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OSA FiO 2013 / LS XXIX Owen Miller*: Post-doc, MIT Math Eli Yablonovitch : UC Berkeley, LBNL

Solar Cells as Light Emitters: The Key to Record Efficiencies and Approaching the Shockley- Queiser Limits. OSA FiO 2013 / LS XXIX Owen Miller*: Post-doc, MIT Math Eli Yablonovitch : UC Berkeley, LBNL. Slides/Codes/Relevant Papers: math.mit.edu/~ odmiller /publications.

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OSA FiO 2013 / LS XXIX Owen Miller*: Post-doc, MIT Math Eli Yablonovitch : UC Berkeley, LBNL

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  1. Solar Cells as Light Emitters:The Key to Record Efficiencies and Approaching the Shockley-Queiser Limits OSA FiO 2013 / LS XXIX Owen Miller*: Post-doc, MIT MathEli Yablonovitch: UC Berkeley, LBNL Slides/Codes/Relevant Papers: math.mit.edu/~odmiller/publications *Currently working with Steven Johnson @MIT

  2. Value of High Photovoltaic Efficiency Efficiency and Cost of Electricity (COE) inversely related: • Factors that impact COE: • Location: decides the available input energy • Efficiency: decides the portion that can be converted to electricity

  3. Which PV technology? Ask Shockley-Queisser • Canonical method for fundamental limits • solar cell = absorber • absorber = emitter • internals = black-box (equilibrate rates through surface) • constant quasi-Fermi level separation (thermalization) Shockley & Queisser J. Appl. Phys. 32, 510 (1961) Single-Junction Intermediate-Band Multi-Carrier Multi-Junction < 65% < 45% < 50% < 33.5% Many more: concentrating, hot-carrier, spectrum-splitting, nanowires, etc.

  4. Fundamental limits should be… Shockley-Queisser Absolutely. In simplest case, bandgap only General (few parameters) Robust No! By hiding internals, important photon dynamics are obscured A real system will never be perfect. But small imperfections in material/optics should yield small losses in performance. Two consequences: (a) For technology selection, need a “modified” SQ (b) To approach SQ: explicitly design for photon extraction

  5. Fundamental limits should be… Shockley-Queisser Absolutely. In simplest case, bandgap only General (few parameters) Robust No! By hiding internals, important photon dynamics are obscured A real system will never be perfect. But small imperfections in material/optics should yield small losses in performance. Two consequences: (a) For technology selection, need a “modified” SQ (b) To approach SQ: explicitly design for photon extraction

  6. Open-Circuit Voltage Determines Operating-Point Voltage To extract current, voltage at contacts must be slightly lower than Voc But, operating voltage linked directly to Voc We only need to understand the open-circuit voltage Any bad things that can happen, will happen. Can’t extract the charges before, say, non-radiative recombination

  7. Photon Extraction  VOC • Basic solar cell definition: absorbs sunlight • Thermodynamics: absorber = emitter • Equilibrium: • Non-eq: detailed balance (Kirchhoff's Law) open-circuit, steady-state Emission (through front) is not a loss mechanism! Any alternate path for photons: (a) represents loss (b) reduces effective carrier lifetimes

  8. The Voltage Penalty: kT |lnhext| • Mathematically formulated by Ross, 1967 • So what? Generalized: Rao, PRB 76, 085303 (2007) Kirchartz & Rau, PSSA 205, 2737 (2008) depends very non-linearly on internal parameters!

  9. Why do many solar cells have small VOC? Photon extraction is hard! (Ask LED designers) outgoing luminescence solar radiation Absorbed by contact? Outside escape cone? Non-ideal reflectivity? Heat? For a typical high-index material: Consequently a99% internal radiative efficiency re-absorption/re-emission events or a 99% reflective back mirror bounces off the rear mirror …before escape Only half of the photons escape!

  10. The Fragility of Shockley-Queisser Many material systems have fundamental limits to GaAs: c-Si: a-Si:

  11. Single-Junction Efficiency Records: 1990-2013 GaAs 34 33.5% Theory 32 30 Efficiency (%) 28 26.4% Previous Record (2010) Voc=1.03V 26 25.1% 25.0% 24 Record (1990- 2007) Best Si (1999- ) 0.8 1 1.2 1.4 1.6 Bandgap (eV)

  12. Single-Junction Efficiency Records: 1990-2013 GaAs 34 33.5% Theory 32 30 ~30% Efficiency (%) 28 Voc=1.12V (2012) 28.8% 26.4% Previous Record (2010) Voc=1.03V 26 Alta Devices 25.1% 25.0% 24 Record (1990- 2007) Best Si (1999- ) 0.8 1 1.2 1.4 1.6 Bandgap (eV)

  13. Efficiency vs. Rear Mirror Reflectivity 33.5 GaAs 3mm 33.2% 90% Rear Reflectivity Is Not Enough! 32.5 32.2% 31.9% Cell Efficiency (%) 31.5 30.5 0 0.2 0.4 0.6 0.8 1 Reflectivity 1.16 32.6 32.50 1.145 32.46 1.14 32.43 32.4 1.115 1.12 Jsc (mA/cm2) Voc (Volts) 1.104 1.10 32.2 1.08 32 1.06 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Reflectivity Reflectivity

  14. h h h (<25%) e- h+ h h hg hg h (>25%) e- h+

  15. 2013 GaAs (Alta) 2010 GaAs (ISE) GaAs ISE (x20) GaAs Alta (x1) M. A. Green, “Radiative Efficiency of state-of-the-art photovoltaic cells” Courtesy of Alta Devices

  16. Clarification: enhanced extraction photon recycling Photon recycling is one way to achieve light extraction, and thereby high Voc. However, there are ways to improve light extraction without enhancing photon recycling. For example: surface texturing. Voc increases. Light extraction is the general parameter that determines Voc, not photon recycling. cf. also Lush & Lundstrom, Solar Cells 30, 337 (1991)

  17. Fundamental limits should be… Shockley-Queisser Absolutely. In simplest case, bandgap only General (few parameters) Robust No! By hiding internals, important photon dynamics are obscured A real system will never be perfect. But small imperfections in material/optics should yield small losses in performance. Two consequences: (a) For technology selection, need a “modified” SQ (b) To approach SQ: explicitly design for photon extraction

  18. Application to many solar technologies GaAs Single-Junction Multi-Junction Large bandgap Eg2 Eg1 Small bandgap Photon up-conversion Photon down-conversion 3Eg 2Eg Eg 0

  19. Multiple-exciton generation: Shockley-Queisser 3Eg 2Eg Eg 0 Hanna & NozikJ. Appl. Phys. 100, 074510 (2006)

  20. Robustness analysis: multi-exciton generation The absolute voltage penalty is independent of bandgap The relative voltage penalty is much worse for small • Depends on exact assumptions – geometry, refractive index • Illustrates how important it is to look at robustness, photon dynamics

  21. Sub-wavelength solar cells: a new wrinkle Atwater et. al., “Design Considerations for PlasmonicPhotovoltaics,” 2010 Pillai et. al. “Surface plasmon enhanced silicon solar cells,” 2007 Zhu et. al. “Nanodome Solar Cells with Efficiency Light Management…,” 2009 New physics: emission partially de-coupled from absorption emission can occur into near-field (plasmons, quenching, etc.)

  22. Modeling emission: fluctuation-dissipation theorem Joint work led by Xiang Zhang group Phys. Rev. Lett. 109, 138701 (2012)

  23. Example system: air-Si-Au thin film ray optics near field (FDT) Emission into plasmon modes: - reduces extraction through the front - reduces carrier lifetimes - reduces Here, plane waves don’t couple to plasmons no absorption effect (JSC unaffected) This is ONLY an emission/VOC effect!

  24. Photon extraction: driver behind record 28.8% efficiency • Power output = current * voltage • voltage = extraction (difficult!) • There are significant returns to:>90% material quality>90% rear mirror reflectivity • New considerations at nano-scale • Technology selection: Shockley-Queisser is fragile • Adding a single parameter, , enables robustness analysis • Can be applied everywhere SQ can be applied Slides/Codes/Relevant Papers: math.mit.edu/~odmiller/publications

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