New generalization of dielectric screening in electronic devices with heavily doped semiconductor region(s). I. Treatment for the quasi-neutral bulk region

Abstract

A closed-form analytical method has been developed for determining a new function for spatially variable dielectric constant of semiconductors. The method leads to the development of a new and generalized model for screening potential in heavily doped semiconductors. Calculated results from the new function for the spatially variable dielectric constant show close correspondence with those from well-known earlier functions. The present model for the screening potential predicts improved behaviour at smali distances. It reduces automatically to the Dingle potential at very large distances. The proposed potential is used to estimate the bandgap narrowing of n-Si, p-Si, and n-Ge as a function of the doping density. Calculated results for bandgap narrowing show striking agreement with data from various experiments. AIthough much simpler, the present method appears to predict bandgap narrowing of semiconductors more accurately than by many-body quantum mechanical methods.