Finite Mobility Effects on the Radiative Efficiency Limit of Pn-Junction Solar Cells

The maximum power conversion efficiency of a solar cell as defined by the Shockley-Queisser (SQ) radiative recombination limit relies on the assumption that the collection probability for all photogenerated electron/hole-pairs is unity. This assumption implies a virtually infinite mobility mu of the photogenerated charge carriers. In order to compute the radiative efficiency limit with finite mobility, we solve the continuity equation for minority carriers including an additional integral term that accounts for emission of photons by radiative recombination and their subsequent reabsorption. Even when assuming radiative recombination as the only recombination mechanism, the achievable efficiency is reduced drastically when mu drops below a critical value mu_c. This critical value depends on the absorption coefficient and the doping density of the semiconductor. Thus, we give a criterion that has to be fulfilled by any photovoltaic material in order to guarantee charge separation even in an otherwise most ideal case. Finally, we extend our theory to finite non-radiative lifetimes thereby spanning the gap between the SQ theory and the classical textbook description of a pn-junction solar cell