We model charge transport in disordered semiconducting polymers by hopping of charge carriers on a square lattice of sites with Gaussian on-site energy disorder, using Fermi-Dirac statistics. From numerically exact solutions of the Master equation, we study the dependence of the charge-carrier mobility on temperature, carrier density, and electric field. Our results are used in calculating current-voltage characteristics of hole-only polymer diodes. It is found that very good fits to experimental current-voltage characteristics can be obtained at different temperatures, with reasonable fitting parameters for the width of the Gaussian density of states and the lattice constant. In agreement with the experiments we find that the density dependence is dominant over the field dependence. Only at high fields and low temperatures the field dependence becomes noticeable. The potential and current distribution show strong inhomogeneities, which may have important consequences for the operation of polymer opto-electronic devices.
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