Solar Cell Physics: recombination and generation

NCN Summer School: July 2011 Solar Cell Physics: recombination and generation Prof. Mark Lundstrom lundstro@purdue.edu Electrical and Computer Engineering Purdue University West Lafayette, Indiana USA

copyright 2011 This material is copyrighted by Mark Lundstrom under the following Creative Commons license. Conditions for using these materials is described at http://creativecommons.org/licenses/by-nc-sa/2.5/ 2

acknowledgement Dionisis Berdebes, Jim Moore, and Xufeng Wang played key roles in putting together this tutorial. Their assistance is much appreciated. 3

solar cell physics A solar cell is a simple device just a pn junction with light shining on it. To maximize efficiency, we must maximize the generation of e-h pairs and minimize the recombination of e-h pairs. This lecture is a short introduction to the physics of crystalline solar cells specifically Si. 4

outline 1) Introduction 2) Recombination at short circuit 3) Recombination at open circuit 4) Discussion 5) Summary 5

dark current and recombination - N + P I D s.s. excess holes electron-injecting contact s.s. excess electrons hole-injecting contact V A + 6

recombination in the N-type QNR N - - P + I D electron-injecting contact hole-injecting contact V A + Anytime an electron and hole recombine anywhere within the diode, one electron flows in the external circuit. 7

Shockley-Read-Hall recombination minority carriers injected across junction Fn qv A FP E T SRH recombination I D V A + 8

recombination at a contact minority carriers injected across junction Fn qv A FP I D V A + 9

light-current and generation V bi V A E F base (absorbing layer) emitter V A + I D < 0 10 Every time a minority electron is generated and collected, one electron flows in the external current.

light-current and recombination 3 e-h pairs generated emitter 1 e in external circuit Every time a minority electron is generated and recombines before being collected, the solar cell current suffers. 11

solar cells and recombination Carrier recombination lowers the short-circuit current and reduces the open-circuit voltage. To optimize solar cell performance, we need a clear understanding of how many carriers are recombining and where they are recombining. Then we need to establish a quantitative relation between recombination and solar cell performance. 12

solar cells and recombination J p ( 0) N P Jn ( L) 0 L x I D ( ) ( ) ( ) J V = q R V G R D A TOT A TOT TOT L p = R x dx 0 L 0 ( ) ( ) GTOT = Gop x dx ( 0) ( ) J J L q n q For a formal derivation of this result, see the appendix. 13

outline 1) Introduction 2) Recombination at short circuit 3) Recombination at open circuit 4) Discussion 5) Summary 14

generic crystalline Si solar cell 200 um S F = 1000 cm/s n + emitter (0.3 μm) p-type base (198.9 μm) p + Back Surface Field (BSF) (0.8 μm) key device parameters base doping: N A = 10 16 /cm 3 emitter doping N D = 6 x 10 19 /cm 3 minority carrier lifetime τ n = 34 μs (base) base thickness W = 198.9 μm front junction depth x jf = 0.3 μm back junction depth x jb = 0.8 μm 15

light-generated current 200 um S F = 1000 cm/s n + emitter (0.3 μm) p-type base (198.9 μm) p + Back Surface Field (BSF) (0.8 μm) 1) What is G TOT? 2) How is G TOT spatially distributed? 3) What is R TOT? ( ) ( 0) ( 0) J = q R G D TOT TOT 4) How is R TOT spatially distributed? 5) How do things change if we remove the BSF? 16

light-generated current: numbers 200 um p-type base (198.9 μm) n + emitter (0.3 μm) W 0.3 µ m D Ln 320 µ m p + Back Surface Field (BSF) (0.8 μm) ( 0) ( ) J = J V = = q R G SC D A TOT TOT G G x dx MAX 2L 0 ( ) G = G x dx = 2.79 10 cm s TOT J SC q TOT 0 op op 17-2 -1 ( ) 2.97 10 cm s = = 17-2 -1 2 39.4 ma/cm 2.46 10 17 cm -2 s -1 = = q 16-2 -1 ( 0) 3.31 10 cm s R = 17 CE = 0.88

light-generated current: understanding entire device near surface x j xj + WD 18

light-generated current: summary G G x dx MAX 17-2 -1 ( ) 2.97 10 cm s = = 0 op 2L 0 ( ) G = G x dx = 2.79 10 cm s TOT op 17-2 -1 low lifetime (Auger recombination) surface recombination 19 good collection minority carrier lifetime BSF

recombination at short circuit entire device near surface x + W x j j D 20

recombination at short circuit: summary J SC q 2 39.4 ma/cm 2.46 10 17 cm -2 s -1 q R 0 = 3.31 10 cm s = = ( ) 16-2 -1 TOT (0.37) (0.14) (0.49) low lifetime (Auger recombination) surface recombination 21 good collection minority carrier lifetime BSF

about recombination in the base expect: R( x) ( ) n x τ n 2 d n n 0 2 dx = Ln= Dτ n n L n We find the excess minority electron profile by solving the minority carrier diffusion equation: n ( ) = ( ) J L qs n L n back d ( J n q ) = R dx d n J qd dx n n ( 0 ) = ( 0 ) J qs n n j = + W 0 xj L = L x BSF x xj + W L 22

Adept simulation results ( ) R x ( ) n x τ n n( x) 23

the BSF E = 0.13 ev E C E I E F S back υ th e E k BT ; 0.6 10 7 cm s E V What happens if we remove the BSF? E C E I S back υ th E F ; 1 10 7 cm s 24 E V

without the BSF BSF no BSF With BSF Without BSF J SC = 2 39.4 ma/cm J SC = 2 38.2 ma/cm 25 qr TOT = CE = 0.88 2 5.3 ma/cm qr TOT = CE = 0.85 2 6.5 ma/cm

internal quantum efficiency With BSF No BSF IQE = J D ( V = 0, λ ) F ( λ ) inc 26

questions 1) Can you determine a way to find the actual back surface recombination velocity from the Adept simulation results. (Hint: Use plots of n(x) and J n (x).) 2) How much could the performance improve if the back surface recombination velocity could be reduced to zero? 3) With the original BSF, how much would the performance increase if the minority carrier lifetime was 10 times longer? 4) In the original design, how would the short-circuit current change if the base was twice as thick? 27 5) Since most of the recombination loss occurs in the emitter, why not just make the emitter junction depth a lot smaller?

2D effects I D I( x) D V V ( x) < VD x j dx dr = ρs W ρ S ρ 1 = = x N qµ x j D n j distributed series resistance 28

outline 1) Introduction 2) Recombination at short circuit 3) Recombination at open circuit 4) Discussion 5) Summary 29

dark I-V ( ) ( ) ( ) J V = q R V G D A TOT A TOT ( ( ) ) 0 = q RTOT VA = VOC GTOT Under open circuit conditions: ( ) R V = V = G TOT A OC TOT 30

superposition ( ) ( ) ( ) J V = q R V G D A TOT A TOT J D dark IV dark: dark ( ) = ( ) J V qr V dark D A TOT A D J SC qvd nkbt ( ) J = J e 0 1 illuminated: V OC V A ( ) light ( ) ( ) J V = q R V G light D A TOT A TOT J SC J L < 0 illuminated at V OC : superposition: ( ) R V = G light TOT OC TOT? ( ) ( ) J V = J dark D OC SC R V = J q dark TOT OC SC 31

dark D dark current characteristics (sketch) qv ( ) 0 ( 1) A nkbt A = J V J e dark D qva kbt qva ( ) ( ) ( 2 kbt A = 01 1 + 02 1) J V J e J e series resistance or log 10 dark J D shunt resistance or n = 2 n = 1 V A 32

dark D dark current characteristics (Adept) qv ( ) 0 ( 1) A nkbt A = J V J e dark D qva kbt qva ( ) ( ) ( 2 kbt A = 01 1 + 02 1) J V J e J e n > 1 n = 1 n 2 33

what determines J 0 and n? dark D qv ( ) 0 ( 1) A nkbt A = J V J e Answer: dark ( ) = ( ) J V qr V dark A A TOT A Electron-hole recombination determines I 0. The location of recombination within the solar cell determines the ideality factor, n. 34

recombination in the dark (V A = 0.7 V) Emitter Base 35

recombination summary: (V A = 0.7 V) Short-circuit recombination V A = 0.7 V recombination light qr = TOT 2 ( 0) 5.3 ma/cm TOT 2 ( 0.7) 465 ma/cm dark qr = 36

what happens if we remove the BSF? (V A = 0.7 V) With BSF Without BSF ~70% ~85% 2 ( 0.7) 644 ma/cm J = D D 2 ( 0.7) 1372 ma/cm J = 37

dark current physics (n = 1) FB: minority carriers injected across junction ( ) = ( ) I V qr V D A TOT A 1) Recombination in QNRs: F n qv A F P I D > 0 2) Electrons and holes can also recombine within the SCR of the junction. 38

n = 1 device physics ( ) = ( ) I V qr V D A TOT A ( V ) qv bi A F n n P ( ) 0 n e qva B 0 P n n N 2 0P i A k T F P qr Q t n n TOT n ( V ) = n N 2 i A A Q t n ( qv 1) A kbt e : minority carier lifetime or base transit time Recombination in quasi-neutral regions gives rise to n = 1 currents. 39

dark D dark current characteristics (sketch) qv ( ) 0 ( 1) A nkbt A = J V J e dark D qva kbt qva ( ) ( ) ( 2 kbt A = 01 1 + 02 1) J V J e J e series resistance or log 10 dark J D shunt resistance or n = 2 n = 1 V A 40

recombination in the dark (V A = 0.2 V) emitter region base region 41

recombination summary: (V A = 0.2 V) V A = 0.7 V recombination V A = 0.2 V recombination 2 ( 0.7) 465 ma/cm dark qr = TOT qr dark TOT 6 2 ( 0.7) = 8.4 10 ma/cm 42

dark current physics FB: minority carriers injected across junction ( ) = ( ) I V qr V D A TOT A 1) Recombination in QNRs: F n qv A F P I D > 0 2) Electrons and holes can also recombine within the SCR of the junction. 43

recombination in SCRs ( V ) qv bi A Fn FP dark ( ) = ( ) J V qr V D A TOT A Maximum recombination occurs when n(x) p(x) 2 qva B ( ) ( ) = ne n x p x qva 2kBT ˆ ˆ i n p ne i k T np = n e qv k T 2 A B i qr dark TOT ( V ) A qn e i τ qv A eff 2k T B Recombination in space-charge regions gives rise to n = 2 currents. 44

recombination in SCR ( ) = ( ) J V qr V D A TOT A qva 2kBT ˆ ˆ i n p ne ( ) RV ˆ A nˆ = = τ eff ne i qv τ A eff /2k T B ( ) = ˆ J V qrw D A eff kt B q W eff = E ˆ E ˆ = 4 2.3 10 V cm kt B q W eff = 11 nm Eˆ 45

dark IV D ( ) ( qv 2 ) ( 1 ) ( ) A kbt qva kbt qva nkbt A = 02 1 + 01 1 = 0 1 J V J e J e J e Recombination in depletion regions J n e 02 i E G /2k T large bandgaps and low temperatures B Recombination in neutral regions J n e 01 2 i E G / k T small bandgaps and high temperatures B 46

questions 1) What do you expect to happen if the BSF were removed? Run an Adept simulation to confirm. 2) What do you expect to happen if the minority carrier lifetime were reduced to 0.1 microseconds? Run an Adept simulation. 3) Why is recombination in the emitter so important under shortcircuit conditions, but not under FB in the dark? 4) How much could V OC be increased if a BSF with near-zero surface recombination velocity could be achieved? 5) Series resistance affects the dark current, but it has no effect at open-circuit. What are the implications? 47

outline 1) Introduction 2) Recombination at short circuit 3) Recombination at open circuit 4) Discussion 5) Summary 48

reducing recombination higher material quality (longer lifetimes) ( ) ( ) ( ) J V = q R V G D A TOT A TOT thinner base layer (but optically thick) built-in fields back-surface-fields / minority carrier mirrors reducing contact areas. 49

high-efficiency Si solar cells 24.5% at 1 sun Martin Green Group UNSW Zhao, et al, 1998 50

how good is superposition? V = 0.62 V - Dark V = 0.62 V - Illuminated OC 51

how good is superposition? (ii) dark J Ddark J dark D light D ( V 0) + J = superposition light J D 52

outline 1) Introduction 2) Recombination at short circuit 3) Recombination at open circuit 4) Discussion 5) Summary 53

summary 1) Diode current = q times (total recombination total generation) 2) At V OC, recombination = optical generation 3) At V = 0, recombination lowers the collection efficiency 4) Dark current tells us much about the internal recombination mechanisms 5) Solar cell design is all about maximizing total generation and minimizing total recombination. 6) Simulations can be useful for understanding especially if you look inside and not just at the IV. 54

questions 1) Introduction 2) Recombination at short circuit 3) Recombination at open circuit 4) Discussion 5) Summary 55

Appendices 1) Formal derivation of the relation between current and recombination/generation. 2) Mathematical justification of superposition 56

Appendix 1: current and recombination Formal derivation of the relation between current and recombination/generation. J p ( 0) N P Jn ( L) 0 L x I D R ( ) = ( ) J V q R G D TOT TOT TOT L p = R x dx 0 L 0 ( ) ( ) GTOT = Gop x dx ( 0) ( ) J J L q n q 57

continuity equation for electrons Wabash River Rate of increase of water level in lake = (in flow - outflow) + rain - evaporation n = ( J q) n t Lundstrom 582011 + G R 58

solar cell physics semiconductor equations Conservation Laws: D =ρ = ( J ) ( ) n q Gop R = ( J ) ( ) p q Gop R (steady-state) 59 Relations: D= κε E = κε V 0 0 ( + ) D A ρ = q p n+ N N Jn = nqµ ne + qdn n J = pqµ E qd p p p p R= fnp (, ) G op etc. = optical generation rate

= diode current and recombination ( J ) n q ( Gop R) d ( J n q ) = G op R (1D) dx L L n = ( ) op ( ) 0 0 dj q R x G x dx I D N P 0 L x I D ( ) ( 0) = ( ) ( ) n n op 0 L J L J q R x G x dx 60

current and recombination-generation L ( ) ( 0) = ( ) ( ) + J ( 0) J ( 0) J L J q R x G x d x n n op p p 0 L { Jn ( 0) J p ( 0) } J D ( V ) q R( x) Gop ( x) dx Jn ( L) J p ( 0) + = = 0 ( ) = ( ) J V q R G D TOT TOT L ( ) ( ) ( 0) qr = q R x dx J L J TOT n p 0 L ( ) GTOT = Gop x dx 0 Lundstrom 612011 N P 0 L x I D 61

current and generation-recombination ( ) ( ) ( ) J V = q R V G D A TOT A TOT The diode current is q times the total recombination minus the total generation. The total recombination is the integrated recombination rate within the device plus the flux of minority carriers into each contact. 62 62

Appendix 2: justifying superposition ( ) ( ) ( ) J V = q R V G (valid in light or dark) D A TOT A TOT dark ( ) ( ) J V = qr V (dark current) dark D A TOT A ( ) light ( 0) ( 0) J = q R G (short circuit current) light D TOT TOT dark light ( ) ( ) J V = J + J (principle of superposition) super D A D D 0 ( ) dark light ( ) ( ) ( ) J V qr V q R G super D A = TOT A + TOT 0 TOT (How does this compare to the exact answer?) 63

mathematical justification for superposition J D ( V A )= q R TOT V A ( ) G TOT ( ) (valid in light or dark) J D light light ( V A )= q R TOT ( V A ) G TOT ( ) J D super dark ( V A )= qr TOT light ( V A )+ q R TOT ( 0) G TOT ( ) (principle of superposition) light R TOT dark ( V A )= R TOT light ( V A )+ R TOT ( 0)?? (criterion to justify superposition) 64