Electrical Resistivity of a Thin Metallic Film

TL;DR

This paper investigates how boundary conditions affect the electrical resistivity of thin metallic films, showing that resistivity varies with boundary setup and scales inversely with film thickness, supported by theoretical and computational methods.

Contribution

It demonstrates that boundary conditions significantly influence thin film resistivity, combining free-electron model calculations with ab initio relativistic computations.

Findings

Resistivity is zero for free-standing films at low temperature.

Resistivity is nonzero when films are sandwiched between materials.

Resistivity scales inversely with the number of monolayers.

Abstract

The electrical resistivity of a pure sample of a thin metallic film is found to depend on the boundary conditions. This conclusion is supported by a free-electron model calculation and confirmed by an ab initio relativistic Korringa-Kohn-Rostoker computation. The low-temperature resistivity is found to be zero for a free-standing film (reflecting boundary conditions) but nonzero when the film is sandwiched between two semi-infinite samples of the same material (outgoing boundary conditions). In the latter case, this resistivity scales inversely with the number of monolayers and is due to the background diffusive scattering by a finite lattice.