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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First-principles prediction of electron grain boundary scattering in fcc metals
The electron reflection probability r at symmetric twin boundaries Σ3, Σ5, Σ9, and Σ11 is predicted from first principles for the eight most conductive face-centered cubic (fcc) metals. r increases with decreasing interplanar distance of atomic planes parallel to the boundary. This provides the basis for an extrapolation scheme to estimate the reflection probability r r at random grain boundaries, which is relatively small, r r = 0.28–0.39, for Cu, Ag, and Au due to their nearly spherical Fermi surfaces, but approximately two times higher for Al, Ca, Ni, Rh, and Ir with a predicted r r = 0.61–0.72. The metal resistivity in the limit of small randomly oriented grains with fixed average size is expected to be proportional to the materials benchmark quantity ρ o λ × r r /(1 − r r ), where ρ o and λ are the bulk resistivity and bulk electron mean free path, respectively. Cu has the lowest value for this quantity, indicating that all other fcc metals have a higher resistivity in the limit of small randomly oriented grains. Thus, the conductivity benefit of replacement metals for narrow Cu interconnect lines can only be realized if the grains are larger than the linewidth or exhibit symmetric orientation relationships where r < r r .
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- Award ID(s):
- 1712752
- NSF-PAR ID:
- 10349176
- Date Published:
- Journal Name:
- Applied Physics Letters
- Volume:
- 120
- Issue:
- 24
- ISSN:
- 0003-6951
- Page Range / eLocation ID:
- 241603
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1063/5.0098822
