Stochastic Transport in a Disordered Solid. II. Impurity Conduction

In a previous paper, the authors have developed a general theory of stochastic transport in disordered systems. In the present paper, the theory is applied, in detail, to a prototype of transport in a disordered system - impurity conduction in semiconductors. The complete frequency dependence of the real and imaginary part of the conductivity is calculated. In particular, the calculation details the transition from an ${\ensuremath{\omega}}^{s}$ dependence to essentially dc behavior (at a finite frequency), where $s\ensuremath{\sim}0.6\ensuremath{-}0.8$, depending on temperature and concentration. The theoretical results for frequency, temperature, and concentration dependence of the conductivity are shown to be in good agreement with the measurements of Pollak and Geballe (PG). In addition, the ac conductivity data of PG interpreted with the present theory yield experimental evidence for the existence of two-channel hopping in $n$-type Si.