A Dielectric Approach to Impurity Conduction

Abstract

Impurity conduction is formulated on a dielectric basis. It is assumed here that the condition for the transition from insulator to metal is provided by the dielectric catastrophe which occurs through the polarizability of the neutral particle. On the basis of the Onsager formula, the contribution to the permittivity arising from the hydrogenic donor atoms is calculated assuming all catastrophic excited states merge with the continuum. The upper temperature limit of the phase transition from N discrete levels to N - 1 discrete levels can then be estimated and in this way the donor activation energy is found to be a stepwise decreasing function of both temperature and donor concentration. The dielectric theory is next extended to include screening by the conduction electrons. With an appreciable number of carriers present the hydrogen model breaks down and there is no polar contribution to the dielectric constant. Furthermore, the donor activation energy decreases smoothly and more rapidly with increasing temperature and donor concentration than it would do had only the unscreened catastrophe been operative in producing the band model.