Phonon cascade theory

Abstract

A generalized formulation is given of the Lax electron cascade capture model. An electron capture cross-section is obtained, via an essentially classical argument, in terms of quantum mechanical transition probabilities, which may include various suitable electron-boson interactions. The electronic potential energy, in the presence of an impurity centre, has been assumed to behave as r − n . Cross-sections have been obtained for electron capture with emission of either acoustic or optical phonons. In the latter case computations have been made yielding new cross-sections for both neutral ( n = 4) and Coulomb attractive centres ( n = 1), in germanium and silicon. The “sticking probabilities” were taken from previous literature. When comparable with earlier work, the cross-sections obtained are smaller (by at most a factor 10). The present treatment is distinguished from earlier ones by systematically confining the wave vectors of the emitted phonons to the first Brillouin zone. New estimates include cross-sections for electron capture by neutral centres in silicon, with optical phonon emission, over a range of temperatures.