Low-frequency hopping conductivity in amorphous semiconductors

Abstract

The excess a.c. conductivity [sgrave]_A(ω) = [sgrave](ω) - [sgrave](0) due to hopping processes in a disordered material is usually interpreted in terms of the ω⁵ law, s< 1, predicted by the pair approximation. However, recent data on [sgrave]_A(ω) for amorphous germanium shows a roll-off behaviour as ω → 0; [sgrave]_A(ω) falls off faster than ω⁵ below a characteristic frequency ω_c which exhibits a strong temperature dependence. In the present work it has been found that the roll-off is obtained within the extended pair approximation (EPA)—it marks the onset of a.c. loss by subsets of sites contained in the infinite cluster determining [sgrave](0). Decreasing ω through ω_c changes s from less than unity to 2. To within a scale factor, the EPA gives a good account of the observed frequency dependence of [sgrave]_A(ω) and the temperature dependence of ω_c.