The influence of Fermi surface anisotropy and the charge carrier surface scattering kinetics on the electrical conductivity of a thin metal film in the view of the quantum size effect

Abstract

The electrical conductivity of a thin metal film in an alternating electric field is calculated considering the quantum size effect. The Fermi surface of the metal has the shape of an ellipsoid of rotation, the main axis of which is parallel to the plane of the film. The quantum kinetic equation obtained from the von Neumann equation (the Liouville quantum equation) is solved. The Soffer model is used as the boundary conditions for the distribution function. The dependence of the electrical conductivity on the film thickness is analyzed. A comparison is made with experimental data on the electrical conductivity of bismuth thin films.

Calculation electrical conductivity a two-dimensional electron gas of AlGaN/GaN-based transistors with high electron mobility

“…The electrical conductivity of metallic and semiconductor nanolayers was studied using quantum transfer theory in works [13,14]. The solution method the problem consists in finding the diagonal elements of the density matrix (nonequilibrium distribution function) from the solution of the Liouville equation.…”

Galvanomagnetic properties of a thin metal film considering dimensional quantization and diffuse surface scattering of electrons

“…The solution method without using boundary conditions is difficult to obtain, mathematical expressions are cumbersome and not very transparent. In [9,10], these boundary conditions were used, which took into account the charge carrier scattering on film surfaces. Surface scattering was considered using boundary conditions for the density matrix.…”

“…The method considered in [9,10] is used to calculate galvanomagnetic parameters of a thin film in this paper, using diffuse boundary conditions.…”

“…The kinetic equation, considering impurity scattering of charge carriers, will be written in a form similar to [9,10]…”

“…Equating the coefficients for p x and p y in the equation (22a), (22b), we obtain a system of differential equations for the functions c xn and c yn solution of the system (23), we use the boundary conditions(9), which, considering (15)-(17), look as follows Calculation of free electron concentration The momentum projection value can be obtained by switching from the canonical (2) to the parametric equation of the circle, considering (3): j is a parameter that varies from 0 to p 2 .The charge carrier velocity /For subsequent calculations, it is more convenient to switch from Cartesian coordinates in the momentum space ( The transition Jacobian from the Cartesian (54) to the polar coordinates is equal to ( ) e j = J m , . The charge carrier concentration (16) considering (2), (3), (15)-(18) is equal toThe charge carrier concentration in a macroscopic sample has the form[15] where n cV and e FV are the concentration and Fermi energy of electrons (holes) in a macroscopic sample.…”