Model of Thermally Activated Hopping Motion in Solids

Abstract

A simple idealized model is formulated for the purpose of deriving the transport properties of a particle that moves through a lattice primarily by means of thermally activated jumps. In its present form, the model is designed to represent the gross features of the properties of a "small polaron," that have been derived from previous microscopic theories. The model consists of a single particle, confined to a set of equivalent localized states, which may move either by tunneling or by thermally activated jumps. The properties of the model are solved exactly for the case when there are only two sites. The solution exhibits how the thermally activated and tunneling processes combine to transfer the particle from site to site. The various transport properties of the model are then obtained for the cases when the particle is trapped at a color center (idealized by two-site model) and when it moves through a periodic lattice. These properties are derived from those of the "natural" motion of the system, in the absence of any applied field, by means of the fluctuation-dissipation theorem.