Multiphonon, non-radiative transition rate for electrons in semiconductors and insulators

Abstract

A quantum-mechanical calculation of the multiphonon, non-radiative transition rate for electrons in solids is carried out without assuming the Condon approximation. A relatively simple result is obtained by adopting a single-frequency model. An expression valid at low and intermediate temperatures (0<T<or approximately=300K) is derived. The enhancement of rate over that derived in the Condon approximation is roughly (p/2)2, where p is the depth of the level in units of the phonon energy. It arises from a combination of enhanced mixing of initial and final electronic states and the introduction of three- and four-phonon processes within a single vibrational mode. The result is shown to agree very well with experimentally determined temperature dependence of the electron capture cross section for the B centre in GaAs. An expression valid at very high temperatures is shown to have the same form as the semi-classical rate derived by Henry and Lang (Phys. Rev. B., vol.15, p.989 (1977)).