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Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
Solar Cells Lecture 2: Physics of Crystalline Solar Cells
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Solar Cells Lecture 2: Physics of Crystalline Solar Cells

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Mark Lundstrom (2011), "Solar Cells Lecture 2: Physics of Crystalline Solar Cells," http://nanohub.org/resources/11890.

Mark Lundstrom (2011), "Solar Cells Lecture 2: Physics of Crystalline Solar Cells," http://nanohub.org/resources/11890.

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  • 1. 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
  • 2. copyright 2011This material is copyrighted by Mark Lundstromunder the following Creative Commons license.Conditions for using these materials is described athttp://creativecommons.org/licenses/by-nc-sa/2.5/ Lundstrom 2011 2
  • 3. acknowledgementDionisis Berdebes, Jim Moore, and Xufeng Wangplayed key roles in putting together this tutorial.Their assistance is much appreciated. Lundstrom 2011 3
  • 4. solar cell physicsA solar cell is a simple device – just a pn junction withlight shining on it.To maximize efficiency, we must maximize thegeneration of e-h pairs and minimize the recombinationof e-h pairs.This lecture is a short introduction to the physics ofcrystalline solar cells – specifically Si. Lundstrom 2011 4
  • 5. outline1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary Lundstrom 2011 5
  • 6. dark current and recombination - + N P ID s.s. excess s.s. excess holes electrons electron-injecting hole-injecting contact contact − VA + Lundstrom 2011 6
  • 7. recombination in the N-type QNR N - - P + ID electron-injecting hole-injecting contact contact − VA +Anytime an electron and hole recombine anywhere within the diode, oneelectron flows in the external circuit. 2011 Lundstrom 7
  • 8. Shockley-Read-Hall recombinationminority carriers injected across junction ET Fn qVA FP SRH recombination ID − VA + Lundstrom 2011 8
  • 9. recombination at a contactminority carriers injected across junction Fn qVA FP ID − VA + Lundstrom 2011 9
  • 10. light-current and generation Vbi − VA “base” EF (absorbing layer) “emitter” − VA + ID < 0 Every time a minority electron is generated and collected, one10 electron flows in the external current. Lundstrom 2011
  • 11. light-current and recombination 3 e-h pairs generated “emitter” 1 e in external circuitEvery time a minority electron is generated and recombines before beingcollected, the solar cell current suffers. 2011 Lundstrom 11
  • 12. 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. Lundstrom 2011 12
  • 13. solar cells and recombination = q ( RTOT (VA ) − GTOT ) J D (VA )J p ( 0) Jn ( L) ID L J p ( 0) Jn ( L) RTOT= ∫ R ( x )dx − 0 q − q N P L GTOT = ∫ Gop ( x )dx 00 L xFor a formal derivation of this result, see the appendix. Lundstrom 2011 13
  • 14. outline1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary Lundstrom 2011 14
  • 15. generic crystalline Si solar cell SF = 1000 cm/s key device n+ “emitter” (0.3 μm) parameters p-type “base” base doping: NA = 1016 /cm3 emitter doping ND = 6 x 1019 /cm3200 um (198.9 μm) minority carrier lifetime τn = 34 μs (base) p+ “Back Surface Field” (BSF) base thickness W = 198.9 μm (0.8 μm) front junction depth xjf = 0.3 μm back junction depth xjb = 0.8 μm Lundstrom 2011 15
  • 16. light-generated current SF = 1000 cm/s = q ( RTOT ( 0 ) − GTOT ) J D ( 0) n+ “emitter” (0.3 μm) 1) What is GTOT? p-type “base” 2) How is GTOT spatially distributed?200 um 3) What is RTOT? (198.9 μm) 4) How is RTOT spatially distributed? p+ “Back Surface Field” (BSF) 5) How do things change if we (0.8 μm) remove the BSF? Lundstrom 2011 16
  • 17. light-generated current: numbers J SC J D (V= 0= q ( RTOT − GTOT ) = A ) n+ “emitter” (0.3 μm) ∞ WD ≈ 0.3 µ m = GMAX ∫ Gop ( x = 2.97 ×1017 cm -2s -1 )dx 0200 um 2L G= TOT ∫ Gop ( x )dx 2.79 ×1017 cm -2s -1 = p-type “base” 0 (198.9 μm) Ln ≈ 320 µ m J SC 39.4 mA/cm 2 p+ “Back Surface Field” (BSF) = = 2.46 ×1017 cm -2s -1 q q (0.8 μm) RTOT ( 0 ) 3.31×1016 cm -2s -1 = 17 CE = 0.88 Lundstrom 2011
  • 18. light-generated current: understanding entire device near surface xj x j + WD18 Lundstrom 2011
  • 19. light-generated current: summary ∞ 2L = ∫ Gop ( x = 2.97 ×10 cm s )dx G= ∫ Gop ( x )dx 2.79 ×1017 cm -2s -1 = 17 -2 -1GMAX TOT 0 0low lifetime (Auger recombination) good minority carrier lifetimesurface recombination collection BSF19 Lundstrom 2011
  • 20. recombination at short circuit entire device near surface xj x j + WD20 Lundstrom 2011
  • 21. recombination at short circuit: summary J SC 39.4 mA/cm 2 = = 2.46 ×1017 cm -2s -1 RTOT ( 0 ) 3.31×1016 cm -2s -1 = q q (0.37) (0.49) (0.14)low lifetime (Auger recombination) good minority carrier lifetimesurface recombination collection BSF21 Lundstrom 2011
  • 22. about recombination in the base ∆n ( x ) d 2 ∆n ∆n expect: R ( x ) ≈ 2 − = 0 Ln = Dnτ n τn dx Ln We find the excess minority electron profile by solving the ∆n minority carrier diffusion equation: J n = q sback ∆n ( L′ ) ( L′ ) d ( J n −q ) =R − dx 0′ x j + W = d ∆n J n ( 0′ ) q s j ∆n ( 0′ ) = L′ L − xBSF = J n ≈ qDn dx x xj +W L22 Lundstrom 2011
  • 23. Adept simulation results ∆n ( x ) R ( x) ≈ τn ∆n ( x )23 Lundstrom 2011
  • 24. the BSF ∆E = eV 0.13 EC EI Sback ≈ υ th e− ∆E kBT EF  ; 0.6 × 10 7 cm s EV What happens if we remove the BSF? EC EI Sback ≈ υ th EF  ; 1 × 10 7 cm s EV24 Lundstrom 2011
  • 25. without the BSF BSF no BSF With BSF Without BSF J SC = 39.4 mA/cm 2 J SC = 38.2 mA/cm 2 qRTOT = 5.3 mA/cm 2 qRTOT = 6.5 mA/cm 225 CE = 0.88 Lundstrom 2011 CE = 0.85
  • 26. internal quantum efficiency With BSF No BSF J D (V = 0, λ ) IQE = Finc ( λ )26 Lundstrom 2011
  • 27. 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 Jn(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? 5) Since most of the recombination loss occurs in the emitter, why not just make the emitter junction depth a lot smaller?27 Lundstrom 2011
  • 28. 2D effects ID I ( x) VD V ( x ) < VD xj dx dR = ρ S W ρ 1 ρS = = x j N D qµn x j distributed series resistance28 Lundstrom 2011
  • 29. outline1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary Lundstrom 2011 29
  • 30. dark I-V= q ( RTOT (VA ) − GTOT )J D (VA ) = q ( RTOT = VOC ) − GTOT ) 0 (VAUnder open circuit conditions: RTOT = VOC ) GTOT (VA = Lundstrom 2011 30
  • 31. superposition JD= q ( RTOT (VA ) − GTOT )J D (VA ) dark IV J SCdark: = J 0 ( e qVD JD nk B T − 1) J dark D (VA ) = q Rdark TOT (VA ) VAilluminated: VOC = q ( RTOT (VA ) − GTOT ) J D (VA ) light light − J SC JL < 0 illuminated at VOC: superposition: J D (VOC ) = J SC dark RTOT (VOC ) = GTOT light ? Lundstrom 2011 RTOT (VOC ) = J SC q dark 31
  • 32. dark current characteristics (sketch)= J 0 ( e qVAJ D (VA ) dark nk B T − 1)J D (VA ) J 01 ( e qVA = dark kBT − 1) + J 02 ( e qVA 2 kBT − 1) series resistance or… n=1 dark log10 J D shunt resistance or… n=2 VA Lundstrom 2011 32
  • 33. dark current characteristics (Adept)= J 0 ( e qVAJ D (VA ) dark nk B T − 1) = dark (J D (VA ) J 01 e qVA kBT ) ( − 1 + J 02 e qVA 2 kBT ) −1 n >1 n =1 n≈2 Lundstrom 2011 33
  • 34. what determines J0 and n? J D (VA ) = J 0 e qVA dark ( nk B T ) −1 J A (VA ) = q RTOT (VA ) dark darkAnswer:Electron-hole recombination determines I0.The location of recombination within the solar celldetermines the ideality factor, n. Lundstrom 2011 34
  • 35. recombination in the dark (VA = 0.7 V) Emitter Base Lundstrom 2011 35
  • 36. recombination summary: (VA = 0.7 V)Short-circuit recombination VA = 0.7 V recombination qRTOT ( 0 ) = 5.3 mA/cm light 2 qRTOT ( 0.7 ) = 465 mA/cm 2 dark Lundstrom 2011 36
  • 37. what happens if we remove the BSF? (VA = 0.7 V) With BSF Without BSF ~70% ~85% J D ( 0.7 ) = 644 mA/cm 2 J D ( 0.7 ) = 1372 mA/cm 2 Lundstrom 2011 37
  • 38. dark current physics (n = 1)FB: minority carriers injected across junction I D (VA ) = qRTOT (VA )1) Recombination in QNRs: Fn qVA FP 2) Electrons and holes can also recombine within the SCR of ID > 0 Lundstrom 2011 the junction. 38
  • 39. n = 1 device physics I D (VA ) = qRTOT (VA ) nP ( 0′ ) ≈ n0 P e qVA kBT Qn qRTOT (VA ) = tnq (Vbi − VA ) ni2 qVA Qn ∝ NA e ( kBT −1 ) Fn FP tn : minority carier lifetime n0P ≈ ni2 N A or base transit timeRecombination in quasi-neutral regions gives rise to n = 1 currents. Lundstrom 2011 39
  • 40. dark current characteristics (sketch)= J 0 ( e qVAJ D (VA ) dark nk B T − 1)J D (VA ) J 01 ( e qVA = dark kBT − 1) + J 02 ( e qVA 2 kBT − 1) series resistance or… n=1 dark log10 J D shunt resistance or… n=2 VA Lundstrom 2011 40
  • 41. recombination in the dark (VA = 0.2 V) emitter region base region Lundstrom 2011 41
  • 42. recombination summary: (VA = 0.2 V)VA = 0.7 V recombination VA = 0.2 V recombinationqRTOT ( 0.7 ) = 465 mA/cm 2 dark qRTOT ( 0.7 ) 8.4 ×10−6 mA/cm 2 dark = Lundstrom 2011 42
  • 43. dark current physicsFB: minority carriers injected across junction I D (VA ) = qRTOT (VA )1) Recombination in QNRs: Fn qVA FP 2) Electrons and holes can also recombine within the SCR of the junction. ID > 0 Lundstrom 2011 43
  • 44. recombination in SCRs J D (VA ) = qRTOT (VA ) dark q (Vbi − VA ) Maximum recombination occurs when n(x) ≈ p(x) n ( x ) p ( x ) = ni2 e qVA kBT Fn FP n ≈ p ∝ ni e qVA ˆ ˆ 2 kBT qni e qVA 2 kBT np = ni2 e qVA kBT qRTOT (VA ) ∝ dark τ effRecombination in space-charge regions gives rise to n = 2 currents. Lundstrom 2011 44
  • 45. recombination in SCR J D (VA ) = qRTOT (VA ) n ≈ p ∝ ni e qVA ˆ ˆ 2 kBT ˆ n ni e qVA / 2 kBT R (VA ) ˆ = = τ eff τ eff J D (VA ) = q R Weff ˆ k BT q Weff = Eˆ k BT qE ˆ = 2.3 × 104 V cm = Weff ≈ 11 nm E ˆ Lundstrom 2011 45
  • 46. dark IVJ D (VA )= J 02 e qVA ( 2 kBT ) ( ) − 1 + J 01 e qVA = J 0 e qVA 1k B T −1 ( nk B T ) −1 Recombination in Recombination in depletion regions neutral regions J 02 ∝ ni ∝ e − EG / 2 kBT J 01 ∝ ni2 ∝ e − EG / kBTlarge bandgaps and small bandgaps andlow temperatures high temperatures Lundstrom 2011 46
  • 47. questions1) 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 short- circuit conditions, but not under FB in the dark?4) How much could VOC 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? Lundstrom 2011 47
  • 48. outline1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary Lundstrom 2011 48
  • 49. reducing recombination higher material quality (longer lifetimes) thinner base layer (but optically thick)J D (VA ) q ( RTOT (VA ) − GTOT ) built-in fields back-surface-fields / minority carrier mirrors reducing contact areas …. Lundstrom 2011 49
  • 50. high-efficiency Si solar cells24.5% at 1 sunMartin Green Group UNSW – Zhao, et al, 1998 Lundstrom 2011 50
  • 51. how good is superposition?V = 0.62 V - Dark VOC = 0.62 V - Illuminated Lundstrom 2011 51
  • 52. how good is superposition? (ii) dark JD Jdark light JD J D + J D (V = 0 ) dark light superposition Lundstrom 2011 52
  • 53. outline1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary Lundstrom 2011 53
  • 54. summary1) Diode current = q times (total recombination – total generation)2) At VOC, recombination = optical generation3) At V = 0, recombination lowers the collection efficiency4) Dark current tells us much about the internal recombination mechanisms5) Solar cell design is all about maximizing total generation and minimizing total recombination.6) Simulations can be useful for understanding –especially Lundstrom 2011 if you look “inside” and not just at the IV. 54
  • 55. questions1) Introduction2) Recombination at short circuit3) Recombination at open circuit4) Discussion5) Summary Lundstrom 2011 55
  • 56. Appendices1) Formal derivation of the relation between current and recombination/generation.2) Mathematical justification of superposition Lundstrom 2011 56
  • 57. Appendix 1: current and recombinationFormal derivation of the relation between current andrecombination/generation. J D (V ) q ( RTOT − GTOT ) = J p ( 0) Jn ( L) ID L J p ( 0) Jn ( L) RTOT= ∫ R ( x )dx − 0 q − q N P L GTOT = ∫ Gop ( x )dx 0 0 L x Lundstrom 2011 57
  • 58. continuity equation for electronsWabash RiverRate of increase ofwater level in lake = (in flow - outflow) + rain - evaporation ∂n  ∂t = ( −∇ • J n −q )+ G − R Lundstrom 2011 58 58
  • 59. solar cell physics “semiconductor equations”Conservation Laws: Relations:    κε −κε D = 0 E = 0 ∇V ∇• D =ρ ρ q( p − n + N D − N A ) = + −     J= nq µn E + qDn∇n (∇ • J n −q = ) (G op − R)  n   J= pq µ p E − qD p ∇p p  R = f (n, p ) (∇• Jp = q ) (G op − R) Gop = optical generation rate (steady-state) etc. Lundstrom 201159
  • 60. diode current and recombination  ( ∇ • J n −q = ) (G op − R) d ID ( J n −q ) = Gop − R (1D) ID dx L L N P= q ∫  R ( x ) − Gop ( x )  dx∫ dJ n   0 0 0 L x L J n ( L ) − J n ( 0= q ∫  R ( x ) − Gop ( x )  dx )   0 Lundstrom 2011 60
  • 61. current and recombination-generation L J n ( L ) − J n ( 0= q ∫  R ( x ) − Gop ( x )  d + J p (x ) − J p ( 0 ) )   0 0 L − { J n ( 0 ) + J p ( 0 )} = J D (V ) = q ∫  R ( x ) − Gop ( x )  dx − J n ( L ) − J p ( 0 )   0J D (V ) q ( RTOT − GTOT )= ID LqRTOT q ∫ R ( x )dx − J n ( L ) − J p ( 0 ) = 0 L N PGTOT = ∫ Gop ( x )dx 0 61 Lundstrom 2011 0 L x 61
  • 62. current and generation-recombination = q ( RTOT (VA ) − GTOT ) J D (VA )The diode current is q times the total recombination minus the totalgeneration.The total recombination is the integrated recombination rate withinthe device plus the flux of minority carriers into each contact. Lundstrom 2011 62 62
  • 63. Appendix 2: justifying superposition= q ( RTOT (VA ) − GTOT )J D (VA ) (valid in light or dark) J D (VA ) = qRTOT (VA ) dark dark (dark current) = q ( RTOT ( 0 ) − GTOT ) J D ( 0) light light (short circuit current) J D (= J D + J D ( 0 ) super VA ) dark light (principle of superposition) J D (VA ) = qRTOT (VA ) + q ( RTOT ( 0 ) − GTOT ) super dark light (How does this compare to the exact answer?) Lundstrom 2011 63
  • 64. mathematical justification for superposition ( ) ( ( )J D V A = q RTOT V A − GTOT ) (valid in light or dark) ( ) ( ( )J D V A = q RTOT V A − GTOT light light ) ( ) ( ) (J D V A = qRTOT V A + q RTOT 0 − GTOT super dark light () ) (principle of superposition) ( ) light ( ) dark light ()RTOT V A = RTOT V A + RTOT 0 ?? (criterion to justify superposition) Lundstrom 2011 64

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