High-Frequency Behavior of Graphene-Based Interconnects—Part I: Impedance Modeling

This paper presents the first detailed methodology for the accurate evaluation of high-frequency impedance of graphene-based structures relevant to on-chip interconnect and inductor applications. Going beyond the simplifying assumptions of Ohm's law, the effects of electric-field variation within a mean free path and current dependency on the nonlocal electric-field are taken into account to accurately capture the high-frequency behavior of graphene ribbons (GRs). At the same time, a simplified approach that may be adopted at lower frequencies is also explained. Starting from the basic Boltzmann equation and combining with the unique dispersion relation for graphene in its hexagonal Brillouin zone, the current density across the GR structure is derived. First, a semi-infinite slab of GR is analyzed using the theory of Fourier integrals, which is followed by the development of a rigorous methodology for practical finite structures based on a self-consistent numerical calculation of the derived current density using the Green's function approach.