First-principles prediction of electron grain boundary scattering in fcc metals

The electron reflection probability r at symmetric twin boundaries sigma 3, sigma 5, sigma 9, and sigma 11 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 rho(o)lambda x r(r)/(1 - r(r)), where rho(o) and lambda 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). Published under an exclusive license by AIP Publishing.

Automated summary

The electron reflection probability at symmetric twin boundaries in eight face-centered cubic (fcc) metals was predicted from first principles. The results showed that the reflection probability increases as the interplanar distance decreases. An extrapolation scheme was proposed to estimate the reflection probability at random grain boundaries. It was found that Cu, Ag, and Au have relatively small reflection probabilities due to their nearly spherical Fermi surfaces, while Al, Ca, Ni, Rh, and Ir have approximately two times higher probabilities. The resistivity of metals with randomly oriented grains was found to be proportional to the bulk resistivity, electron mean free path, and reflection probability. Cu had the lowest resistivity, suggesting that other fcc metals have higher resistivity in the limit of small randomly oriented grains. Therefore, the conductivity benefit of replacement metals for narrow Cu interconnect lines can only be achieved if the grains are larger than the linewidth or exhibit symmetric orientation relationships.