Us = 0 2 x Find t Equation Gn. Soln: B.C. s: Δp = A d dx x L 2 Δp Δp 2 = ; L 2 2 L + B x n L At Junction/n-typ bordr ( x=0 ) D τ pn b = pn 0 qv kt p n > 0 for x A = 0
Un-illuminatd ( DARK ) p-n Diod Rspons Particular Solutions of Minority Carrir Dnsitis in Quasinutral Rgions p n ( x) pn + p 0 n0 qv kt = [ 1] x L n p ( x') np + n 0 p) qv kt = [ 1] x L Wr x, x ar displacmnts away from junction-quasinutral Rgion intrfac
Distribution of carg carrirs undr forward bias Dnsitis Known Hr Exponntial Dcay Hr
Carg Carrir Distributions Known Can Find Currnts Now: For Minority Carrir Currnts in Quasinutral Rgion E.g. on n-typ sid J ( x) = qd dp dx Tus find minority carrir currnts: J J ( x) = qd qv pn 0 kt = ( 1) L qd n L p 0 ( qv kt 1) x' x L L
Known Currnt distribution across p-n diod (so far ) J ( x) J qd qv pn 0 kt = ( 1) L qdn p0 ( x') = L ( qv kt x L 1) x' L
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 Intgrat across junction to find cang in currnt: δj = δj = q 0 ( U G ) W dx Usually W << L, L è Cang in Currnt Is Small & Implis
IF G=0. Currnt Across Junction is ~Constant & Currnt Distribution Looks Lik: Constant Currnt Across Junction
How to Find Majority Currnt in Quasinutral Rgion? Don t Know Currnt Hr
Q: How to Find Majority Currnt in A: W Know J total = Constant So Us Our Otr Solutions (J minority ~ xp(-x/l) To Find Quasinutral Rgion? J total qdn p qd pn = J + J = kt L L ( xp( qv / ) 1) 0 0 +
WE FOUND WHAT WE SEEK: J=J(V) Currnt Dnsity vs Voltag Across Diod: J total qdn p qd pn = J + J = kt L L ( xp( qv / ) 1) 0 0 + 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 + L L
I-V Caractristics of p-n diod