The anisotropic size effect of the electrical resistivity of metal thin films: Tungsten

The resistivity of nanoscale metallic conductors is orientation dependent, even if the bulk resistivity is isotropic and electron scattering cross-sections are independent of momentum, surface orientation, and transport direction. This is demonstrated using a combination of electron transport measurements on epitaxial tungsten layers in combination with transport simulations based on the ab initio predicted electronic structure, showing that the primary reason for the anisotropic size effect is the non-spherical Fermi surface. Electron surface scattering causes the resistivity of epitaxial W(110) and W(001) layers measured at 295 and 77 K to increase as the layer thickness decreases from 320 to 4.5 nm. However, the resistivity is larger for W(001) than W(110) which, if describing the data with the classical Fuchs-Sondheimer model, yields an effective electron mean free path λ* for bulk electron-phonon scattering that is nearly a factor of two smaller for the 110 vs the 001-oriented layers, with λ(011)*= 1...