Impurity Conduction in the Intermediate Concentration Region

The impurity conduction in semiconductors in the intermediate impurity concentration region is investigated theoretically by using the data available on antimony-doped germanium with small compensations. The origin of the activation energy ${\epsilon }_2$ which characterizes the resistivity in a certain temperature range is discussed on the basis of the $D^{-}$-band model, which is provided by the formation of a band as a result of the interaction between the states of negatively charged donors, the $D^{-}$ states. The hydrogenic model is employed for the donor ground state, and we assume that the wave function describing the behavior of an electron in the weakly bound $D^{-}$ state is of an exponential type. By using the tight-binding approximation, it is shown that the interaction between these states leads to the formation of the $D^{-}$ band. Thus, the energy gap from the donor ground state, which is assumed to be localized, to the bottom of the $D^{-}$ band is related to the observed activation energy ${\epsilon }_2$. The numerical estimations are in qualitative agreement with the observed values.