A two-level system as a model for a photovoltaic solar cell

The operation of a photovoltaic solar cell is discussed with a quantum two-level system as a model. A detailed-balance calculation is carried out, from which the parameters of the converter, illuminated by radiation from a black body, are exactly obtained in different geometries, taking into account radiative recombination processes. It is shown that in a 4π geometry (source fully surrounding the converter) with total radiative recombination, the thermodynamic efficiency is equal to the Carnot efficiency at zero current (open circuit): the converter behaves as an ideal thermal engine, fully reversible when delivering no power (the practical efficiency is evidently zero). The reversibility is ensured by the complete exchange of photons between the source and the converter. The current-voltage relation is obtained in all cases, and it is shown that the two-level system follows the ideal diode equation. The calculation of the thermodynamic efficiency is generalized to an energy band system (real semiconductor) with radiative recombination and is shown to be maximum at open circuit, but lower than the Carnot efficiency because of irreversibilities induced by the thermalization of carriers. The effective source temperature concept is discussed. It is shown to be valid for a two-level system, but has less physical meaning for a two-band system.