Resistivity Size Effect in Epitaxial Rh(001) and Rh(111) Layers

Abstract

Rh(001) and Rh(111) layers with thickness d = 8-181 nm are sputter deposited onto MgO(001) and Al2O3(112̅0) substrates and their resistivity ρ measured in situ and ex situ at room temperature and 77 K in order to quantify the resistivity size effect. Rh(001) layers are epitaxial single crystals and show a resistivity increase with decreasing d that is well described with the classical Fuchs and Sondheimer model, indicating an effective electron mean free path λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> = 9.5 ± 0.8 nm at 295 K. Rh(111) layers exhibit an epitaxial microstructure with two 60°-rotated domains with a lateral width of 19 ± 2 nm, as determined from the X-ray coherence length. The grain boundaries between the domains cause a thickness-independent resistivity contribution Δρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gb</sub> = 0.74 and 0.59 μΩcm at 295 and 77 K, indicating an electron reflection coefficient R = 0.16 ± 0.03 for a boundary characterized by a 60° rotation about the (111) axis. Air exposure causes a nearly negligible (<; 6%) resistivity increase which suggests a possible reduction in the surface scattering specularity by Δp <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = -0.3 ± 0.2 during surface oxidation. The overall results yield a temperature-independent product of the bulk resistivity times the electron mean free path ρ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> λ = (4.5 ± 0.4) × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-16</sup> Ωm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . This is 1.4 times larger than previously predicted from first principles, but 33%, 55%, 63%, and 11% smaller than for Cu, W, Co, and Ru, respectively, suggesting great promise for Rh as an alternative metal for narrow interconnects.