The charge-carrier mobility of organic semiconductors is a fundamental material property and one of the central quantities for the optimization of device performance in, e.g., organic transistors and solar cells. In order to investigate the intrinsic fundamental (i.e., not device-specific) charge-transport phenomena in organic solids, molecular crystals are ideal candidates because of their high degree of structural order. Nonetheless, even for such ultrapure organic crystals, the theoretical and numerical description of the charge transport is a highly nontrivial task due to the strong coupling between the electronic and vibronic degrees of freedom. Here, we present a theory for charge transport in organic crystals which generalizes Holstein's small polaron model to polarons of arbitrary size and allows to calculate the carrier mobilities using ab-initio techniques (density-functional theory). The generalized mobility expression includes both the coherent band transport as well as the thermally induced hopping on equal footing. As a prototypical example, the theory is applied to herringbone-stacked crystals where the temperature dependence of the mobilities is simulated and compared to experimental data. Finally, the mobility anisotropy is analyzed by a novel 3D visualization technique for the relevant transport channels. [1] K. Hannewald et al., Phys. Rev. B 69, 075211 & 075212 (2004). [2] K. Hannewald and P.A. Bobbert, Appl. Phys. Lett. 85, 1535 (2004). [3] F. Ortmann, F. Bechstedt, and K. Hannewald, Phys. Rev. B 79, 235206 (2009). [4] F. Ortmann, F. Bechstedt, and K. Hannewald, New J. Phys. 12, 023011 (2010). [5] F. Ortmann, F. Bechstedt, and K. Hannewald, Phys. Stat. Sol. B 248, 511 (2011).
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