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

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Abstract
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.