Improvement of electrical-resistivity model for polycrystalline films of metals with non-spherical Fermi surface: A case for Os films

Abstract

Osmium (Os) is a hexagonal-close-packed metal with a non-spherical Fermi surface that seriously deviates from the assumption in the Mayadas-Shatzkes electrical-resistivity model (MS model) for the size effects of polycrystalline films of metals due to electron scattering by grain boundaries. In this work, we studied the resistivity of the Os films with different thicknesses as a function of temperature in the range of 20 to 296 K. The electron scattering by the surface was found to be unimportant in the contributions to the size effects of resistivity of Os films with a sufficient thickness. Based on the first-principles calculations, an analytical equation was suggested for correction to the MS model and used for fitting the temperature-dependent resistivity of the Os films. The results show that correction to the MS model is necessary and the residual resistivity caused by the defects and impurities cannot be neglected. In addition, the inhomogeneity of resistivity in the direction perpendicular to the film surface was discussed under an assumption of parallel circuits.