Electron Scattering at Ru–TiN–Ru Interface Stacks

Electron transport across Ru-TiN–Ru interfaces is quantified using multilayers containing five 10-nm-thick Ru(0001) layers separated by TiN interlayers with nominal thicknesses <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}}$ </tex-math></inline-formula> ranging from 0.01 to 1.6 nm. The multilayers are deposited by sputtering on Al2O3(0001) substrates at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$700~^{\circ }$ </tex-math></inline-formula>C. Their resistivity parallel to the interfaces increases linearly from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho = {7.8}$ </tex-math></inline-formula>–<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${11.2}~\mu \Omega $ </tex-math></inline-formula>-cm with increasing <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}} =0$ </tex-math></inline-formula>–0.2 nm and saturates at a constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rho = 13.3~\pm ~2.5~\mu \Omega $ </tex-math></inline-formula>-cm for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}} \ge 0.4$ </tex-math></inline-formula> nm. The linear increase is attributed to electron impurity scattering at a discontinuous TiN layer while resistivity saturation is associated with parallel conduction in individual Ru layers without coherent transport between Ru layers. The data indicate a critical <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}} =0.4$ </tex-math></inline-formula>–0.6 nm above which electron transport across Ru-TiN–Ru is completely diffuse, leading to a Ru-TiN–Ru contact resistance that is proportional to the TiN layer thickness. This critical thickness is in good agreement with the onset <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}} =0.4$ </tex-math></inline-formula>–0.6 nm of a decrease in the out-of-plane X-ray coherence length, the onset at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}} =0.4$ </tex-math></inline-formula> nm of a detectable X-ray diffraction (XRD) superlattice peak, and the development of X-ray reflectivity (XRR) superlattice fringes for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${d}_{\text {TiN}} \ge 0.4$ </tex-math></inline-formula> nm.