Non-radiative de-excitation of deep centres

We develop a quantitative theory of the ratio R of radiative to non-radiative de-excitation based on the Dexter-Klick-Russell criterion for the occurrence of luminescence. The model invokes three essential elements: a promoting mode, an accepting mode, and a set of lattice modes which ultimately absorb the vibrational energy. The ratio R is determined by the relative population of the relaxed excited and ground states. We show that Rnx(a)/ng(a), where nx(a) and ng(a) are the numbers of vibrational quanta in the accepting mode associated with the excited state and the ground state, respectively, at the crossing of their adiabatic potential energy curves. The result is consistent with experiment.