First-principles calculation of copper impurity diffusion in hexagonal ruthenium

Ruthenium is a promising material for use in microelectronic devices as a diffusion barrier layer to prevent copper diffusion. However, there are few data on quantitative assessments of the diffusion coefficients of any impurities in hexagonal bulk Ru, which is the stable structural phase of Ru. In this work, we performed a density functional theory study of Cu impurity diffusion in bulk hexagonal Ru. Impurity diffusion coefficients are computed as a function of temperature using the «8-frequency model', which provides the relevant impurity and solvent jump frequencies and correlation factors. The effect of temperature-dependent expansion of the ruthenium lattice volume is taken into account within the quasi-harmonic approximation. The Arrhenius equation for the diffusion coefficient is D_|| = 6.12·10^-5exp (-5.01 eV/kT) m²s^-1 for diffusion within the basal plane and D_⟂= 2.18·10^-4exp (-5.11 eV/kT) m²s^-1 for diffusion between adjacent basal planes in the lattice. Our calculations serve as a foundation for a more accurate understanding of experimental data.