Electrical Conductivity of a Thin Metal Layer Taking into Account Deviations from the Wiedemann–Franz Law

Abstract—The problem of the effect of deviation from the Wiedemann–Franz law on the electrical conductivity of a thin metal layer is solved for the first time. Admissible values of the layer thickness are limited by the dimensions at which quantum effects and the skin effect do not appear. In this case, the ratio of the layer thickness to the electron mean free path can be arbitrary. A modified kinetic equation is solved with a collision integral that takes into account the deviation of metal properties from the Wiedemann–Franz law at low temperatures. This solution takes into account the fact that for pure metals at low temperatures, electron–electron collisions are significant, in which the total momentum of the electron subsystem is preserved, and corresponding electron scattering is not isotropic. The conditions of the specular-diffuse reflection of electrons from the layer surfaces are taken as the boundary conditions of the problem. An analysis is made of the dependence of the electrical conductivity of the layer on the frequency of volumetric and surface collisions of electrons, the specularity coefficients of its surfaces, and the parameter describing the deviation from the Wiedemann–Franz law. Correspondence of the obtained theoretical results of calculating the electrical conductivity of a thin metal layer to an alternative method of calculation in the absence of a correction to the refined experimental law is shown.