Phonon-assisted transition rates I. Optical-phonon-assisted hopping in solids

Abstract

Abstract An extensive calculation of the optical-phonon-assisted transition rates for non-adiabatic electronic hopping motion in a solid is presented. Holstein's Molecular Crystal Model is used as a basis for study and the computation involves no restrictions on either the magnitude of the electron-lattice coupling strength, the temperature, or the difference between the electronic energies of the initial and final sites. In the strong-coupling small-polaron regime, the jump rates, associated d.c. conductivity, a.c. conductivity, and electric-field dependence of the d.c. conductivity, for a crystal are all calculated. These transport properties manifest qualitatively distinct behaviours corresponding to whether the temperature is above or well below the optical-phonon temperature. In the low-temperature regime the energy-conserving processes which involve the absorption of the minimum amount of vibrational energy provide the dominant contribution to the thermally activated jump rates. At sufficiently high...