Definition of effective energy and distance of hopping electron transport

Abstract

Hopping conductivity in crystalline semiconductors has been parameterized and there is an analytic expression for conductivity, suitable at very low temperatures. For the arbitrary temperatures, the analytic expression is not available. This work parameterizes the hopping conductivity using two parameters called the effective hopping energy and the effective hopping distance. This report presents a numerical method, which allows extraction of these parameters from a single temperature dependence of conductivity, simulated in a wide range of temperatures. An approximated method is proposed, which allows to extract the effective hopping energy from experimental temperature dependences of conductivity. The results agree qualitatively with the existing theories, created for the low and high-temperature limits, and bridge the gap between them by describing the behavior of effective parameters at moderate temperatures, where the transition from variable range hopping to nearest neighbor hopping occurs, accompanied by modifications of the energy-distribution of the density of localized states.