Impact of Semiconductor Band Tails and Band Filling on Photovoltaic Efficiency Limits

The theoretical maximum efficiency of a solar cell is typically characterized\nby a detailed balance of optical absorption and emission for a semiconductor in\nthe limit of unity radiative efficiency and an ideal step-function response for\nthe density of states and absorbance at the semiconductor band edges, known as\nthe Shockley-Queisser limit. However, real materials have non-abrupt band\nedges, which are typically characterized by an exponential distribution of\nstates, known as an Urbach tail. We develop here a modified detailed balance\nlimit of solar cells with imperfect band edges, using optoelectronic\nreciprocity relations. We find that for semiconductors whose band edges are\nbroader than the thermal energy, kT, there is an effective renormalized bandgap\ngiven by the quasi-Fermi level splitting within the solar cell. This\nrenormalized bandgap creates a Stokes shift between the onset of the absorption\nand photoluminescence emission energies, which significantly reduces the\nmaximum achievable efficiency. The abruptness of the band edge density of\nstates therefore has important implications for the maximum achievable\nphotovoltaic efficiency.\n