Nonradiative Transitions in Deep Impurities in Semiconductors—Study in a Semiclassical Model

Abstract

Nonradiative transitions in the deep impurity states in semiconductors are studied by a semiclassical model, in which the lattice distortion around the impurity is approximated as a classical harmonic oscillator modulating the potential depth for the electron. An integral equation is derived and solved numerically describing the nonadiabatic transition from the bound state to the scattering states which corresponds to the thermal ionization. Peculiar features in the transition dynamics are clarified in contrast with the transitions between discrete levels. In the adiabatic limit, which covers the situation at high temperatures in real semiconductors, the transition rate obeys the Arrhenius law with the pre-exponential factor given by the phonon frequency as pointed out by Sumi.