Electron mean free path of tungsten and the electrical resistivity of epitaxial (110) tungsten films

Abstract

This work describes a study of the classical electrical resistivity size effect in tungsten. The important length scale for this size effect is the isotropic average electron mean free path (EMFP), which was determined to be 19.1 nm for W at 293 K by employing density functional theory. To explore the size effect experimentally, (110) oriented epitaxial W films with thicknesses ranging from 9.8 to 299.7 nm were prepared by sputter deposition onto (1120) Al 2 O 3 substrates at 520 • C followed by postdeposition annealing in Ar-4%H 2 at 850 • C. Film resistivities were measured at room temperature and at liquid He temperature. The Fuchs-Sondheimer (FS) surface scattering model with a low specularity parameter (p = 0.11) was shown to provide a good description of the film resistivity as a function of film thickness. Further, it is shown that an upper bound to the EMFP cannot be established by fitting resistivity data to the FS model, whereas a lower bound can be assessed.

Crystallographic anisotropy of the resistivity size effect in single crystal tungsten nanowires

“…The wire-widths were in the range of 15–451 nm, with the anisotropy of the size effect observed for wire-widths below ~50 nm, i.e., at widths comparable to the directionally averaged electron mean free path of 19.1 nm for W 12. A reduction in incremental resistivity of a factor of two was observed at the width of approximately 15 nm for the <111> orientation compared with other orientations.…”

From solid solutions to fully phase separated interpenetrating networks in sputter deposited “immiscible” W–Cu thin films

“…in a combined Fuchs-Sondheimer and Mayadas-Shatzkes formulation with electron mean free path k 0 , film thickness h, surface specularity factor p, grain size D and grain boundary (GB) reflection parameter R. It should be noted that p and R values are reported with highly inconsistent magnitudes in literature [60][61][62]. Nevertheless, several microstructural regimes can be distinguished and related to the individual contributions.…”

“…Highest resistivity values were determined between 50 and 75 at.% W. These high resistivities can be attributed to two scattering effects. The refined microstructure of the co-sputtered as-deposited state results in extended scattering at grain boundaries as grain size decreases below k 0 (39 nm for Cu [61], 19.1 nm for W [62]). Furthermore, scattering occurs at impurities.…”

Growth, structure and properties of magnetron sputtered ultra-thin WTi films

“…Hence, size-dependent resistivity is detected. Diffuse scattering becomes apparent here for ultra-thin films with thickness (9.5 ± 0.5 nm) that is lower than electron mean path (estimated at 19.1 nm for W films [12]). A slight increase of resistivity is measured as working pressure increases.…”