Quantum yield of electron-hole pairs in semiconductors

It is shown that the two existing theories, the "crazy-carpentry" and the probability method, are essentially equivalent in evaluating quantum yield and variance in semiconductors. Quantum yield is determined by an integro-differential equation represented in terms of the density of states, the loss parameter, and the threshold energy. The analytical method used to calculated the relative yield, i.e., the inverse of the average $e-h$ pair-creation energy, is developed for the two cases: extended crazy-carpentry and free-particle models. The optical-mode deformation-potential and the polar-mode electrostatic-potential contributions to the phonon loss are taken into account.