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- 1. NCN Summer School: July 2011Introduction to Photovoltaics Prof. Mark Lundstrom lundstro@purdue.edu Electrical and Computer Engineering Purdue University West Lafayette, Indiana USA
- 2. 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 Lundstrom 2011
- 3. acknowledgement Dionisis Berdebes, Jim Moore, and Xufeng Wang played key roles in putting together this tutorial. Their assistance is much appreciated.3 Lundstrom 2011
- 4. modern solar cell Chapin, Pearson, and Fuller, Bell Labs. 1954 http://www.bell-labs.com/org/physicalsciences/timeline/span10.html#4 Lundstrom 2011
- 5. solar cell progress 55 http://en.wikipedia.org/wiki/File:PVeff(rev100921).jpg
- 6. solar cell industry SunPower / Applied MaterialsMark Pinto, “Renewable Solar Energy: Has the Sun Finally Risen on Photovoltaics?”https://nanohub.org/resources/6332 6
- 7. solar cellA solar cell is a junction (usually a PN junction) with sunlight shining on it. To understand how a solar cell works, we need to understand: 1) how a PN junction works (w/o the light) 2) how light is absorbed in a semiconductor (without a PN junction) 3) what happens when we put the two together. 7
- 8. outline 1) Introduction 2) PN junction fundamentals (dark) 3) Model solar cell: dark IV 4) Optical absorption / light-generated current 5) Model solar cell: illuminated 6) Discussion 7) Summary8 Lundstrom 2011
- 9. silicon energy bands conduction empty states “band” T=0K EC valence EG = 1.1 eV “band” EV filled states “core levels”9 Lundstrom 2011
- 10. intrinsic n-type p-type − + n0 N ≈ ND p0 P ≈ NA EC EC EC EFEF EF EV EV EV “hole” EV EV EV “holes” filled states filled states filled states10 Lundstrom 2011
- 11. Fermi level + n0 N ≈ ND − p0 P ≈ NA 1 f0 (E ) = EC 1 + e(E − EF ) kBT EC 1 EF E = EF → f0 (E ) = 2 EF EV E << EF → f0 (E ) = 1 EV EV “holes” EV filled states E >> EF → f0 (E ) = 0 filled states11 Lundstrom 2011
- 12. intrinsic semiconductor EC n0 = ni EF = EI p0 = ni EV n0 p0 = ni2 “hole” EV filled states ni ∝ e− EG kBTL ni (300 K ) ≈ 1010 cm -312 Lundstrom 2011
- 13. n-type semiconductor + n0 N ≈ N D EC + n0 ≈ ND EF n0 p0 = ni2 + EV p0 = ni2 ND EV filled states n0 = ND ≈ 1017 cm -3 ni (300 K ) ≈ 1010 cm -313 p0 ≈ 10 3 cm -3 Lundstrom 2011
- 14. p-type semiconductor EC − p0 ≈ NA n0 p0 = ni2 EF − EV n0 = ni2 NA “holes” EV filled states p0 = NA ≈ 1017 cm -3 ni (300 K ) ≈ 1010 cm -314 n0 ≈ 10 3 cm -3 Lundstrom 2011
- 15. PN junction + n0 N ≈ ND − p0 P ≈ NA EC EC EF What happens if we bring the p and n EF regions together? EV EV EV “holes” EV filled states filled states15
- 16. PN junction in equilibrium n0 N ≈ N D n0 P ≈ ni2 NA Fermi level EC lower is constant! EC = -qV qVbi p-type V = Vbi EF EF V=0 n-type p0 P ≈ NA p0 N ≈ ni2 ND slopeVbi ~ EG ID = 0 proportional toqVbi = kBT NA ND ln VA = 0 electric field q ni2 16
- 17. PN junction in equilibrium n0 P ≈ ni2 NA P0 = ? qVbiEF EF P 0 = e− ∆E kBT n0 N ≈ N D p0 P ≈ NA p0 N ≈ ni2 ND 17 Lundstrom 2011
- 18. PN junction under forward bias nP > ni2 NA P = P 0 eqVA kBT q (Vbi − VA ) P = e− q(Vbi −VA ) kBTFN n0 N ≈ N D FP “excess carriers” p0 P ≈ NA A positive voltage on p-side pulls the bands down. p0 N ≈ ni2 ND Energy barrier is lowered. 18 Lundstrom 2011
- 19. PN junction under forward bias Excess electron concentration on the p-side. ∆nP (x) q (Vbi − VA ) WP Qn = q ∫ ∆nP (x)dxFN n0 N ≈ N D 0 FP p0 P ≈ NA Qn Q p ID = + tn tp The time, t n is the average time for an electron on the p-side to “recombine” or to diffuse to the contact and recombine. Let’s see why recombination leads to current. 19
- 20. recombination leads to current minority carriers injected across junction Fn qVA FP ID − VA + Every time a minority electron recombines on the p-side, one20 electron flows in the external current.
- 21. recombination at a contact minority carriers injected across junction Fn qVA FP ID − VA + Every time a minority electron recombines on the p-side, one21 electron flows in the external current.
- 22. forward bias summary ∆nP (x) I n1 ∝ e qVA kBT 1) Injected current produces a population of “excess” electrons in the P-type q (Vbi − VA ) region... 2) Excess electrons in the P-FN type region recombine… n0 N ≈ N D FP 3) Every time an electron and p0 P ≈ NA hole recombine, an electron flows in the p0 N ≈ ni2 ND external circuit. 0 < ID 22 VA > 0 Lundstrom 2011
- 23. ideal diode equation Qn Q p ID = tn + tp Qn ∝ NA (e ni2 qVA kBT − 1) 0 < ID I D = I 0 (eqVA kBT − 1) − VA + “ideal diode equation” I D = I 0 (eqVA nkBT − 1)23 n =1 Lundstrom 2011
- 24. outline 1) Introduction 2) PN junction fundamentals (dark) 3) Model solar cell: dark IV 4) Optical absorption / light-generated current 5) Model solar cell: illuminated 6) Discussion 7) Summary24 Lundstrom 2011
- 25. generic crystalline Si solar cell SF = 1000 cm/s key device n+ “emitter” (0.3 μm) parameters base doping: NA = 1016 /cm3 p-type “base” emitter doping ND = 6x1019 /cm3 minority carrier lifetime τn = 34 μs (198.9 μm) (base) base thickness W = 198.9 μm p+ “Back Surface Field” (BSF) (0.8 μm) front junction depth xjf = 0.3 μm back junction depth xjb = 0.8 μm25 R Lundstrom 2011 s = 1 Ohm-cm2
- 26. equilibrium e-band diagram EF EF 199.2 20026 Lundstrom 2011
- 27. dark I-V J D = J 0 (eqVA nkBT − 1) n >1 n =1 n≈227 Lundstrom 2011
- 28. recombination: V = 0.7 V entire device front surface region ~70% ~10% ~20% ~20% x ∫ R(x′ )dx′ R(x) 0 L28 ∫ R(x′ )dx′ 0 Lundstrom 2011
- 29. series resistance − VA + RS 0 < ID − VA + I D = I 0 (eqVA kBT − 1) VD = VA + I D RS ( ) I D = I 0 eq(VD − I D RS ) kBT − 129 Lundstrom 2011
- 30. dark I-V and series resistance I D RS30 Lundstrom 2011
- 31. outline 1) Introduction 2) PN junction fundamentals (dark) 3) Model solar cell: dark IV 4) Optical absorption / light-generated current 5) Model solar cell: illuminated 6) Discussion 7) Summary31 Lundstrom 2011
- 32. absorption of light EC hc λ< E = hf > EG EG EG EV c hc fλ = c f= E = hf = λ λ32 Lundstrom 2011
- 33. solar spectrum (outer space) space AM0 = “air mass 0” AM 0 Earth Integrated power = 136.6 mW/cm233 Lundstrom 2011
- 34. solar spectrum (terrestrial) atmosphere 1 θX AMX = AM1.5 : θ x = 48.2 deg cos θ x “G” = “global” Earth Integrated power = 100 mW/cm2) 34http://en.wikipedia.org/wiki/Air_mass_(solar_energy)
- 35. how many photons can be absorbed?Example: Silicon Eg = 1.1eV. Only photons with a wavelengthsmaller than 1.1 m will be absorbed. solar spectrum (AM1.5G)35 Lundstrom 2011
- 36. wasted energy for E > EG Energy is lost for photons with energy greater than the bandgap.hf > EG Electron is excited above However, extra energy is lost due to the conduction band. thermalization as electron relaxes back to the band edge.36 Lundstrom 2011
- 37. how many photons are absorbed in a finite thickness?Incident flux: Φ 0Flux at position, x : Φ (x) = Φ 0 e−α (λ )x optical absorption coefficient: α (λ ) > 0 for E > EG (λ < hc EG )Generation rate at position, x : d Φ (x) G (x) = − = Φ 0α (λ )e−α (λ )x dx L Gtot = ∫ ∫ G (x, λ )dx dλ 0 37
- 38. what determines alpha? E E conduction conduction band band p2 EG E= EG need 2m phonon p p valence valence band bandDirect gap: strong absorption Indirect gap: weaker absorption(high alpha) lower alpha) 38
- 39. light absorption vs. semiconductor thicknessThe direct bandgap of CIGS allows it to absorb light much faster than Silicon.A layer of silicon must be 104 microns thick to absorb ~100% of the light,while CIGS need only be about 2 microns thick. CIGS (direct) Si (indirect) 39 Lundstrom 2011
- 40. maximizing light absorption / generation1) Maximize the number of phonons anti-reflection (AR) coating that get into the solar cell (AR coating, texturizing).2) Maximize the “effective” thickness of the absorber. solar cell40 Lundstrom 2011
- 41. light-trapping in high-efficiency Si solar cells 370 − 400 µm 24.5% at 1 sun Martin Green Group UNSW – Zhao, et al, 199841 Lundstrom 2011
- 42. collection of e-h pairs 1) Light generates electron-hole pairs ECE = hf > EG EV 2) PN junction collects e-h pairs n-region collects the minority carrier EF electrons p-region collects the minority carrier holes 42 Lundstrom 2011
- 43. collection efficiencyPhoto-generated carriers should diffuse But some mayto the junction and be collected. recombine in the base. “base” EF (absorbing layer) “emitter” And some may diffuse to the contact and JL recombine.CE ≡ J L max 43“collection efficiency” Lundstrom 2011
- 44. voltage-dependence of collection Vbi − VA “base” EF (absorbing layer) “emitter”As long as VA < Vbi, the applied bias should affect the collection of carriers.44 Lundstrom 2011
- 45. current collection The generated carriers are only useful to us if they are able to be collected. Electron diffusion length: Distance e will travel before recombining n+ p t < Ln = Dnτ n Generated e- For Si: μn~1200 cm2/V-s; n~34s Ln~320 m 0 t Therefore we cannot make the absorbing layer arbitrarily thick.45 Lundstrom 2011
- 46. real thickness vs. optical thickness 24.5% at 1 sun Martin Green Group UNSW – Zhao, et al, 199846 Lundstrom 2011
- 47. outline 1) Introduction 2) PN junction fundamentals (dark) 3) Model solar cell: dark IV 4) Optical absorption / light-generated current 5) Model solar cell: illuminated 6) Discussion 7) Summary47 Lundstrom 2011
- 48. diode current under illumination 1) Light generates e-h pairs EF48 Lundstrom 2011
- 49. diode current under illumination2) PN junction collects e-h pairs 3) Current flows through load IL < 0 EF ID > 0 RL − VL + forward bias across PN junction IL < 0 develops49 Lundstrom 2011
- 50. net current 4) Forward bias reduces current 5) IV characteristic is a superposition ID I 0 (eqVD nkBT −1 )Fn qVD Fp VD IL < 0 I D = I 0 (eqVD nkBT ) − 1 − IL 50 dark current - light-generated Lundstrom 2011 current
- 51. IV characteristic6) Maximum power point I D = I 0 (eqVD nkBT ) − 1 − IL ID Pout I SCVOC FF η= = Pin Pin VOC VD Pout = I DVOC = 0 − I SC IL < 0 Pout = I SCVD = 0 PD = I DVD < 0 51 Pout = I mpVmp = I SCVOC FF
- 52. “superposition” IL < 0 IL > 0 + RL VL > 0 −light-generated current dark current I D = I 0 (eqVD )(bias independent) nkBT −1 52
- 53. effect of series and shunt resistorshttp://upload.wikimedia.org/wikipedia/commons/thumb/c/c4/Solar_cell_equivalent_circuit.svg/601px-Solar_cell_equivalent_circuit.svg.png 53
- 54. series and shunt resistors Effect of series resistance Effect of shunt resistance FF FF 0.84 0.84 0.79 0.71 0.74 0.58 I = I L − I0 eq (V + IRS )/ k B T − 1 − V + IRS Modified Diode Equation: R SH54 Lundstrom 2011
- 55. model solar cell simulation ADEPT 2.0 nanoHUB.org Results: VOC = 616 mV J SC = 39.4 mA/cm 2 FF = 0.83 η = 20.1% (See slide 26 for parameters)55 Lundstrom 2011
- 56. outline 1) Introduction 2) PN junction fundamentals (dark) 3) Model solar cell: dark IV 4) Optical absorption / light-generated current 5) Model solar cell: illuminated 6) Discussion i) superposition ii) efficiency limits iii) costs 7) Summary56 Lundstrom 2011
- 57. i) principle of superposition I D (VD ) > 0 I TOT + IL < 0 RL V = VD > 0 VD −Photo-generated current collected bythe junction. Generally assumed to I DARK = I 0 (eqVD nkBT ) −1be independent of the junctionvoltage. determined by recombination Superposition says that we can processes in the dark add the two solutions to get the 57 total response of the solar cells.
- 58. superposition We can superimpose two solutions when the differential equations describing the problem are linear.58 Lundstrom 2011
- 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 − R ) n J= pq µ p E − qD p ∇p p R = f (n, p ) ( ∇• Jp ) q= (G − R ) G = optical generation rate (steady-state) etc.59 Lundstrom 2011
- 60. when does superposition apply? 1) the junction space-charge region may contribute importantly to either the photocurrent or the dark current, but not to both; 2) the carrier concentrations in the quasi-neutral regions must stay within low-injection levels; 3) the series resistance (and shunt resistance) must contribute negligilbly to the cell current-voltage characteristics; 4) the material parameters, such as the minority-carrier lifetime, must be essentially independent of the illumination level; 5) the volume of the regions that contribute appreciably to the photocurrent must stay essentially constant as the cell is loaded.F. A. Lindholm, J.G. Fossum, and E.L. Burgess, “Application of the SuperpositionPrinciple to Solar-Cell Analysis,” IEEE Trans. Electron Devices, 26, 165-171, 197960 Lundstrom 2011
- 61. ii) solar cell efficiency limits 1) Fill factor: Determined by diode characteristic and series resistances. 2) Short-circuit current: Pout I SCVoc FF η= = Increases as the bandgap decreases. Pin Pin For a given bandgap, determined by reflection, absorption, recombination. 3) Open-circuit voltage: Increases as the bandgap increases. For a given bandgap, determined by61 recombination.
- 62. Shockley-Queisser Limit1) Smaller bandgaps give higher short circuit current2) Larger bandgaps give higher open-circuit voltage3) For the given solar spectrum, an optimum bandgap exists.W. Shockley, and H. J. Queisser, “Detailed Balance Limit of Efficiency of p‐nJunction Solar Cells”, J. Appl. Phys., 32, 510, 1961. 62 Lundstrom 2011
- 63. iii) costs: three approaches 1) High-efficiency , but high-cost solar cells (high-quality crystalline materials) 2) Acceptable efficiency, but very low costs (thin-film, amorphous/polycrystalline materials) 3) Concentration (high efficiency cells with optical concentration)63 Lundstrom 2011
- 64. “grid parity”For a photovoltaic power generation system to be economicallycompetitive the total costs of an installed PV system must be ~ $1/W,which translates to 5-6 cents per kilowatt-hour.A system includes: 1) Module costs 2) Power conditioning electronics 3) Installation and balance of systems.Current costs are $3.40/W (2011).Projected to decrease to $2.20/W by 201664 Lundstrom 2011
- 65. the dollar per Watt goal The U.S. Department of Energy is calling for research to meet the $1/W goal. This requires modules at $0.50/W, with ~20% modules with 20-30 system lifetimes. http://www1.eere.energy.gov/solar/65 Lundstrom 2011
- 66. outline 1) Introduction 2) PN junction fundamentals (dark) 3) Model solar cell: dark IV 4) Optical absorption / light-generated current 5) Model solar cell: illuminated 6) Discussion 7) Summary66 Lundstrom 2011
- 67. solar cell summary1) Light is absorbed and produces e-h pairs2) PN junctions separate e-h pairs and collect the carriers.3) Current flow in external circuit produces a FB voltage and the FB diode current reduces the total current.4) Power out is ISCVOC FF.5) Unlike integrated circuit chips, where the value added comes from the design/system, manufacturing costs are critical in PV.67 Lundstrom 2011
- 68. referencesTextbooks:Martin Green, Solar Cells: Operating Principles, Technology, and SystemApplications, Prentice-Hall, 1981.Jenny Nelson, Physics of Solar Cells, Imperial Collage Press, 2003Antonio Lugue and Steven Hegedus, Handbook of Photovoltaic Science andEngineering, John Wiley and Sons, 2003.Compilation of current cell efficiencies:Martin Green, et al., “Solar cell efficiency tables (version 37)”, 19, Prog. inPhotovoltaics, 2011Survey of 3rd generation PV concepts:Martin Green, Third generation photovoltaics: advanced solar energyconversion, Springer, 2006.68 Lundstrom 2011
- 69. questions1) Introduction2) PN junction fundamentals (dark)3) Model solar cell: dark IV4) Optical absorption / light-generated current5) Model solar cell: illuminated6) Discussion7) Summary69 Lundstrom 2011

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