The Resistivity Size Effect in Epitaxial Nb(001) and Nb(011) Layers

Epitaxial Nb(011) and Nb(001) layers are sputter deposited onto ${a}$ -plane and ${r}$ -plane sapphire substrates, respectively, and their resistivity $\rho $ measured in situ , ex situ , and at 77 K as a function of layer thickness ${d}= 4$ –400 nm. The resistivity increase with decreasing ${d}$ is independent of layer orientation and is described with the model by Fuchs and Sondheimer (FS), providing a value for the bulk electron mean free path $\lambda = {20} \pm {2}$ nm at room temperature. Exposure to air causes a 1.5-nm-thick surface oxide and an increase in $\rho $ by up to 74%, suggesting a decrease in the surface scattering specularity from ${p}_{{{1}}}= {0.9} \pm {0.1}$ at the Nb-vacuum interface to completely diffuse scattering ( ${p}_{{{1}}}= {0}$ ) at the oxidized Nb surface. Alternatively, this increase in resistance can be attributed to roughening during surface oxidation while retaining completely diffuse scattering, yielding a lower bound for the room-temperature $\lambda $ of 9.0±0.4 nm. The product of the bulk resistivity $\rho _{o}$ times $\lambda $ is temperature-independent and, depending on either choosing the roughness or the specularity interpretation, $\rho _{o}\,\,\lambda = {14}\times {10}^{{-{16}}}$ or ${30} \times {10}^{{-{16}}}\,\,\Omega \text{m}^{{{2}}}$ , respectively. These values are 3.9 and 8.5 times larger than $\rho _{o}~\lambda $ from a previous theoretical prediction, indicating a dramatic break down of the classical FS model for Nb and indicating that the resistivity size effect in Nb is considerably larger than predicted earlier. They are also larger than for W, Ru, and Co, making Nb not promising for high-conductivity narrow interconnect lines.