A theoretical model of the high-frequency electrical conductivity of a semiconductor nanolayer is constructed within the framework of the quantum theory of transport phenomena. The layer thickness can be comparable to and less than the de Broglie wavelength of charge carriers. The isoenergy surface has the shape of an ellipsoid of revolution, the main axis of which is parallel to the layer plane. Analytical expressions are derived for the conductivity tensor components as a function of dimensionless thickness, electric field frequency, chemical potential, ellipticity parameter, and surface roughness parameters. The dependences of the longitudinal and transverse conductivity tensor components on the above parameters are analyzed. The results are compared for the cases of a degenerate and non-degenerate electron gas. A comparative analysis of theoretical calculations with known experimental data for a silicon film is performed.
The task about calculation of high-frequency conductivity and Hall constant of a thin semiconductor film is solved by the kinetic method. This film is placed in transverse stationary magnetic field and longitudinal alternative electric field. The ratio between film thickness and mean free path of charge carriers is assumed to be arbitrary. Skin effect is negligible. The diffuse-specular mechanism of charge carriers scattering from film surfaces is considered in the view of equal mirrority coefficients of the upper and lower film surfaces. The dependences of non-dimensional conductivity and Hall constant on non-dimensional parameters: electric field frequency, magnetic field induction and film thickness are investigated. The comparative analysis of obtained results with the calculations for the case of a metal film are made.
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