Fundamental Photovoltaic Efficiency Limits Due to Semiconductor Band Tails

The theoretical maximum efficiency of a solar cell is given by the Shockley-Queisser limit, which assumes an abrupt onset of absorption near the band-edge. However, real materials always have an imperfect band-edge, which is usually characterized by an Urbach tail. By using optoelectronic reciprocity relations and explicitly accounting for band filling, we develop a modified detailed balance model that explicitly accounts for non-abrupt band-edges. We find that large band tails can result in an effective Stokes shift between the absorption onset and luminescence peak, which results in a penalty on the maximum efficiency of a solar cell.