On the Statistical Mechanics of Impurity Conduction in Semiconductors

The statistical mechanics of the impurity electron states for a semiconductor with a low density of donors, and a small amount of acceptor compensation, is analyzed. Expressions are obtained for the number of dissociated donor ion states according to the Mott model, and for the effects of multiple trapping, and of dispersion of the trapping energies, on this number. An expression for the thermoelectric power according to the Mott model is obtained. If a small proportion of “minority” donors, of a different chemical species with a smaller electron binding energy than the majority donors, were added to the impurity content they should act as additional traps for donor ion states: The statistical mechanics of this system is analyzed.