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Ru(0001) and Co(0001) films with thickness d ranging from 5 to 300 nm are sputter deposited onto Al2O3(0001) substrates in order to quantify and compare the resistivity size effect. Both metals form epitaxial single crystal layers with their basal planes parallel to the substrate surface and exhibit a root-mean-square roughness < 0.4 nm for Ru and < 0.9 nm for Co. Transport measurements on these layers have negligible resistance contributions from roughness and grain boundary scattering which allows direct quantification of electron surface scattering. The measured resistivity ρ vs d is well described by the classical Fuchs-Sondheimer model, indicating a mean free path for transport within the basal plane of λ = 6.7 ± 0.3 nm for Ru and λ = 19.5 ± 1.0 nm for Co. Bulk Ru is 36% more resistive than Co; in contrast, Ru(0001) layers with d ≤ 25 nm are more conductive than Co(0001) layers, which is attributed to the shorter λ for Ru. The determined λ-values are utilized in combination with the Fuchs-Sondheimer and Mayadas-Shatzkes models to predict and compare the resistance of polycrystalline interconnect lines, assuming a grain boundary reflection coefficient R = 0.4 and accounting for the thinner barrier/adhesion layers available to Ru and Co metallizations. This results in predicted 10 nm half-pitch line resistances for Ru, Co, and Cu of 1.0, 2.2, and 2.1 kΩ/µm, respectively.
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Electron scattering at interfaces in epitaxial W(001)–Mo(001) multilayers
Epitaxial W–Mo multilayers are employed as a model system to demonstrate how resistivity measurements parallel to metal–metal interfaces can be used to quantify the specific interface resistance without sub-10-nm patterning that would be required for direct transport measurements across the interface. 50-nm-thick epitaxial multilayer stacks containing 2–60 individual W(001) and Mo(001) layers are deposited on MgO(001) substrates and their resistivity ρ measured as a function of superlattice period Λ at 293 and 77 K. The measured room temperature ρ increases from 7.10 to 8.62 μΩ cm with decreasing Λ = 50–1.7 nm, which is attributed to the increasing electron-interface scattering. The semiclassical Fuchs–Sondheimer model for surface scattering dramatically overestimates the resistivity, which is attributed to coherent electron transmission across multiple interfaces. A new Boltzmann transport model treats each interface as a boundary condition where electrons either scatter diffusely or traverse without momentum loss with a probability T for the first encountered interface and with 100% transmission at subsequent interfaces until they are relaxed by a bulk scattering event. This model has a single unknown parameter T, which becomes the fitting parameter for experimental data analysis, yielding a temperature-independent T = 0.8 ± 0.1 and a corresponding contact resistance at the W(001)–Mo(001) interface of 2.6 × 10−16 Ω m2.
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- Award ID(s):
- 2328906
- PAR ID:
- 10593653
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Journal of Applied Physics
- Volume:
- 136
- Issue:
- 7
- ISSN:
- 0021-8979
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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