Statistics of electrons and holes in heavily doped n-silicon

In an earlier paper [1] the authors have given a model for the effective electrical bandgap narrowing in silicon at moderate levels of doping by considering the impurity-band broadening. In this paper more elaborate calculations have been done for uncompensated n-doped silicon by defining a partition function for the electron distribution within the impurity band and a mobility edge above which electrons can be considered as free. Also, calculations have been done by incorporating the effect of potential energy fluctuations on the density of states within the conduction and valence bands. It has been shown that these fluctuations considerably increase the effective density of states within these bands, though the tail states are mainly due to the impurity band. The calculations show that the electrical bandgap narrowing is largely nonrigid. The rigid band shift is comparatively small.