The degenerate semiconductor thin films II—The longitudinal electrical conductivity

Abstract

A quantum theory of the longitudinal electrical conductivity of the mono-crystalline strongly degenerate semiconductor thin films is developed under some simplifying assumptions (no surface states are assumed, the effective mass of the carriers, as well as their relaxation time, are taken isotropic, constant and independent of the film thickness, the external electrical field is assumed so small that the Ohm's law may be in force, etc.). The n-type InSb films with donor concentrations 10 13–10 16 cm −3 may represent objects being most interesting in regard to the topic of the paper. In order to formulate a suitable boundary condition for the diffuse scattering of the conduction electrons on the film surface, the Wigner representation of the one-electron density matrix is taken into account. When the film thicknesses are comparable with (or smaller than) the mean interelectronic distance, then only the values of the longitudinal electrical conductivity are found seriously enough different from those obtained in frame of the semi-classical theory having been presented for metallic films by Fuchs.