Three-dimensional master equation simulations of charge-carrier transport and recombination in organic semiconductor materials and devices

Three-dimensional master equation modeling for disordered semiconductor devices is provided. Charge transport is modeled as incoherent hopping between localized molecular states, and recombination is modeled as a nearest-neighbor process where an electron at a first location and a hole at a second location can recombine at either the first location or the second location. Here the first and second locations are any pair of nearest neighbor locations. We have found that this nearest neighbor recombination model performs substantially better than the conventional local recombination model where an electron and a hole must be at the same location to recombine. The recombination rate is modeled as a product of a prefactor γ, hopping rates and state occupancies. Importantly, we have found that sufficient simulation accuracy can be obtained by taking γ to be given by an empirically derived analytic expression.