Interconnect wires are major technology components of modern high-speed integrated circuits. To overcome the latter's degradation caused by increasing miniaturization, there is an urgent need to look for alternative technologies. Since carbon based materials generate promising results, this paper focuses on describing the electrical properties of carbon based materials, in particular the use of graphene nanoribbon (GNR) as well as trilayer graphene nanoribbon (TGN) as next generation interconnects: since the conductance of TGN is less affected by external fields compared to GNR, it forms an improved choice for on-chip interconnects. The conductance model of TGN is derived and discussed in detail.