Multiple-Scattering Approach to the Formation of the Impurity Band in Semiconductors

The electronic structure of doped semiconductors is studied by using the best approximation of Klauder's impurity-scattering theory which yields a wave-vector- and energy-dependent self-energy $\Sigma (\overrightarrow{\mathrm{k}},E)$. An approximation is used for electron correlation effects. It is shown that as the impurity concentration is decreased, the conduction-band tail progressively splits off, giving an impurity band. The link between the formation of the latter and the general theory of bifurcation is outlined.