The reduction of critical dimensions in transistor scaling means that a severe bottleneck arises from the lowest levels of device interconnects. Copper is currently used as an interconnect metal, but requires separate barrier, to prevent Cu diffusion, and liner, to promote Cu deposition, materials. Advanced interconnect technology will require coating of very high aspect ratio trench structures which means that the copper barrier + liner stack should take up only a very small volume of the trench to maintain the low copper resistivity. The current industry standard for Cu diffusion barriers is TaN and Ru is a widely used liner. In this paper we use first principles density functional theory (DFT) computations to explore in detail the interaction of Cu atoms at models of TaN, Ru and combined TaN/Ru barrier/liner materials. This model allows us to explore the role of these materials in Cu adsorption and diffusion (over the surface and into the bulk) at the very early stage of Cu film growth. As a benchmark we studied the behaviour of Cu and Ru adatoms at the low index surfaces of ε-TaN, and the interaction of Cu adatoms with the (0 0 1) surface of hexagonal Ru. These results confirm the barrier and liner properties of TaN and Ru, respectively, while also highlighting the weaknesses of both materials. We then investigate the adsorption and diffusion of Cu adatoms at Ru-passivated and Ru-doped ε-TaN(1 1 0) surfaces. Ru passivated TaN enhances the binding of Cu adatoms compared to the bare TaN and Ru surfaces. On the other hand, the activation energy for Cu diffusion at the Ru passivated TaN surface is lower than that on the bare TaN surface which may promote Cu agglomeration. For Ru-doped TaN we find a decrease in Cu binding energy. In addition, we find favourable migration of the Cu adatoms toward the doped Ru atom, compared with unfavourable migration of Cu away from the Ru site, into the bulk. This suggests that Ru doping sites on the TaN surface can act as nucleation points for Cu growth with high activation energies for agglomeration and can promote electroplating of Cu. Therefore we propose Ru-doped TaN as a candidate for a combined barrier/liner material which will have reduced thickness compared to individual barrier/liner material stacks.