## 1 Introduction  
Due to their outstanding physical properties, graphene and its allotropes (carbon nanotubes (CNTs) and graphene nanoribbons (GNRs)) are the major candidates to become the silicon of the 21 st century and open the era of so-called carbon electronics [1,2]. Amongst all such applications, the low electrical resistivity, high thermal conductivity, high current carrying capability, besides other excellent mechanical properties, make graphene a serious candidate to replace conventional materials in realizing VLSI nano-interconnects [3, 4]. A carbon-based VLSI technology is not yet a pure theoretical wish, since in the last few years, the rapid progress in graphene fabrication made possible the first examples of real-world applications. The works [5, 6] present high frequency CMOS oscillators integrating CNT or GNR interconnects, whereas [7] shows the first example of a computer with PMOS transistors entirely made of CNTs. Carbon nanotubes or graphene interconnects are also successfully integrated into innovative organic transistors for flexible plastic electronics [8]. The increasing interest in carbon nano-interconnects leads to the quest for more and more accurate and reliable models, able to include all the quantum effects arising at the nanoscale. This topic has been given great attention by the recent literature, which presented several modeling approaches, like phenomenological [9] and semi-classical ones [10]. Based on such models, many papers predicted that carbon materials could outperform copper for IC on-chip interconnects and vias [11, 12, 13, 14, 15, 16]. In the typical working conditions of nano-interconnects, namely a frequency up to THz and low bias conditions, such nano-structures do not exhibit tunneling transport. Thus, the electrodynamics may be studied by using a semi-classical description of the electron transport. This leads to the derivation of a constitutive relation between the electrical field and the density of the current in the form of a generalization of the classical Ohm's law, introducing non-local interactions and dispersion. By coupling such a relation to Maxwell equations, it is possible to derive a generalized transmission line model for such nano-interconnects. This approach has been followed by the authors to model isolated metallic CNTs in [16], CNTs with arbitrary radius and chirality in [17, 18], multi-walled CNTs [19] and GNRs [20]. The semi-classical model gives results consistent with those provided by an alternative hydrodynamic model [21]. In this paper, a comprehensive and self-consistent analysis of the electrical properties of graphene is presented, with special emphasis on its application as an innovative material for nano-interconnects. The self-consistency is guaranteed by the fact that the used transport model is derived from an electrodynamical model described in terms of physically meaningful parameters. This differs from what can be obtained by means of heuristics approaches. In particular, a self-consistent model provides a clear analytical relation between the model parameters and the physical and geometrical properties of the investigated structure. The considered frequency range of applications is limited to values up to 1 THz, and the operational conditions fall into the low bias regime (the longitudinal electric field along the interconnect should be \(E_{x}<0.54\) V/\(\upmu\)m). For such cases, interband transitions are absent and non-linear effects are negligible, and thus, a simple linear transport of the conducting electrons (\(\uppi\)-electrons) may be derived based on the tight-binding model and the semi-classical Boltzmann equation. Section 2 is devoted to a brief resume of the main properties of the band structure for a graphene sheet and for a graphene nanoribbon. In Section 3, the transport model is presented, derived from a semi-classical model based on the linearized Boltzmann transport equation.