The Influence of Imperfect Band-edges on the Maximum Efficiency of a Solar Cell

The theoretical maximum efficiency of a solar cell is given by the Shockley-Queisser Limit, which assumes a step-function absorbance near the band-edge. However, real materials always have an imperfect band-edge, which is usually characterized by an Urbach tail. In this work, we utilize optoelectronic reciprocity relations to develop a modified detailed balance limit of solar cells with imperfect band-edges. We find that for band-edges that are not sharper than the thermal energy, an effective renormalized band-gap is given by the quasi-Fermi level splitting within the solar cell. This renormalized bandgap creates a Stokes shift between the onset of absorption and the photoluminescence peak position, which drastically lowers the maximum achievable efficiency. The band-edge density of states therefore has important implications for the performance of photovoltaic devices.