Second-Order Cumulant Approach for the Evaluation of Anisotropic Hole Mobility in Organic Semiconductors

The anisotropic field effect mobilities of four prototypical semiconducting materials, that is, single crystals of pentacene, tetracene, picene, and rubrene, are evaluated by using the hopping model with time averaged rates obtained at the second-order cumulant (SOC) expansion of the time-dependent reduced density matrix. It is shown that the SOC approach allows for correcting the two known failures of the hopping mechanism: the highly overestimated mobilities provided by the Fermi golden rule and the incorrect temperature dependence predicted by the semiclassical Marcus' approach.