Auger transitions in semiconductors and their computation

Abstract

To obtain an accurate theoretical determination of Auger transition rates from first principles it is essential that the multidimensional integral of the transition probabilities should not be approximated, particularly with regard to the overlap functions, as has been done previously. In considering general interband Auger transitions (with direct or indirect bands) the difficulty of complicated limits imposed by energy and momentum conservation is removed by a transformation of the variables, resulting in an integration over a complete six-dimensional solid angle. This makes accurate computation possible without approximating the integrand-within the limitation of the best available overlap functions and band structure. The initial application is to InSb where small- and large-signal Auger lifetimes, mass-action constants and impact ionisation rates are determined using Fermi-Dirac statistics, non-parabolic energy bands for all states and overlap functions derived from the four-band k.p model.