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.

Resistivity scaling model for metals with conduction band anisotropy

“…Atomistic studies for extremely small nanowires with few grain boundaries with different orientations have been done [25,39,40], but require a full numerical treatment for which metal thin films with realistic grain profiles are too complicated. In recent work, Li et al introduced a phenomenological correction for conduction band anisotropy and argued that it was responsible for the sharper resistivity increase at small thicknesses for Os films [26]. Our results do not agree with this as they cannot explain an underestimation of the resistivity for small thicknesses merely based on conduction band anisotropy.…”

“…The impact is more pro-nounced in case of an isotropic collision time as compared to an isotropic mean free path and this can be understood by having a closer look at the conductivity expressions in Eqs. ( 11), ( 20) and (26). In case of an isotropic collision time, both the effective mass along the transport direction and the parameter for grain boundary scattering are renormalized w.r.t.…”

“…Recently, Li et al proposed a phenomenological correction to the Fuchs-Sondheimer model for metal thin films of Os with a nonspherical Fermi surface to explain the experimental findings [26]. In this work, we derive a model to describe resistivity scaling of imperfect metal thin films, while retaining some features of the electronic structure to capture the impact of conduction band anisotropy.…”