Numerical simulation of hopping conductivity in granular metal films

Abstract

We numerically simulate the temperature dependence of thermally activated tunnelling conductance in granular metal films. By mapping the grains on to a simple-cubic lattice and considering hops up to third-nearest neighbours, it is shown that the hopping conductivity α follows - In σ α 1/T^1/2 accurately over several orders of magnitudes. These results support the interpretation that this widely observed behaviour results from interpolating the high-temperature activation behaviour and the low-temperature - Inσ α 1/T^1/4 behaviour.