Linear-Response Theory of the Electron Mobility in Molecular Crystals

The effect of the fluctuations of the polarization energy and the transfer integrals on the excess electron and hole motion in aromatic crystals, in particular anthracene, has been studied. The Kubo linear-response theory and the Wannier representation have been used. At temperatures higher than the Debye temperature, the electron-phonon interaction through the fluctuation of polarization energy is found to be considerably greater than that due to the transfer-integral fluctuation for anthracene crystal. A high-temperature formula for the mobility tensor has been derived, which may be considered as a generalization of the random-walk diffusion-model formula. This mobility expression consists of two parts, representing tunneling with and without phonon assistance. The temperature dependence due to electron-phonon interaction comes in through the thermal-equilibrium occupation number of phonon modes, $n\left(\lambda \right)$, and well-defined quantities $\alpha (i, j)$. Fairly good agreement between the calculated and measured values of mobility has been obtained.