Electronic Energy Transfer via Virtual-Phonon Processes

Abstract

A model is presented for transfer of electronic energy between impurity ions in a solid, via virtual-phonon processes. When the energy being transferred is much greater than the maximum phonon energy in the solid, the transfer rate varies approximately as ${R}^{\ensuremath{-}6}$ for electricd ipole, and as ${R}^{\ensuremath{-}10}$ for electric-quadrupole transitions of the impurity ions, where $R$ is the range between the impurities. One difference between our treatment and that of Orbach and Tachiki, in which an exponential range dependence is obtained, is that our electron-lattice coupling involves distant, not just nearest, neighbors. These results apply when no local modes are present. Local modes produce additional effects which, under certain conditions, dominate strongly over band-mode contributions to energy transfer.