Shockley-Queisser Model: Analytical Solution, Thermodynamics, and Kinetics

We consider the generalized Shockley-Queisser (GSQ) model, which is based on a single assumption that photocarriers and emitted photons are in chemical equilibrium and described by the Boltzmann distribution functions with the same chemical potential. The model takes into account the frequency-dependent absorption (emission), photon trapping and recycling, photocarrier multiplication, and nonradiative recombination processes. For the noninteracting photocarriers, we obtain an exact analytical solution of the GSQ model. We present the conversion efficiency and other photovoltaic (PV) characteristics in a convenient form via the Lambert W function. Photocarrier multiplication and recombination via three-body Auger processes are also directly included in this formalism. We derive universal formulas for useful energy, thermal losses, and emission losses per absorbed photon. We show that the relation between the maximal conversion efficiency and the photo-induced chemical potential, obtained by Henry [J. Appl. Phys. 51, 4494 (1980)] for the ideal SQ limit, is also valid in the GSQ model. In the general case of interacting electrons, in particular for the Shockley-Read-Hall processes, the solution is presented in an iterative form. We analyze photocarrier kinetics and derive a general relation between the optimal photocarrier collection time and photocarrier lifetime with respect to all radiative and nonradiative processes. Finally, we analyze finite mobility limitations and show that PV devices with photon trapping and recycling provide the fast photocarrier collection required by the GSQ model.