The impurity conduction in the low concentration limit has been analyzed in terms of hopping process. Starting from the Liouville's equation, we have derived an expression for the electrical current and a boltzmann-type equation for diagonal elements of the density matrix in the lowest order of the electron-phonon interaction. If we only take into account the lowest order of W (overlapping integral), the Miller-Abraham's network model has been obtained. By improving the method of averaging we have shown the resistance to be proportional to Kl/3 in low temperature limit, where K is the degree of compensation.Furthermore, using the network model we have analyzed the different parts of the density matrix. The behavior of the diagonal part is much different from that in the ordinary conduction process, and is connected with appearance of the activation energy.By estimating the overlapping integral and energy fluctuation, we conclude that the carriers are mainly not localized in the low compensation case (K-2), if the impurity concentration is larger then a critical value (1014cm-3 in Ge and 1016cm-3 in Si). This does not contradict the experimental facts, if we take into account the Coulomb interaction between electrons.
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