  We consider a simple model for the geminate electron-hole separation process
in organic photovoltaic cells, in order to illustrate the influence of
dimensionality of conducting channels on the efficiency of the process. The
Miller-Abrahams expression for the transition rates between nearest neighbor
sites was used for simulating random walks of the electron in the Coulomb field
of the hole. The non-equilibrium kinetic Monte Carlo simulation results
qualitatively confirm the equilibrium estimations, although quantitatively the
efficiency of the higher dimensional systems is less pronounced. The lifetime
of the electron prior to recombination is approximately equal to the lifetime
prior to dissociation. Their values indicate that electrons perform long
stochastic walks before they are captured by the collector or recombined. The
non-equilibrium free energy considerably differs from the equilibrium one. The
efficiency of the separation process decreases with increasing the distance to
the collector, and this decrease is considerably less pronounced for the three
dimensional system. The simulation results are in good agreement with the
extension of the continuum Onsager theory that accounts for the finite
recombination rate at nonzero reaction radius and non-exponential kinetics of
the charge separation process.
