Importance of Volume Discretization of Single and Coupled Interconnects

This paper presents figures of merit and error formulae to determine which interconnects require volume discretization in the GHZ range. Most of the previous work focused mainly on efficient modeling of volume discretized interconnects using several integration and reduction techniques. However, little work has been done to characterize when using the simple DC model has an impact on critical circuit metrics such as delay, impedance etc. Most of the previous work simply assumes that when skin depth becomes smaller than the wire cross section dimensions, volume discretization becomes essential. However, careful analysis in this paper shows that this assumption is invalid and a figure of merit is derived to characterize when volume discretization of single and coupled wires is required. This derived figure of merit is shown to depend solely on the interconnect dimensions and spacing and is independent of the type of the materials used or technology scaling