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 Math Eli Yablonovitch: UC Berkeley, LBNL *Currently working with Steven Johnson @MIT Slides/Codes/Relevant Papers: math.mit.edu/~odmiller/publications math.mit.edu/~odmiller/publications

2. From Allen Barnett Univ. of Delaware 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-BandMulti-CarrierMulti-Junction < 33.5% < 65%< 45%< 50% Many more: concentrating, hot-carrier, spectrum-splitting, nanowires, etc.

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

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

6. 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 Open-Circuit Voltage Determines Operating-Point Voltage Any bad things that can happen, will happen. Can’t extract the charges before, say, non-radiative recombination

7. Photon Extraction  V OC 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 |ln  ext | 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 V OC ? Photon extraction is hard! (Ask LED designers) Heat? Outside escape cone? solar radiation outgoing luminescence Absorbed by contact? Non-ideal reflectivity? For a typical high-index material: re-absorption/re-emission events bounces off the rear mirror …before escape a 99% internal radiative efficiency or a 99% reflective back mirror Consequently Only half of the photons escape!

10. The Fragility of Shockley-Queisser GaAs: c-Si: a-Si:

11. Single-Junction Efficiency Records: 1990-2013 24 26 28 30 32 34 0.8 11.21.41.6 GaAs 33.5% 26.4% Theory Previous Record (2010) V oc =1.03V 25.1% Record (1990- 2007) Bandgap (eV) Efficiency (%) 25.0% Best Si (1999- )

12. Single-Junction Efficiency Records: 1990-2013 24 26 28 30 32 34 0.8 11.21.41.6 GaAs 33.5% 26.4% Theory Previous Record (2010) V oc =1.03V 25.1% Record (1990- 2007) ~30% Alta Devices 28.8% V oc =1.12V (2012) Bandgap (eV) Efficiency (%) 25.0% Best Si (1999- )

13. 00.20.40.60.81 30.5 ReflectivityCell Efficiency (%) 00.20.40.60.81 1.16 Reflectivity Voc (Volts) 1.14 1.12 1.10 1.08 1.06 Reflectivity 00.20.40.60.81 Jsc (mA/cm 2 ) 32 32.2 32.2% 33.2% 31.9% 1.104 1.115 1.145 32.43 32.46 32.50 31.5 32.5 33.5 32.4 32.6 90% Rear Reflectivity Is Not Enough! GaAs 3  m Efficiency vs. Rear Mirror Reflectivity

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

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

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

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

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

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

21. Sub-wavelength solar cells: a new wrinkle Atwater et. al., “Design Considerations for Plasmonic Photovoltaics,” 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) Here, plane waves don’t couple to plasmons  no absorption effect (J SC unaffected) This is ONLY an emission/V OC effect!

25. Slides/Codes/Relevant Papers: math.mit.edu/~odmiller/publicationsmath.mit.edu/~odmiller/publications