Anisotropic Resistivity Size Effect in Epitaxial Mo(001) and Mo(011) Layers

Mo(001) and Mo(011) layers with thickness d = 4-400 nm are sputter-deposited onto MgO(001) and α-Al₂O₃(112¯0) substrates and their resistivity is measured in situ and ex situ at room temperature and 77 K in order to quantify the resistivity size effect. Both Mo(001) and Mo(011) layers are epitaxial single crystals and exhibit a resistivity increase with decreasing d due to electron surface scattering that is well described by the classical Fuchs and Sondheimer model. Data fitting yields room temperature effective electron mean free paths λ^*= 14.4 ± 0.3 and 11.7 ± 0.3 nm, respectively, indicating an anisotropy with a smaller resistivity size effect for the Mo(011) orientation. This is attributed to a smaller average Fermi velocity component perpendicular to (011) surfaces, causing less surface scattering and a suppressed resistivity size effect. First-principles electronic structure calculations in combination with Boltzmann transport simulations predict an orientation dependent transport with a more pronounced resistivity increase for Mo(001) than Mo(011). This is in agreement with the measurements, confirming the effect of the Fermi surface shape on the thin-film resistivity. The predicted anisotropy λ001*/λ011* = 1.57 is in reasonable agreement with 1.66 and 1.23 measured at 77 and 295 K. The overall results indicate that the resistivity size effect in Mo is relatively small, with a measured product of the bulk resistivity times the effective electron mean free path ρ_oλ^* = (7.7 ± 0.3) and (6.2 ± 0.2) × 10^-16 Ωm² for Mo(001) and Mo(011) layers. The latter value is in excellent agreement with the first-principles-predicted ρ_oλ = 5.99 × 10^-16 Ωm² and is 10% and 40% smaller than the reported measured ρ_oλ for Cu and W, respectively, indicating the promise of Mo as an alternate conductor for narrow interconnects.