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Tom Markvart Solar Energy Laboratory School of Engineering Sciences University of Southampton, UK

SOLAR ENERGY CONVERSION: KINETICS, THERMODYNAMICS AND RECIPROCITY. Tom Markvart Solar Energy Laboratory School of Engineering Sciences University of Southampton, UK. Introduction / Outline. Classical thermodynamics (Carnot cycle; T s ≈6000K  T o ≈300K).

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Tom Markvart Solar Energy Laboratory School of Engineering Sciences University of Southampton, UK

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  1. SOLAR ENERGY CONVERSION: KINETICS, THERMODYNAMICS AND RECIPROCITY Tom Markvart Solar Energy Laboratory School of Engineering Sciences University of Southampton, UK

  2. Introduction / Outline Classical thermodynamics (Carnot cycle; Ts≈6000K To≈300K) Detailed balance in luminescence (Einstein, Kennard, Stepanov, van Roosbroeck & Shockley) Detailed balance in photovoltaics / photosynthesis (Shockley & Queisser, Ross & Calvin, …) Thermodynamics of solar energy conversion (Duysens, Landsberg, photothermal, endoreversible, …)

  3. Solar spectra on the ground IR UV O3 H2O H2O H2O, CO2 H2O, CO2

  4. 1 2 The basic philosophy : energy & charge separation DE top contacts ARC p-n junction Voltage V =  back contact

  5. Compare with Shockley solar cell equation where etc… Shockley & Queisser, J. Appl. Phys. 1961; Ross & Calvin, Biophys J. 1967. Simple kinetics “Forward” rate: photogeneration g “Reverse” (dark) rate = recombination of e- andh+

  6. Kinetic equation / I-V characteristic Free energy per e-h pair Photogeneration rate

  7. Kinetic equation - power generation Maximum power is extracted at Vmaxor Imax: need for control of the operating point ! Pmax

  8. At “open circuit” (K = 0): From detailed balance (Einstein, 1917) Rose, J. Appl. Phys. 1960; Baruch et al, J. Appl. Phys. 1985. A first hint of thermodynamics

  9. emission absorption Thermodynamics of light beams i work (w)

  10. … or a volume element in the phase space, an invariant, and a measure of the number of photon states: Counting sunrays: an aside on etendue Etendue - a geometric characteristic of light beams … (e.g. for isotropic incidence)

  11. Ts uin (sin) i w q (q/To) To Solar cell as a heat engine

  12. Losses as entropy generation Non-radiative recombination Finite “turnover rate” of the conversion “engine” Entropy generation by: Etendue expansion Es  Eout Cooling of photon gas TS  To Markvart, Appl. Phys. Lett. 2007

  13. Entropy generation : two-dimensional ideal photon gas = kB ln(/s) for a planar solar cell Make use of hot carriers ?

  14. Nature of thermodynamic losses heat rejection into To reservoir (Carnot cycle) photon cooling (= thermalisation) étendue expansion power per photon (a.u.) photon emission (finite “turnover rate”) kinetic losses normalised current / reaction rate

  15. Reciprocity: light harvesting hcoll LH LH RC

  16. Reciprocity : detrapping / "carrier" injection m1 hinj LH LH RC m2

  17. ideal dm observed Reciprocity : theory & application There are no shortcuts round the basic principles of PV/ photochemical conversion Static (energy) and kinetic (current) losses are (to some approximation) independent dK

  18. Conclusion • Thermodynamics can be used to describe the basic energy conversion processes in photovoltaics and photosynthesis • Parallels with kinetic theory but the origins of losses are elucidated in detail, in terms of entropy generation • A fundamental similarity between PV and photosynthetic conversion but differences in • Reciprocity: • Electricity v. electricity + chemical energy • Nano/molecular v. macroscale • Expression of microscopic reversibility which extends the link between kinetics & thermodynamics to realistic transport processes • Provides a description of constraints on the conversion process on account of the 2nd law of thermodynamics

  19. Postscript : nothing new under the Sun Jonathan Swift: Gulliver’s Travels (1726): the Academy of Lagado. With special thanks to Peter Landsberg

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