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Quantum theory of electronic properties in doped semiconductors by an extension of the method of the bent-band theory.

A quantum theory of the electronic states in doped semiconductors is given on the basis of the Green's-function formalism by an extension of the bent-band theory. This semiclassical theory neglects all quantum correction terms for the ease of summing up all terms of multisite and multiple Born scatterings and therefore gives a poor explanation of impurity band tails observed in heavily doped semiconductors. The present theory includes quantum correction terms of all orders in a series expansion, and a formally exact solution is obtained for the one-particle Green's function by an extension of the method developed previously for the bent-band model. By picking up dominant terms for practical calculation, it is shown that the present theory gives a better explanation of observed band tails but a worse explanation of observed low-temperature conductivities than the bent-band theory. For obtaining a good explanation of the conductivities, it is assumed that there are localized levels with degeneracy unity at energies below some value. By also taking into account the exchange effect, experimental data of both the density of states and the low-temperature conductivity are shown to be well explained by the present theory.