Interaction of Electron on the Donor Center with the Crystal Lattice in Germanium and Silicon

Abstract

The diagonal matrix element of interaction of the bound electron with longitudinal acoustic phonon, squared and averaged over all directions of the phonon wave vector, was calculated for $n$-type Ge and Si assuming a single-deformation-potential constant. The donor wave functions have been taken in the elipsoidal form. Some simple integrals containing the squared and averaged matrix element are given and are used, as an example, to get the one-phonon transition rate in the impurity conduction by hopping and the relaxation energy of the lattice deformed by interaction with the donor electron. Appreciable differences are found between the case of elipsoidal and spherical donor wave functions.