The anisotropy and temperature dependence in the mobility of rubrene

Abstract

Abstract The mobility in molecular crystals exhibits anisotropy and power-law temperature dependence. In this work, we developed an analytic expression to account for the anisotropic mobility observed in molecular crystals. The charge mobility is related to the friction coefficient in the Drude model, and the latter is expressed in terms of force–force correlation function through the fluctuation–dissipation theorem, calculated with a polaron model Hamiltonian under the Merrifield transformation. With electronic couplings and reorganization energies derived from first-principle calculation, and both acoustic and optical phonons considered, the temperature dependence of mobility calculated follows the power law, μ ∝ T−2.06 (90–210 K), close to the observed T−2. The anisotropy of mobility calculated as the ratio of mobility of the fast-axis over slow-axis, μa/μb, was 2.9 (300 K). With most parameters determined by first-principle calculation, our model offers a way to predict and understand the behavior of charge mobilities of molecular crystals.