Calculations of the commonly neglected terms in the matrix element for Auger and impact ionisation processes in semiconductors

In studies of Auger and impact ionisation processes in semiconductors it is conventional to employ a standard formula involving overlap integrals of the periodic parts of the electronic Bloch functions to calculate the important rate-determining matrix element. However, this formula is only an approximation which arises as a result of the neglect of terms which appear in the full calculation. In this paper the authors make use of the non-local pseudopotential band structure of Chelikowsky and Cohen (1976) to evaluate the size of the correction resulting from a full calculation of the matrix element in direct-gap semiconductors. The correlation is negligible for narrow gap materials but becomes significant as the forbidden band gap increases.