Relationship between energetic disorder and open-circuit voltage in bulk heterojunction organic solar cells

Abstract

We simulate organic bulk heterojunction solar cells. The effects of energetic disorder are incorporated through a Gaussian or exponential model of density of states. Analytical models of open-circuit voltage (${V}_{\mathrm{OC}}$) are derived from the splitting of quasi-Fermi potentials. Their predictions are backed up by more complex numerical device simulations including effects such as carrier-density--dependent charge-carrier mobilities. It is predicted that the V${}_{\mathrm{OC}}$ depends on: (1) the donor-acceptor energy gap; (2) charge-carrier recombination rates; (3) illumination intensity; (4) the contact work functions (if not in the pinning regime); and (5) the amount of energetic disorder. A large degree of energetic disorder, or a high density of traps, is found to cause significant reductions in ${V}_{\mathrm{OC}}$. This can explain why ${V}_{\mathrm{OC}}$ is often less than expected in real devices. Energetic disorder also explains the nonideal temperature and intensity dependence of ${V}_{\mathrm{OC}}$ and the superbimolecular recombination rates observed in many real bulk heterojunction solar cells.