From DOS Tails to Urbach Energies: Mitigating Radiative Losses in Photovoltaics

Mitigating radiative losses in photovoltaics is crucial to attaining high power conversion efficiencies. Sub-band-gap absorption, characterized by an exponential Urbach tail, is a major contributor to these losses. Exponential tails in the density of states (DOS) have been shown to create large Urbach energies that dramatically reduce efficiency. In this work, we generalize this analysis to generalized-Gaussian DOS tails and find that Gaussian tails result in significantly smaller Urbach energies than exponential tails. Additionally, by considering the position of the Fermi level, we show that the Fermi function can be used to empty heavy DOS tails and reduce the Urbach energy. We then apply this analysis to understand the effects of doping on the radiative efficiency of organic photovoltaics (OPVs). In OPVs, dopant-induced disorder broadens the DOS and increases Urbach energy while shifting the Fermi level deep into the DOS and truncating its tail. These competing effects cause radiative efficiency to decrease initially but then recover at high doping concentrations. For highly disordered polymers, we find that heavy doping may be optimal for radiative efficiency, which will guide future development.