Thermodynamic properties of hexagonal and cubic phases of ruthenium from the quasi-harmonic approximation

Ruthenium is a promising material for use in microelectronics, either as a diffusion barrier layer that prevents copper diffusion, or as a complete replacement for copper in a metallization system. Its hexagonal lattice structure has been widely studied in the literature, but there is still limited information available on the less stable face centered cubic phase. This paper presents the results of first-principles calculations on the thermodynamic properties of hexagonal and cubic phases of ruthenium using a quasi-harmonic approximation. These calculations allow us to obtain temperaturedependent thermodynamic solid body properties that take into account the thermal expansion of the crystal lattice.