Effect of backward carrier jumps on variable-range hopping in disordered materials

Abstract

A variable-range hopping model is described that accounts for the effect of back-and-forth carrier jumps between occasionally close hopping sites isolated from the rest of the hopping network. It is shown that accounting for this effect for constant density of states (DOS) does not change the Mott ${T}^{\ensuremath{-}1/4}$ law but yields a modified coefficient that can be considered as a percolation threshold for dc conductivity in a positionally and energetically disordered hopping system. In a system with an exponential DOS distribution, the backward jumps significantly reduce dc conductivity but only slightly affect its functional dependence upon temperature.