By providing a barrier layer stack including a thin SiCN layer for enhanced adhesion, a silicon nitride layer for confining a copper-based metal region (thereby also effectively avoiding any diffusion of oxygen and moisture into the copper region), and a SiCN layer, the total relative permittivity may still be maintained at a low level, since the thickness of the first SiCN layer and of the silicon nitride layer may be moderately thin, while the relatively thick silicon carbide nitride layer provides the required high etch selectivity during a subsequent patterning process of the low-k dielectric layer.