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

Classical thermodynamics (Carnot cycle; T s ≈6000K  T o ≈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, …)

O3O3 H2OH2O H2OH2O H 2 O, CO 2 UV IR

ARC top contacts p-n junction back contact Voltage V =  11 22 EE

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

Photogeneration rate Free energy per e-h pair

P max Maximum power is extracted at V max or I max : need for control of the operating point !

At “open circuit” (K = 0): From detailed balance (Einstein, 1917) Rose, J. Appl. Phys. 1960; Baruch et al, J. Appl. Phys

ii work (w) absorption emission

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

TsTs ToTo u in (s in ) q (q/T o ) w ii

Entropy generation by: Cooling of photon gas T S  T o Etendue expansion E s  E out Finite “turnover rate” of the conversion “engine” Non-radiative recombination Markvart, Appl. Phys. Lett. 2007

Make use of hot carriers ? = k B ln(  /  s ) for a planar solar cell

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

LH RC  coll

LH RC  inj 11 22

 ideal observed KK There are no shortcuts round the basic principles of PV/ photochemical conversion Static (energy) and kinetic (current) losses are (to some approximation) independent

 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

Jonathan Swift: Gulliver’s Travels (1726): the Academy of Lagado. With special thanks to Peter Landsberg