Modeling III-V Semiconductor Solar Cells

Transcription

1 Modeling III-V Semiconductor Solar Cells Ideal limits to real device modeling A. W. Walker Fraunhofer Institute for Solar Energy Systems ISE PROMIS Workshop Cadiz, Spain May th,

2 Motivation [1] M. Green, et al. Solar Cell Efficiency Tables. Progress in Photovoltaics: Research and Applications. 1

3 OVERVIEW IDEAL MODELING REAL MODELING 2

4 Photon Flux [W/m 2 /nm] Ideal Limits Single Junction Solar Cell Direct sunlight ~ Spectrum E G Contacts Perfect Antireflection Coating Absorber Rear Mirror Wavelength [ m] E C E G E V 3

5 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Contacts Absorber Direct sunlight ~0.267 Perfect Antireflection Coating Rear Mirror E C E V W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

6 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Contacts Absorber Direct sunlight ~0.267 Perfect Antireflection Coating Rear Mirror E C E V W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

7 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Contacts Absorber Direct sunlight ~0.267 Perfect Antireflection Coating Rear Mirror E C E V W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

8 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission No nonradiative recombination Contacts Absorber Direct sunlight ~0.267 Perfect Antireflection Coating Rear Mirror E C E C E V E V W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

9 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties J 0 = 2πq h 3 c 2 n o 2 E g exp E 2 E qv kt de 1 Contacts Solar cell emission n o = 1 Absorber Direct sunlight ~0.267 Perfect Antireflection Coating Rear Mirror W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

10 Current Density [A/cm 2 ] Power [W/cm 2 ] Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: P mpp 100% absorption above bandgap J sc =J ph Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties J 0 = 2πq h 3 c 2 n o 2 E g exp E 2 E qv kt J V = J ph J 0 exp qv kt 1 de 1 Voltage [V] V oc V OC = kt q log J ph J 0 1 η = P mpp P in FF = P mpp J sc V oc W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

11 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties J 0 = 2πq h 3 c 2 n o 2 E g exp E 2 E qv kt J V = J ph J 0 exp qv kt 1 de 1 Solar Cell V OC = kt q log J ph J 0 1 η = P mpp P in FF = P mpp J sc V oc W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

12 Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties Computing efficiency Factors include Spectrum Concentration of light (C) J SC (C) = CJ SC (C = 1) V OC (C) = V OC (C = 1)+ kt q η = J mppv mpp P in log C W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

13 Efficiency [%] Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties Computing efficiency Factors include Spectrum Concentration of light (C) Bandgap Single junction under AM1.5 Si GaAs Bandgap [ev] W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), ,

14 Efficiency [%] Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties Computing efficiency Factors include Spectrum Concentration of light Bandgap Single junction under AM % Si GaAs Bandgap [ev] 28.8% W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), , M. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop. Solar cell efficiency tables (version 47), 24(1), 3-11,

15 Efficiency [%] Ideal Limits Single Junction Solar Cell Shockley & Queisser limit: 100% absorption above bandgap Perfect carrier collection efficiency Radiative recombination via spontaneous emission Photonic properties Computing efficiency Factors include Spectrum Concentration of light Bandgap Single junction under AM1.5 Si GaAs Bandgap [ev] Concentration increases efficiency logarithmically W. Shockley, H. J. Queisser. Detailed balance limit of efficiency of p-n junction solar cells, Journal of Applied Physics, 32(3), , M. Green, K. Emery, Y. Hishikawa, W. Warta, E. D. Dunlop. Solar cell efficiency tables (version 47), 24(1), 3-11,

16 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Radiative Recombination Ideal diode equation Current Transport Ideal Photonic Properties 4

17 Photon Flux [W/m 2 /nm] Ideal Limits Beyond the Limit of a Single Junction Solar Cell Single junction Partial absorption of spectrum Multiple junctions Complete absorption of spectrum Voltages of each junction add up! Introduces constraints Series connection requires current matching 1.4 Spectrum Wavelength [ m] 5

18 Efficiency [%] Ideal Limits Multi-Junction Solar Cell Computed for multi-junction solar cells No resistances No reflections and no shading (100% transmission) J1 sub-cell Tunnel diode 1 J2 sub-cell Tunnel diode 2 J3 sub-cell Tunnel diode 3 J4 sub-cell 6 30 One sun (AM1.5D) A. De Vos. Journal of Physics D: Applied Physics, 13, , A. Marti, G. L. Araujo. Solar Energy Materials and Solar Cells, 43, , Number of Junctions (Adopted from Kurtz et al.) G. Letay, A. W. Bett. 17 th European Photovoltaic Solar Energy Conference, Munich, Germany, Oct , S. Kurtz, D. Myers, W. E. McMahon, J. Geisz, M. Steiner. Progress in Photovoltaics: Research and Applications, 16, , G. Arbez, et al. 39 th IEEE Photovoltaic Specialists Conference, Tampa, FL, USA, June 16-21, 2013.

19 J1 Bandgap (ev) Ideal Limits Multi-Junction Solar Cell Computed for multi-junction solar cells No resistances No reflections and no shading (100% transmission) Fraunhofer ISE developed etaopt for arbitrary number of junctions Optimization current matching Example 4J Device J3 Bandgap (ev) Fixed GaAs (J2=1.42 ev) and Ge (J4=0.67 ev) bandgaps G. Letay, A. W. Bett. 17 th European Photovoltaic Solar Energy Conference, Munich, Germany, Oct ,

20 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Radiative Recombination Ideal diode equation Current Transport Ideal Photonic Properties 7

21 Multi-Junction Solar Cell Concepts 8

22 Multi-Junction Solar Cell Concepts Lattice matched 3-junction on Ge GaInP 1.9 ev GaInAs 1.4 ev Ge 0.7 ev 9

23 Multi-Junction Solar Cell Concepts Lattice matched 3-junction on Ge Lattice matched 4-junction on Ge GaInP 1.9 ev GaInP 1.9 ev GaInAs 1.4 ev GaInAs 1.4 ev GaInNAs 1.0 ev Ge 0.7 ev Ge 0.7 ev 9

24 Multi-Junction Solar Cell Concepts Lattice matched 3-junction on Ge Lattice matched 4-junction on Ge Inverted metamorphic GaInP 1.9 ev GaInAs 1.4 ev Ge 0.7 ev GaInP 1.9 ev GaInAs 1.4 ev GaInNAs 1.0 ev Ge 0.7 ev GaInP 1.9 ev GaAs 1.4 ev Metamorphic GaInAs 1.0 ev Metamorphic GaInAs 0.7 ev carrier 9

25 Multi-Junction Solar Cell Concepts Lattice matched 3-junction on Ge Lattice matched 4-junction on Ge Inverted metamorphic 4-junction bonded to InP GaInP 1.9 ev GaInP 1.9 ev GaInP 1.9 ev GaInP 1.9 ev GaInAs 1.4 ev GaAs 1.4 ev GaAs1.4 ev GaInAs 1.4 ev GaInNAs 1.0 ev Metamorphic GaInAs 1.0 ev Bonding GaInAsP 1.0 ev Ge 0.7 ev Ge 0.7 ev Metamorphic GaInAs 0.7 ev GaInAs 0.7 ev carrier 9

26 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Absorption Thicknesses Radiative Recombination Ideal diode equation Current Transport Ideal Photonic Properties 10

27 Optical Modeling Anti-reflection coating Planar epitaxial stacks are easy to model optically Transfer matrix method Absorption in each junction A λ (including reflection) J ph = q A λ b s λ dλ Reveals absorption losses J1 sub-cell GaInP (1.9 ev) Tunnel junction 1 J2 sub-cell GaAs (1.42 ev) Tunnel junction 2 J3 sub-cell GaInAsP (1.05 ev) Tunnel junction 3 J4 sub-cell GaInAs (0.7 ev) 4J Bonded to InP GaInP/GaAs//GaInAsP/GaInAs 11

28 External Quantum Efficiency [%] Optical Modeling World Record 4J Solar Cell 4J bonded to InP solar cell developed by Soitec/Fraunhofer ISE/CEA-LETI 44.7% under concentrated illumination 297 suns Optical model Assumes perfect carrier collection Bandgaps and overall absorption are well modeled optically Wavelength [ m] J1 J2 J3 J4 J1 (sim) J2 (sim) J3 (sim) J4 (sim) Window R F. Dimroth et al. Wafer bonded four-junction GaInP/GaAs//GaInAsP/GaInAs concentrator solar cells with 44.7% efficiency, Progress in Photovoltaics: Research and Applications, 22(3), ,

29 External Quantum Efficiency [%] Optical Modeling with Diode Modeling World Record 4J Solar Cell Wavelength [ m] J1 J2 J3 J4 J1 (sim) J2 (sim) J3 (sim) J4 (sim) Within equivalent circuit model Photocurrent EQE J1 sub-cell J2 sub-cell J3 sub-cell J4 sub-cell 13

30 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Absorption Thicknesses Radiative Ideal diode equation Recombination Current Transport Radiative Nonradiative Ideal Photonic Properties 14

31 V oc [V] Optical Modeling with Diode Modeling World Record 4J Solar Cell Within equivalent circuit model Photocurrent EQE Voltage Diode saturation current J 0 Radiative limit Realistic V oc based on Wanlass model Empirical in nature V OC = kt q log J ph J Exp. ISE Radiative Limit Wanlass Fit Bandgap [ev] M. W. Wanlass, K. Emery, T. A. Gessert, G. S. Horner, C. R. Osterwald, T. J. Coutts. Practical considerations in tandem cell modeling, Solar Cells, 27, ,

32 V oc [V] Optical Modeling with Diode Modeling World Record 4J Solar Cell Exp. ISE Radiative Limit Wanlass Fit Within equivalent circuit model Photocurrent EQE Voltage Diode saturation current J 0 Radiative limit Realistic V oc based on Wanlass model Empirical in nature Establishes where we should be in terms of voltage J1 sub-cell Bandgap [ev] J2 sub-cell J3 sub-cell J4 sub-cell 15

33 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Absorption Thicknesses Radiative Ideal diode equation Recombination Current Transport Radiative Nonradiative Resistances to diode Ideal Photonic Properties 16

34 Optical Modeling with Diode Modeling World Record 4J Solar Cell Within equivalent circuit model Photocurrent EQE Voltage Diode saturation current J 0 Radiative limit Realistic V oc based on Wanlass fit Efficiency resistances 17

35 Optical Modeling with Diode Modeling World Record 4J Solar Cell Within equivalent circuit model Photocurrent EQE Voltage Diode saturation current J 0 Radiative limit Realistic V oc based on Wanlass fit Efficiency resistances 17 F. Dimroth et al. Wafer bonded four-junction GaInP/GaAs//GaInAsP/GaInAs concentrator solar cells with 44.7% efficiency, Progress in Photovoltaics: Research and Applications, 22(3), , 2014

36 Optical Modeling with Diode Modeling World Record 4J Solar Cell Concentration Within equivalent circuit model Over concentration Photocurrent linear in C Logarithmic increase in voltage V OC (C) = V OC (C = 1)+ kt q log C Efficiency increases logarithmically Until power losses dominate From contact resistances & lateral conduction 18

37 Optical Modeling with Diode Modeling World Record 4J Solar Cell Concentration Diode modeling for each sub-cell in an equivalent circuit How well can this predict efficiencies? Over concentration Lower nonradiative losses Injection level dependence Higher gains in V oc Higher current power losses From contact resistances & lateral conduction 18

38 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Absorption Thicknesses Radiative Ideal diode equation Recombination Current Transport Radiative Nonradiative Resistances to diode Ideal Photonic Properties ARC 19

39 How to gain more insight via modeling Limitations of diode/empirical modeling What happens if the doping of the p- or n-layer is increased/decreased? Or the thickness of the p- or n- layer is increased/decreased without changing the total thickness? How can imperfect carrier collection be modeled? Space-based photovoltaic cells How can the influence of photonic properties on voltage be studied in solar cells? 20

40 Optical Modeling with Device Solver/Diode Modeling Models from the Literature Single junction modeling with emphasis on exploiting photonic properties A. Marti, J. L. Balenzategui, R. F. Reyna. Journal of Applied Physics, 82(8), , 1997 J. L. Balenzategui, A. Marti. Solar Energy Materials and Solar cells, 90, , 2006 M. A. Steiner et al. Journal of Applied Physics, 113, , 2013 M. A. Steiner et al. IEEE Journal of Photovoltaics, 3(4), , 2013 X. Wang et al. IEEE Journal of Photovoltaics, 3(2), , 2013 M. P. Lumb et al. IEEE Journal of Quantum Electronics, 49(5), , 2013 M. P. Lumb et al. Journal of Applied Physics, 116, , 2014 A. W. Walker et al. Journal of Photovoltaics, 5(1), 2015 Multijunction solar cells with photonic effects 21 M. A. Steiner, J. F. Geisz. Applied Physics Letters, 100, , 2012 D. J. Friedman, J. F. Geisz, M. A. Steiner. IEEE Journal of Photovoltaics, 4(3), , 2013 J. F. Geisz et al. IEEE Journal of Photovoltaics, 5(6):1-13, 2015 M. W. Wilkins et al. Journal of Applied Physics, 118, A. W. Walker et al. Journal of Photonics for Energy, 5(1), pp. 2015

41 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Absorption Thicknesses Radiative Recombination Radiative Nonradiative Diffusion lengths Ideal diode equation Current Transport Drift-diffusion solver Ideal Photonic Properties ARC 22

42 Optoelectronic Device Modeling Symmetry Element [ m] Width >> thickness 22 [ m]

43 Optoelectronic Device Modeling Sentaurus Device Solve transport equations selfconsistently over a dynamic mesh using finite element methods ε φ = q p n + N D N A n t = 1 J G R q J = qd n n + qμ n ne Material properties (electrical) Heterointerfaces, thermionic emission, Fermi statistics Nonlocal tunneling in tunnel diodes 23

44 Energy [ev] Optoelectronic Device Modeling Sentaurus Device Energy Band Diagram 3 2 GaInP Top Cell GaAs Middle Cell 1 Spectrum 0-1 E c Depth [ m] Critical to understanding device behavior Identify potential barriers & band bending 24-2 E F E Tunnel Junction v

45 Ext. Quantum Efficiency [%] Optoelectronic Device Modeling Sentaurus Device Results of a 3J on Ge EQE Input includes: Layer structure Material data Diffusion lengths J1 (sim) J2 (sim) J3 (sim) J1 (exp) J2 (exp) J3 (exp) Wavelength [ m] 25

46 Optoelectronic Device Modeling Sentaurus Device Results of a 3J on Ge J-V Azur 3G30C-Advanced Type J sc [ma/cm 2 ] V oc [V] FF [%] Efficiency [%] Exp Sim

47 PR Factor, f [1] Optoelectronic Device Modeling Accounting for Photon Recycling Photon recycling leads to an effective increase in radiative lifetime Via a photon recycling factor f τ radpr = τ rad 1 f Lumb data Simple Approx. Decrease in radiative saturation current Depends on thickness Reabsorption Thickness [nm] Lumb et al. Incorporating photon recycling into the analytical drift-diffusion model for high efficiency solar cells, Journal of Applied Physics, 116, ,

48 Optoelectronic Device Modeling Sentaurus Device Results of a 3J on Ge J-V Azur 3G30C-Advanced Type J sc [ma/cm 2 ] V oc [V] FF [%] Efficiency [%] Exp Sim Sim. with photon recycling

49 Power Loss [%] Optoelectronic Device Modeling Sentaurus Device Results of a 3J on Ge J-V Under concentration: Contact resistance & the sheet resistance are critical! Grid optimization Contact Balancing resistance losses with shading losses Easier to model numerically outside of device simulation Contact suns concentration Pitch [cm] Finger separation Lateral Emitterresist. Shadowing Total Current Rest of structure 29

50 OVERVIEW IDEAL MODELING REAL MODELING 100% absorption Generation Materials Absorption Thicknesses Radiative Recombination Radiative Nonradiative Diffusion lengths Ideal diode equation Ideal Current Transport Photonic Properties Resistances within drift-diffusion solver ARC/photon recycling 30

51 Optoelectronic Device Modeling Inverted Metamorphic 4J Device SolAero achieving high efficiencies ~ 34.5%* Inverted metamorphic Do not reach radiative limit for all sub-cells Threading dislocations deteriorate the minority carrier diffusion lengths** GaInP 1.9 ev GaAs 1.4 ev Metamorphic GaInAs 1.0 ev Metamorphic GaInAs 0.7 ev carrier *Patel et al. Experimental results from performance improvement and radiation hardening of inverted metamorphic multijunction solar cells, IEEE Journal of Photovoltaics, 2(3), , **Yamaguchi et al. Efficiency calculations of thin-film GaAs solar cells on Si substrates, Journal of Applied Physics, 58(9), ,

52 Int. Int. Quantum Int. Quantum Quantum Efficiency Efficiency Efficiency [%] [%] [%] Optoelectronic Device Modeling Inverted Metamorphic 4J Device SolAero achieving high efficiencies ~ 34.5%* Do not reach radiative limit for all sub-cells Threading dislocations deteriorate the minority carrier diffusion lengths** Losses to QE J1 IQE sim. J1 J2 IQE IQE sim. sim. J2 J3 IQE IQE sim. sim. J3 J4 J1 Sim. IQE IQE IQE sim. sim. sim. J4 J1 J2 Exp. IQE IQE IQE sim. exp. sim. J1 J2 J3 IQE IQE IQE exp. exp. sim. J2 J3 J4 IQE IQE IQE exp. exp. sim. J3 J4 J1 IQE IQE IQE exp. exp. exp. J4 R J2 IQE sim. IQE exp. J3 IQE exp. exp. R J4 sim. IQE exp. R sim Wavelength 1.0 [ m] Wavelength 1.0 [ m] Wavelength [ m] *Patel et al. Experimental results from performance improvement and radiation hardening of inverted metamorphic multijunction solar cells, IEEE Journal of Photovoltaics, 2(3), , **Yamaguchi et al. Efficiency calculations of thin-film GaAs solar cells on Si substrates, Journal of Applied Physics, 58(9), ,

53 Current Density [ma/cm 2 ] Optoelectronic Device Modeling Inverted Metamorphic 4J Device SolAero achieving high efficiencies ~ 34.5%* Do not reach radiative limit for all sub-cells Threading dislocations deteriorate the minority carrier diffusion lengths** Losses to QE and V oc SolAero Exp. (Patel et al) 8 4J Sim. IMM (36.4%) (sim) 36.4% Voltage [V] *Patel et al. Experimental results from performance improvement and radiation hardening of inverted metamorphic multijunction solar cells, IEEE Journal of Photovoltaics, 2(3), , **Yamaguchi et al. Efficiency calculations of thin-film GaAs solar cells on Si substrates, Journal of Applied Physics, 58(9), ,

54 Optoelectronic Device Modeling Dilute Nitride-based Multi-junction Solar Cells 4-junction device such as Lattice matched dilute nitride Lattice matched 4-junction on Ge GaInP 1.9 ev GaInAs 1.4 ev GaInNAs 1.0 ev Ge 0.7 ev 32

55 Optoelectronic Device Modeling Dilute Nitride-based Multi-junction Solar Cells 4-junction device such as Lattice matched dilute nitride Diffusion lengths of dilute nitrides? 32

56 Ext. Quantum Efficiency [%] Optoelectronic Device Modeling Dilute Nitride-based Multi-junction Solar Cells 4-junction device such as Lattice matched dilute nitride Diffusion lengths of dilute nitrides? Nice hole diffusion length J1 J2 J3 J1 J2 J2 (0.2 um) J3 (0.4 um) J3 (0.6 um) J4 J3 (0.8 um) J3 (1.0 um) J3 (1.2 um) J3 (1.4 um) J3 (1.6 um) J3 (1.8 um) J4 R Wavelength [ m] 32

57 Ext. Quantum Efficiency [%] Optoelectronic Device Modeling Dilute Nitride-based Multi-junction Solar Cells 4-junction device such as Lattice matched dilute nitride Diffusion lengths of dilute nitrides? Design of dilute nitride subcell becomes critical to device performance Current matching Voltage contribution Poor hole diffusion length J1 J2 J3 J1 J2 J3 (0.2 um) J3 (0.4 um) J3 (0.6 um) J4 J3 (0.8 um) J3 (1.0 um) J3 (1.2 um) J3 (1.4 um) J3 (1.6 um) J3 (1.8 um) J4 R Wavelength [ m] 32

58 Ext. Quantum Efficiency [%] Optoelectronic Device Modeling Dilute Nitride-based Multi-junction Solar Cells 4-junction device such as Lattice matched dilute nitride Diffusion lengths of dilute nitrides? Design of dilute nitride subcell becomes critical to device performance Current matching Voltage contribution 5-junction device: AlGaInP/AlGaAs/GaAs/GaInNAs/ Ge J1 J2 J3 J4 J Wavelength [ m] 32

59 Ext. Quantum Efficiency [%] Optoelectronic Device Modeling Dilute Nitride-based Multi-junction Solar Cells 4-junction device such as Lattice matched dilute nitride Diffusion lengths of dilute nitrides? Design of dilute nitride subcell becomes critical to device performance Current matching Voltage contribution 5-junction device: AlGaInP/AlGaAs/GaAs/GaInNAs/ Ge Wavelength [ m] Current limitation by GaAs Efficiency of 37% J1 J2 J3 J4 J5 32

60 Optoelectronic Device Modeling Conclusions Ideal limits: Guidance for bandgap combinations Optical & empirical diode modeling: Material thicknesses & practical efficiency predictions with resistances Optoelectronic device modeling: Current transport (lateral current & heterointerfaces) Insight into diffusion length limitations Photonic properties can also be studied explicitly via this approach 33

61 Optoelectronic Device Modeling Supplementary Topics for Discussion THE EXCITING STUFF: Photon recycling GaAs single junction device with a rear-side mirror (no substrate) Luminescence coupling between junctions THE BIG UNKNOWN: Nonradiative parameter extraction using powerdependent relative photoluminescence Injection level dependence of Shockley-Read-Hall 34

62 Thank you for your attention! Fraunhofer Institute for Solar Energy Systems ISE Alex Walker, Ph.D. 35

63 THE EXCITING STUFF Photon recycling in Single Junction Devices Influence of rear-side mirror & cell design Luminescence coupling in MJSCs Current matching imposed by series connection ARC Top sub-cell Bottom sub-cell Substrate Luminescence Coupling Tunnel junction ARC Top sub-cell + - Bottom sub-cell + - Substrate Photon Recycling 36

64 Photon Recycling in GaAs Solar Cells Sentaurus Device & Photon Recycling Photon recycling & continuity equation: q n = 0 = q G R t J n Iterative feedback between radiative recombination and generation rates R rad x, y All points G PR (l, k) (x, y) Ω 37

65 Normalized Emission [abs.] Photon Recycling in GaAs Solar Cells Photon Recycling Considerations GaAs spontaneous emission profile: nm Wavelength [ m] 38

66 Extinction Coefficient [abs.] Refractive Index [abs.] Normalized Emission [abs.] Photon Recycling in GaAs Solar Cells Photon Recycling Considerations GaAs spontaneous emission profile: nm Refractive index ~ constant Extinction coefficient varies strongly in this range Wavelength [ m] n k Wavelength [ m] 38

67 Extinction Coefficient [abs.] Refractive Index [abs.] Normalized Emission [abs.] Photon Recycling in GaAs Solar Cells Photon Recycling Equation 1.0 f λ 0.8 For each wavelength of emission: Relative fraction of photons emitted within a wavelength bin f λ Wavelength [ m] 0.08 n k Wavelength [ m] 38

68 Normalized Emission [abs.] Photon Recycling in GaAs Solar Cells Photon Recycling Equation 1.0 f λ 0.8 For each wavelength of emission: Relative fraction of photons emitted within a wavelength bin f λ Correlate absorption at l, k due to emission from x, y r x, y, l, k, λ Wavelength [ m] 38

69 Normalized Emission [abs.] Photon Recycling in GaAs Solar Cells Photon Recycling Equation 1.0 f λ 0.8 For each wavelength of emission: Relative fraction of photons emitted within a wavelength bin f λ Correlate absorption at l, k due to emission from x, y r x, y, l, k, λ Wavelength [ m] Parks, et al. Journal of Applied Physics, 82(7): p , Ω G PR l, k = R rad (x, y) x,y V(x, y) V(l, k) λ f λ r x, y, l, k, λ Walker et al. IEEE Journal of Photovoltaics, 5(6), ,

70 Photon Recycling in GaAs Solar Cells Current Voltage 1 Sun Model validation: cell with and without substrates have identical cell designs Contact ARC Contact ARC 3.5 m GaAs Substrate 3.5 m GaAs Rear Mirror 39

71 Photon Recycling in GaAs Solar Cells Current Voltage 1 Sun Model validation: cell with and without substrates have identical cell designs Cell EXPERIMENTAL J SC [MA/CM 2 ] V OC [V] Substrate No substrate & silver mirror

72 Photon Recycling in GaAs Solar Cells Current Voltage 1 Sun Model validation: cell with and without substrates have identical cell designs Cell EXPERIMENTAL J SC [MA/CM 2 ] V OC [V] Substrate No substrate & silver mirror Photon recycling 2.1% increase 39

73 Photon Recycling in GaAs Solar Cells Current Voltage 1 Sun Model validation: cell with and without substrates have identical cell designs Cell EXPERIMENTAL Simulation without Photon Recycling J SC [MA/CM 2 ] V OC [V] J SC [MA/CM 2 ] V OC [V] Substrate No substrate & silver mirror

74 Photon Recycling in GaAs Solar Cells Current Voltage 1 Sun Model validation: cell with and without substrates have identical cell designs Cell EXPERIMENTAL Simulation without Photon Recycling Simulation with Photon Recycling J SC [MA/CM 2 ] V OC [V] J SC [MA/CM 2 ] V OC [V] J SC [MA/CM 2 ] V OC [V] Substrate No substrate & silver mirror

75 Photon Recycling in GaAs Solar Cells Current Voltage 1 Sun Model validation: cell with and without substrates have identical cell designs Cell EXPERIMENTAL Simulation without Photon Recycling Simulation with Photon Recycling J SC [MA/CM 2 ] V OC [V] J SC [MA/CM 2 ] V OC [V] J SC [MA/CM 2 ] V OC [V] Substrate No substrate & silver mirror Thinner cells (2.35 µm) also grown model predicted similar V oc increase 39

76 Conclusions Maximizing open circuit voltage Contact ARC 3.5 m GaAs Substrate V oc = V +2.1% 3.5 m GaAs +0.8% Highly reflective back mirror V oc = V 2 m GaAs V oc = 1.08 V +3.7% 2 m GaAs High material quality V oc up to 1.12 V Removing the substrate boost of 2.1% Thinning of active region from 3.5 to 2 μm boost of 0.8% Improving material quality boost of up to 3.7% Walker et al. IEEE Journal of Photovoltaics, 5(6), , Walker et al. Journal of Photonics for Energy, 5, ,

77 Current Density [ma/cm 2 ] Luminescence Coupling in GaAs-based MJSCs Cell Designs & Experimental Measurements Current voltage measurements from 3 suns to 100 suns (AM1.5D) at 300 K: Each sub-cell is optically thick (97% absorption) ARC GaAs sub-cell Tunnel junction GaAs sub-cell Bottom Top Substrate Voltage [V] 41

78 Relative Photon Flux [abs.] ARC Tunnel junction Substrate Luminescence Coupling in GaAs-based MJSCs Redistribution Matrix for GaAs Tandem Cell Top cell Depth in Cell [ m] Bottom cell ARC Top sub-cell + - Tunnel junction Bottom sub-cell Substrate

79 Luminescence Coupling in GaAs-based MJSCs Experimental Measurements Coupling strength defined as: J sc Tandem J sc Single 42

80 Coupling Strength [%] Luminescence Coupling in GaAs-based MJSCs Experimental Measurements Coupling strength defined as: J sc Tandem J sc Single As concentration increases, GaAs becomes more radiative: Top cell operating closer to its sub-cell V oc Exp Suns [1] 42

81 Coupling Strength [%] Luminescence Coupling in GaAs-based MJSCs Experimental Measurements vs. Simulation Coupling strength defined as: J sc Tandem J sc Single As concentration increases, GaAs becomes more radiative: Top cell operating closer to its sub-cell V oc Exp el = 50 ns SRH el = 300 ns SRH el = 1 s SRH el = 10 s SRH hole SRH = 2 ns Electron SRH lifetime must increase Not sufficient to explain results Suns [1] 42

82 Coupling Strength [%] Luminescence Coupling in GaAs-based MJSCs Experimental Measurements vs. Simulation Coupling strength defined as: J sc Tandem J sc Single As concentration increases, GaAs becomes more radiative: Top cell operating closer to its sub-cell V oc Electron SRH lifetime must increase Not sufficient to explain results Holes SRH lifetime must also increase from 3 suns to 100 suns Exp =50 ns ( hole =2 ns) el SRH el SRH el SRH SRH =300 ns ( hole =2 ns) SRH =300 ns ( hole =10 ns) el =1 s SRH ( hole SRH =100 ns) SRH el =10 s ( hole =500ns) SRH SRH Suns [1] 42

83 THE BIG UNKNOWN Nonradiative lifetimes of III-V semiconductors Time-resolved photoluminescence effective lifetime Cathodoluminescence diffusion lengths Power-dependent relative photoluminescence Extract nonradiative parameters directly as a function of injection Influences of photon recycling Walker, A. W. & Heckelmann, S. et al. Nonradiative lifetime extraction using power-dependent relative photoluminescence of III-V semiconductor double-heterostructures, Journal of Applied Physics, 119(15), ,

84 Power-Dependent Relative Photoluminescence Setup Monochromator CCD PC Filter Wheel Lens Neutral Filter optional Glass Plate Dichroic Mirror DPSS Laser 532 nm Lens Probe PC Power Meter 500 nw 500 mw 44

85 Norm. Integrated Relative PL [%] PL Intensity [a.u.] Power-Dependent Relative Photoluminescence Measurement Result Radiative limit Wavelength [nm] Regime I Regime II Regime III Laser Intensity [W/m 2 ] 45

86 Power-Dependent Relative Photoluminescence Theory I PL I laser I laser I PL I laser I laser HI = η eff I laser 46

87 Power-Dependent Relative Photoluminescence Theory I PL I laser I laser I PL I laser I laser HI = η eff I laser η int I laser HI = 1 46

88 Power-Dependent Relative Photoluminescence Theory I PL I laser I laser I PL I laser I laser HI = η eff I laser η int I laser HI = 1 τ srh = n eff U rad η U eff eff rad U auger 46

89 Power-Dependent Relative Photoluminescence Theory I PL I laser I laser I PL I laser I laser HI = η eff I laser η int I laser HI = 1 τ srh = n eff U rad η U eff eff rad U auger Sample DH THICKNESS [NM] B EFF RAD [CM 3 S -1 ] τ EFF RAD [NS] DH DH DH DH Doping = 1e17 46

90 Effective Radiative Efficiency [%] Power-Dependent Relative Photoluminescence Measurement Result Different Sample Thicknesses Radiative efficiency decreases for increasing thicknesses Shortest lifetime less PR All samples reach radiative state at nearly same injection Increase in radiative efficiency based on actual carrier concentration Thinnest structure has highest concentration DH-1 (200 nm) DH-2 (500 nm) DH-3 (1000 nm) DH-4 (2000 nm) Laser Intensity [W/m 2 ] 47

91 Effective Radiative Efficiency [%] Power-Dependent Relative Photoluminescence Measurement Result Different Sample Thicknesses Radiative efficiency decreases for increasing thicknesses Shortest lifetime less PR All samples reach radiative state at nearly same injection Increase in radiative efficiency based on actual carrier concentration Thinnest structure has highest concentration Similar behavior seen based on absolute electroluminescence 47 4J IMM MJSC: black GaAs DH-1 (200 nm) DH-2 (500 nm) DH-3 (1000 nm) DH-4 (2000 nm) Laser Intensity [W/m 2 ] Adopted from Geisz et al.

92 Nonradiative Lifetime [s] Power-Dependent Relative Photoluminescence Measurement Result Different Sample Thicknesses Nonradiative lifetime extraction with knowledge of total recombination rates 2000 nm thick sample has longer lifetime Lower doping concentration Can perform thickness analysis to separate bulk vs. interface 10-5 DH-1 (200 nm) DH-2 (500 nm) DH-3 (1000 nm) DH-4 (2000 nm) Carrier Concentration [cm -3 ] Walker, A. W. & Heckelmann, S. et al. Nonradiative lifetime extraction using power-dependent relative photoluminescence of III-V semiconductor double-heterostructures, Journal of Applied Physics, 119(15), ,

93 Detailed Balance Predictions Current Matching? Optimization perfect current matching between sub-cells This may not be the case due to low FF of low bandgap sub-cells Algorithm 1: perfect current matching Algorithm 2: fill factor (efficiency) optimization w/o current matching G. Arbez, et al. 39 th IEEE Photovoltaic Specialists Conference, Tampa, FL, USA, June 16-21,

94 Detailed Balance Predictions Influence of IQE on Bandgaps However, IQE is often less than 1 This increases the optimal bandgap of each sub-cell Trade-off between voltage and current favors the voltage in terms of efficiency Adopted from Zhu et al. L. Zhu et al. Impact of sub-cell internal luminescence yields on energy conversion efficiencies of tandem solar cells: A design principle. Journal of Applied Physics, 104, ,

95 LITTLE SIDE STORY Wanlass Model for GaAs A Little Bit of Romance GaAs laser power converter modeled with Wanlass model over Temperature & concentration using a two diode model Other direct bandgap III-V semiconductors should also be comparable GaInP, GaInAsP & GaInAs all have low W oc = E g -V oc ~ 400 mv O. Höhn et al. Optimal laser wavelength for efficient laser power converter operation over temperature, Applied Physics Letters, to be published,

96 Extinction Coefficient [1] Refractive Index [1] Optical Modeling Material Properties AlInP, GaInP, AlGaAs, GaAs, GaInAs, Ge data are measured via spectroscopic ellipsometry or taken from literature data Alloys are modeled using a morphing algorithm Critical point interpolation of n and k data sets GaInAsP using InP and GaInAs lattice matched to InP: (GaInAs) z (InP) 1-z Similar to Adachi s MDF S. Adachi. Journal of Applied Physics, 66(12), , GaInAs LM to InP InP GaInAsP (z=0.7) Wavelength [ m] GaInAs LM to InP InP GaInAsP (z=0.7) Wavelength [ m]

97 Appendix A Coupling Sdevice to Photon Recycling Redistribution matrix correlates emission from one point to absorption at every other point Scan through influence of each mesh point to all other points. Sentaurus Device: Iterative nature for convergence. Voltage dictates magnitude of recombination rates Influences photon recycling strength V n+1 = V n + V Sentaurus Device [G 0 (x, y), R 0 (x, y, V n )] Internal photon recycling code PR G computed using equation (3) i Insert into G i (x, y) = G o (x, y) + G PR i (x, y) Sentaurus Device [G i (x, y), R i (x, y, V n )] Internal code J i J i 1 < J tol? Yes! Equations converged for V n No 53 Figure 1. Flow chart for iterative procedure to integrate photon recycling into Sentaurus simulation.

98 Relative photon flux BSF/Substrate FSF/ARC Appendix B Redistribution Matrix Advantages: Fixed for a particular device structure Transmission leads to luminescence coupling Disadvantages: Computationally intensive (mesh density dependent) Redistribution matrix computed externally Must import optical generation function Solar cell active region Device depth [ m] 54

99 Relative Photon Flux [abs.] BSF/Substrate FSF/ARC Appendix B Redistribution Matrix Redistribution Matrix Various Points of Emission nm Solar cell active region Device depth [ m]

100 Relative Photon Flux [abs.] BSF/Substrate FSF/ARC Appendix B Redistribution Matrix Redistribution Matrix Various Points of nm Solar cell active region Device depth [ m] Up to 30%! 55

101 Relative Photon Flux [abs.] BSF/Substrate FSF/ARC Relative Photon Flux [abs.] BSF/Mirror FSF/ARC Appendix B Redistribution Matrix Redistribution Matrix Optical Influence of Substrate vs. Mirror Substrate Solar cell active region Device depth [ m] No substrate Solar cell active region Device Depth [ m] 56

102 Relative Photon Flux [abs.] BSF/Substrate FSF/ARC Relative Photon Flux [abs.] BSF/Mirror FSF/ARC Appendix B Redistribution Matrix Redistribution Matrix Optical Losses Substrate Solar cell active region Device depth [ m] No substrate Solar cell active region Device Depth [ m] 56

103 Relative Photon Flux [abs.] ARC Tunnel junction Substrate Appendix B Redistribution Matrix Redistribution Matrix Zoom Top cell Depth in Cell [ m] Bottom cell Transmission to lower sub-cell

104 Appendix C Optical Generation Equations For each absorbing mesh point (l, k) along 1D: r x, y, l, k, λ : relative absorbed photon flux due to emission at point (x, y) f x, y, λ : fraction of spontaneously emitted photons from (x, y) centered at Summed over wavelengths to account for all spontaneous emission Multiplied by ratio of volume elements and magnitude of emission at (x,y) Summed over all emission points! G (l,k) = Ω x,y R rad (x, y) V(x, y) V(l, k) λ f x, y, λ r x, y, l, k, λ 58

105 Iterations [1] Appendix D Iterations Required for Convergence Voltage [V] 59

106 Appendix E Simulation Time Using 12 kernels on 64 bit 2.4 GHz: Optical Redistribution Matrix: Single junction device: 4-5 hours Dual junction device: 8-10 hours Current voltage simulation: Single junction device: hours Dual junction device: 5-7 hours (current mismatched: ~24 hours) Quantum efficiency simulation: Tandem device/dh structure: 2-3 hours for 10 nm steps 60

107 Quantum Efficiency, Refl. [%] Model Validation: Cell without a Substrate Quantum Efficiency R exp EQE exp R sim EQE sim Wavelength [um] 61

108 Open Circuit Voltage [V] How to Improve Single Junction Solar Cell Design? Influential Factors on V oc Electron Lifetime Back mirror reflectivity: 99.9% Restricting emission angle Active region thickness SRH lifetime Electron in base Hole = 2 ns Base = 3.5 um Base = 2.5 um Base = 2 um Base = 1.5 um Electron SRH Lifetime [s] 62

109 Open Circuit Voltage [V] How to Improve Single Junction Solar Cell Design? Influential Factors on V oc Hole Lifetime Back mirror reflectivity: 99.9% Restricting emission angle Active region thickness SRH lifetime Electron = 3 s Hole in emitter Steiner et al. reported 2.7 s Shockley-Read-Hall lifetime V oc = 1.10 V Gold back mirror Base = 3.5 um Base = 2.5 um Base = 2 um Base = 1.5 um Electron SRH lifetime = 3x10-6 s Hole SRH Lifetime [s] Steiner, et al. Journal of Applied Physics, (12): p

110 Open Circuit Voltage [V] How to Improve Single Junction Solar Cell Design? Influential Factors on V oc Summary Back mirror reflectivity: 99.9% Restricting emission angle Active region thickness SRH lifetime Emitter and base must have pristine material quality Base = 3.5 um Base = 2.5 um Base = 2 um Base = 1.5 um Hole SRH Lifetime 10-9 s 10-6 s Electron SRH Lifetime [s] 64

111 Further Design Improvements Front Side Angular Selective Filter Previously shown to improve V oc by up to 4 mv (Braun et al.) Simulation study using multi-layered dielectric filter (Kraus et al.) Measurements at Fraunhofer ISE on cells with no substrate: Improvement 1-2 mv Braun, A., et al., Energy & Environmental Science, (5): p Kraus, T., et al., Journal of Applied Physics, : p

112 V oc Improvement [mv] Further Design Improvements Front Side Angular Selective Filter Influence on V oc Short SRH lifetimes yield no benefit Benefit appears for sufficiently long SRH lifetimes Benefit not as high as previous modeling results (23 mv) Interface recombination Parasitic absorption Real (with SRV) Ideal (no SRV) Electron SRH Lifetime [s] Kraus, T., et al., Journal of Applied Physics, : p

113 EQE [%] Optoelectronic Device Modeling Advantages Diode modeling model lacks in predictions of device phenomena Influence of layer doping Hovel model Influence of diffusion lengths Hovel model breaks down Optoelectronic device modeling Account explicitly for all recombination mechanisms J GaInP/GaAs/Ge R J1 IQE=1 J2 IQE=1 J3 IQE=1 J1 IQE<1 J2 IQE<1 J3 IQE< Wavelength [ m] H. J. Hovel and J. M. Woodall, The effect of depletion region recombination currents on the efficiencies of Si and GaAs solar cells, in Proc. 10th IEEE Photovolt. Specialist Conf., 1973, p. 25. H. J. Hovel, Solar Cells. New York, USA: Academic,