A general formula is derived for the electron occupation numbers appropriate for multicharge centers in semiconductors, including excited states. The results are used to rederive and generalize several formulas of interest in the literature, in order to show exactly how the degeneracies of individual states enter in. Particular attention is paid to certain subjects which are sometimes confusing, such as how the statistics of band states differ from those those of localized states. Another subject of much recent interest, negative-U centers, is dealt with in some detail. We show how the dependence of the average occupation number on Fermi energy and the temperature dependence of the freecarrier concentration differ between positive- and negative-U centers.
Look, D. C.
(1981). Statistics of Multicharge Centers in Semiconductors - Applications. Physical Review B, 24 (10), 5852-5862.