Thermal Ionization of Impurities in Polar Crystals. I. Formal Theory

The method of O'Rourke is used to obtain an expression for the thermal ionization rate of an impurity in a polar crystal. The interaction energy of the trapped electron with the optical vibrational modes is assumed to be linear in the normal vibrational coordinates of the lattice. The eigenvalue equations and perturbation of the Born-Oppenheimer adiabatic potential method are employed, leading to a result identical to that of Huang and Rhys. Multiphonon transitions occur only when the configurational constant $S\ne 0$. An approximation of simple form, for the transition rate, can be made only for low temperatures, where the frequency factor $s$ is independent of temperature.