Theory of localized states in semiconductors. I. New results using an old method

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Abstract
In this paper the Kohn-Luttinger effective-mass theory is reevaluated using first-principles impurity potentials. In the past, it has generally been believed that the theory is valid for shallow levels and inapplicable to deep levels. Here, a new result is obtained, namely that the theory is valid for both shallow and deep levels but only for the special cases when the impurity atom is substitutional and is from the same row of the Periodic Table as the host atom. Such atoms have the same number of core electrons and have been called isocoric for convenience. On the other hand, the theory is found to be invalid in the cases of the general nonisocoric impurities, whether shallow or deep. These results are confirmed by calculations of donors in silicon. Excellent agreement with experiment is found for the isocoric phosphorus and sulfur impurities (both one- and two-electron sulfur levels are deep). No adjustable parameters are employed. These results are understood in physical terms as the one-band approximation can yield correct nodal structure for the impurity-electron wave function only in the case of isocoric impurities.

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