Electronic stability in graphene-based analysis of inter-connects

This template provides authors with most of the formatting specifications needed for preparing electronic versions of their papers. All standard paper components have been specified for three reasons: (1) ease of use when formatting individual papers, (2) automatic compliance to electronic requirements that facilitate the concurrent or later production of electronic products, and (3) conformity of style throughout a conference proceedings. Margins, column widths, line spacing, and type styles are built-in; examples of the type styles are provided throughout this document and are identified in italic type, within parentheses, following the example. Some components, such as multi-leveled equations, graphics, and tables are not prescribed, although the various table text styles are provided. The formatter will need to create these components, incorporating the applicable criteria that follow.Figure 1(a) illustrates a schematic representation of a typical RLC model for a MLGNR interconnect made of Nlayer single GNR layers of the same lengths l and widths W. In this figure, RC, RQ, and RS represent the equivalent resistances introduced by the imperfect contacts, the quantum effect, and the carriers’ scatterings, respectively. One can approximate the quantum contact resistance as RQ≈h{2e2NchNlayer}−1 [5], wherein h, e, and Nch are the Plank’s constant, electron charge, and number of conducting channels in each GNR. When the length of each GNR is greater than its carriers′ mean free path (λ), the equivalent distributed ohmic resistance (per unit length) introduced by carriers scatterings with defects, substrate-induced disorders, and phonons can be written as RS ≡ RQ / λ [6]. Also shown in Fig. 1(a) CE ≈εW/d and CQ≈{RQvF}−1 are the per unit length values of the equivalent capacitances induced by the electrostatic and quantum effects, respectively, in which ε and vF are the dielectric permittivity and the Fermi velocity in graphite, respectively. Note, in order to approximate CE, MLGNR is assumed to be a bundle of ribbons displaced from a ground plane by the same distance, d [5]. Since the separation between any two subsequent layers is much smaller than d, the effect of the electrostatic capacitances between any two subsequent GNR layers is negligible. Furthermore, LK=RQ / vF and LM ≈μd/WNlayer represent the per unit length values of the kinetic and the magnetic inductances, in presence of the ground plane, wherein μ is the graphene permeability. In a practical case, LM<