Effective electron mean free path in TiN(001)

Abstract

The measured resistivity ρ of smooth stoichiometric epitaxial TiN(001) is 13 and 3.0 μΩ cm at 298 and 77 K for bulk layers but is 8 and 25 times higher when the layer thickness d is reduced to 2 nm. The increase in ρ with decreasing d is attributed to diffuse electron-surface scattering and is well described by the classical Fuchs-Sondheimer (F-S) model. This is unexpected because the F-S model is based on the nearly free electron model, while TiN exhibits a highly non-spherical Fermi surface and three bands crossing the Fermi-level. The measured room temperature effective electron mean free path λ for bulk scattering is 45 ± 4 nm, which is an order of magnitude larger than the free-electron prediction. This deviation is attributed to ∼93% of charge transport in TiN being due to two slightly filled bands which represent only 4% of conduction electrons. The F-S model is applicable to TiN because these two bands are nearly parabolic and nearly degenerate, yielding a single value for λ, which is estimated based on the published band structure to be 49 nm, in excellent agreement with the experimental 45 nm. These results demonstrate that the F-S model is applicable to metals with non-spherical Fermi-surfaces as long as the charge transport is dominated by a single (or multiple degenerate) band(s).