Theory of charge transport in organic crystals: Beyond Holstein’s small-polaron model

Abstract

We present a theory for charge transport in organic crystals. A mobility expression is derived based on the evaluation of the Kubo formula and the Holstein Hamiltonian. It covers the whole temperature range from low $T$, where it reproduces an expression from the Boltzmann equation for band transport, via elevated $T$, where it generalizes Holstein's small-polaron theory to finite bandwidths, up to high $T$, for which a temperature dependence equal to Marcus' electron transfer theory is obtained. The general expression treats coherent band transport and thermally induced hopping on equal footing. By avoiding the approximation of narrow polaron bands the theory allows for the description of large and small polarons.