NEW GENERALIZATION OF DIELECTRIC SCREENING IN ELECTRONIC DEVICES WITHHEAVILY-DOPED SEMICONDUCTOR REGION(S) .1. TREATMENT FOR THE QUASI-NEUTRAL BULK REGION

A closed-form analytical method has been developed for determining a n ew function for spatially variable dielectric constant of semiconducto rs. The method leads to the development of a new and generalized model for screening potential in heavily doped semiconductors. Calculated r esults from the new function for the spatially variable dielectric con stant show close correspondence with those from well-known earlier fun ctions. The present model for the screening potential predicts improve d behaviour at small 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 o f the doping density. Calculated results for bandgap narrowing show st riking agreement with data from various experiments. Although much sim pler, the present method appears to predict bandgap narrowing of semic onductors more accurately than by many-body quantum mechanical methods .