A method of determining the overlap integrals used in calculations of Auger transition rates in semiconductors

Overlap integrals of Bloch functions are required for calculations of Auger transition rates in semiconductors. The usual approximations (such as those based on the effective mass sum rule or the simple four-band kp method) are known to be unreliable but the pseudopotential and 15-band kp methods (which produce accurate values) involve too much computation to be directly incorporated in numerical calculations of Auger transition rates. In the work reported here, the overlap integrals obtained from numerical diagonalisation of the kp Hamiltonian, with the effects of remote bands included by the Lowdin procedure, are shown to be in good agreement with those calculated from the empirical non-local pseudopotential band-structure method of Chelikowsky and Cohen (1976). Also it is shown how it is possible to obtain algebraic expressions for overlap integrals from the kp method by using perturbation theory. The perturbation theory is able to explain the general features of the numerical diagonalisation results and in many cases provides a good quantitative description.