Theory of optical cross sections of deep level impurities in covalently bonded semiconductors

A formalism for the calculation of the optical cross section of a deep impurity level in a covalently bonded semiconductor is developed. This formalism, which is based upon quantum mechanical time dependent perturbation theory, assumes a tight binding representation for the bandstructure of the host semiconductor and models the deep level and its associated potential using the Hjalmarson theory of deep levels. The optical cross sections for the deep levels associated with several impurities in selected semiconductors are calculated numerically using a semiempirical tight binding bandstructure model as input into the formalism. The chemical trends which emerge from these calculations are discussed.