Nondispersive polaron transport in disordered organic solids

An analytical theory based on the effective medium approach is formulated to describe nondispersive hopping charge transport in a disordered organic material where polaron effects are important. The treatment of polaron transport in solids with superimposed disorder and polaron effects is based on the Marcus jump rate equation, while the conventional Miller-Abrahams formalism is used to describe charge mobility in polaron-free systems. It is shown that the Poole-Frenkel-type field dependence of mobility $\mathrm{ln}\ensuremath{\mu}\ensuremath{\propto}\sqrt{E}$ occurs for both the bare charge carrier and the polaron transport provided that energetic correlation effects have been taken into account. We show that our polaron model can quantitatively explain the observed magnitudes of temperature- and electric-field-dependent polaron mobilities assuming physically reasonable values of polaron binding energies and transfer integrals; it gives a background for the development of the method for estimation of polaron binding energy and the energetic disorder parameter from these dependences. The results of the calculations are found to be in good agreement with both experimental results obtained for some \ensuremath{\sigma}-conjugated polysilylenes where polaron formation was straightforwardly demonstrated and recent computer simulations of polaron transport.