1960/11/01 by Allen H. Miller, Elihu Abrahams · 10 citations
Physics and Astronomy · Materials Science · #Semiconductor materials and interfaces #Quantum and electron transport phenomena #Silicon Nanostructures and Photoluminescence
paper · doi:10.1103/physrev.120.745
openalex publication_date 1960/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
The conductivity of an n-type semiconductor has been calculated in the region of low-temperature T and low impurity concentration nD. 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 \ensuremathρ\ensuremath∝exp(\frac\ensuremathε3kT). For small K, \ensuremathε3=(\frace2\ensuremathκ0)(\frac4\ensuremathπnD3)(1)/(3)(1\ensuremath-1.35K(1)/(3)), where \ensuremathκ0 is the dielectric constant. At higher K, \ensuremathε3 and \ensuremathρ attain a minimum near K=0.5. The dependence on nD is extracted; the agreement of the latter and of \ensuremathε3 with experiment is satisfactory. The magnitude of \ensuremathρ is in fair agreement with experiment. The influence of excited donor states on \ensuremathρ is discussed.