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

Abstract

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 rr at random grain boundaries, which is relatively small, rr = 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 rr = 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 ρo λ × rr/(1 − rr), where ρo 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 < rr.