Calculating charge-carrier mobilities in disordered semiconducting polymers: Mean field and beyond

We model charge transport in disordered semiconducting polymers by hopping of charges on a regular cubic lattice of sites. A large on-site Coulomb repulsion prohibits double occupancy of the sites. Disorder is introduced by taking random site energies from a Gaussian distribution. Recently, it was demonstrated that this model leads to a dependence of the charge-carrier mobilities on the density of charge carriers that is in agreement with experimental observations. The model is conveniently solved within a mean-field approximation, in which the correlation between the occupational probabilities of different sites is neglected. This approximation becomes exact in the limit of vanishing charge-carrier densities, but needs to be checked at high densities. We perform this check by dividing the lattice in pairs of neighboring sites and taking into account the correlation between the sites within each pair explicitly. This pair approximation is expected to account for the most important corrections to the mean-field approximation. We study the effects of varying temperature, charge-carrier density, and electric field. We demonstrate that in the parameter regime relevant for semiconducting polymers used in practical devices the corrections to the mobilities calculated from the mean-field approximation will not exceed a few percent, so that this approximation can be safely used.