One-Phonon Transition Rate in Impurity Conduction

Abstract

The one-phonon transition rate for carrier transfer from an occupied impurity center to the empty one was calculated on the basis of the formalism given by Gummel and Lax. The deformation potential is used as the perturbation and the dependence of the equilibrium position of the lattice atoms on the state of the carrier is taken into account. This dependence influences seriously the one-phonon transition rate. The general formula for the transition rate was investigated in detail in two regions of temperature. Numerical data are given for $n$- and $p$-type Si and Ge in the approximation of the simple parabolic band. The usefulness of the Gummel and Lax treatment is discussed.