Figure shows that the binding energies of Cu on W-doped TaN are weaker than those on Co-doped TaN. We also observe stronger Cu-Cu interactions compared to Co-doped TaN. The Cu-Cu interaction energies are strongest for the rhombus structures on all but the W 25 surface. This is most likely due to the difference in the shape of the rhombus on W 25 which upon relaxation, resembles the line configuration and thus has fewer interactions between the Cu atoms. The tetrahedral configuration has a favourable adsorption energy on all of the surfaces. On W-doped surfaces, the Cu-substrate and Cu-Cu interaction energies are competitive, while on Co-doped surfaces the Cu-substrate interaction is stronger than the Cu-Cu interaction. Although the tetrahedron is 3D, as the film grows, further tetrahedrons could join into a 2D film, based on this relationship between Cu-substrate and Cu-Cu interaction energies. On the W 50-F and W 100 surfaces where the 2D rhombus is most favourable, a 2D film could form based on this preference, as the Cu-substrate interactions remain favourable despite the strong Cu-Cu interaction energy. Additionally, the W 25 surface may promote wetting, as this is the only surface where all geometries have a Cu-substrate interaction that is stronger than the Cu-Cu interaction. Based entirely on the competition between Cu-substrate and Cu-Cu interaction Cu should wet on this surface. However, the overall binding energy of Cu on this surface is weaker than that computed for Cu on TaN (see reference ). Given that Cu does not wet on TaN, but has a stronger adhesion compared to W 25 , it is not possible to make a conclusive prediction with these models based on the computed adsorption energies and structures alone. In contrast, the Cusubstrate interaction is more favourable than the Cu-Cu interaction energy for all structures on Co-doped surfaces.