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 ($11\overline{2}0$) Al${}_{2}$O${}_{3}$ substrates at 520 \ifmmode^\circ\else\textdegree\fi{}C followed by postdeposition annealing in Ar-4$%$H${}_{2}$ at 850 \ifmmode^\circ\else\textdegree\fi{}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.