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 Σ(→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.
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Ghazali et al. (1982) studied this question.