An analytic approximation with a wide range of applicability for electron initiated Auger transitions in narrow-gap semiconductors

Abstract

Theoretical calculations of Auger transition rates are complicated by the interconnection of energy and momentum conservation. The use of a flat valence band where the heavy holes have infinite mass decouples energy and momentum conservation and greatly simplifies the calculation. This flat valence band model has been used to obtain a simple analytic approximation for Auger transition rates. It requires just two parameters to cover a wide range of temperature and carrier Fermi levels (both degenerate and nondegenerate) and their values may be found either by comparison with an accurate calculation or from Auger lifetimes determined experimentally. The results have been applied to InSb and Cd0.2188Hg0.7812Te where good agreement with accurate theoretical values using realistic band structures has been attained. The same model has also been used to provide a simple analytic approximation for impact ionization probability rates, again agreeing well with accurately determined values. Such approximations will prove to be useful in modeling semiconductor transport effects and devices.