Impurity Conduction at Low Concentrations

The conductivity of an n-type semiconductor has been calculated in the region of low-temperature T and low impurity concentration n₃. The model is that of phonon-induced electron hopping from donor site to donor site where a fraction K of the sites is vacant due to compensation. To first order in the electric field, the solution to the steady-state and current equations is shown to be equivalent to the solution of a linear resistance network. The network resistance is evaluated and the result shows that the T dependence of the resistivity is ({₃}kT). For small K, ₃= (e^{2}{₀}) (4{{n₃}3) }^1{3} (1-1. 35K^1{3}), where ₀ is the dielectric constant. At higher K, ₃ and attain a minimum near K=0. 5. The dependence on n₃ is extracted; the agreement of the latter and of ₃ with experiment is satisfactory. The magnitude of is in fair agreement with experiment. The influence of excited donor states on is discussed.