Quantum transport in a semiconductor nanolayer taking into account the surface scattering of carriers

The problem concerning the electrical conductivity of a thin conducting nanolayer is solved within the quantum theory of transport. The layer thickness can be comparable to or shorter than the de Broglie wavelength of carriers. The isoenergetic surface has the form of an ellipsoid of revolution with the major axis parallel to the layer plane. Analytical equations for the conductivity-tensor components as functions of the dimensionless thickness, chemical potential, ellipticity parameter, and surface roughness are derived. The conductivity is analyzed in the limiting cases of a degenerate and nondegenerate electron gas. The results are compared with the available experimental data for a silicon layer.