Fermi energy and other related aspects in a parabolic band semiconductor under band tailing

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Abstract
Band tailing refers to the effects of impurity states in and near to the band edge in a heavily-doped semiconductor. In the present study, the Fermi energy, screening length and the impurity screening potential are determined for a heavily-doped parabolic band semiconductor. The effects of unperturbed and perturbed bands are both considered in the evaluation of the entities. In the perturbed band, the density-of-states technique, earlier used by Kane, and the E- dispersion relation technique for band tailing, obtained by us, are applied. Our results on Fermi energy are compared with the results of Kane's model and with those for the unperturbed band for a typical semiconductor of n-type GaAs. We find that our model provides much lower values at a low concentrations of 1017-1018 cm-3, as compared to the other two cases and finally merges with the unperturbed band case at a higher doping conditions. On the other hand, the Kane's model offers much higher values over the doping range studied here.