A Theory of Impurity Conduction I

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Abstract
The phenomena of impurity conduction of semiconductors such as G e and S i are treated theoretically by deviding into the following three ranges of impurity concentration: (i) The concentration of impurity atom is fairly large and the impurity levels are merged into the conduction bands. Then the impurity atoms play a role of scatterers. (ii) The concentration of impurity atom becomes fairly small and the impurity levels split from the conduction bands. The energy width of this impurity band is, however, determined mainly by the translational energy of electron in this band. (iii) The concentration of impurity atom becomes very small and the width of the impurity band is determined mainly by the fluctuation of the local potential energy. In this paper we treat the first two cases. For this purpose, the general theory of transport phenomena is developped and the condition that the ordinary Boltzman–Bloch equation is applicable is given on this general theory. The result of impurity conduction given by E. M. Conwell is obtained as a limiting case of our formula. However the condition that the Conwell's formula is applicable is not satisfied in actual cases.

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