Electronic transport and quantum localization effects in organic semiconductors

We explore the charge transport mechanism in organic semiconductors based on a model that accounts for the thermal intermolecular disorder at work in pure crystalline compounds, as well as extrinsic sources of disorder that are present in current experimental devices. Starting from the Kubo formula, we describe a theoretical framework that relates the time-dependent quantum dynamics of electrons to the frequency-dependent conductivity. The electron mobility is then calculated through a relaxation time approximation that accounts for quantum localization corrections beyond Boltzmann theory, and allows us to efficiently address the interplay between highly conducting states in the band range and localized states induced by disorder in the band tails. The emergence of a ``transient localization'' phenomenon is shown to be a general feature of organic semiconductors that is compatible with the bandlike temperature dependence of the mobility observed in pure compounds. Carrier trapping by extrinsic disorder causes a crossover to a thermally activated behavior at low temperature, which is progressively suppressed upon increasing the carrier concentration, as is commonly observed in organic field-effect transistors. Our results establish a direct connection between the localization of the electronic states and their conductive properties, formalizing phenomenological considerations that are commonly used in the literature.