By providing contact plugs having a lower plug portion, formed on the basis of well-established tungsten-based technologies, and an upper plug portion, which may comprise a highly conductive material such as copper or a copper alloy, a significant increase in conductivity of the contact structure may be achieved. For this purpose, after the deposition of a first dielectric layer of the inter-layer stack, a planarization process may be performed so as to allow the formation of the lower plug portions on the basis of tungsten, while, after the deposition of the second dielectric layer, a corresponding copper-based technology may be used for forming the upper plug portions of significantly enhanced conductivity.