Novel closed-form resistance formulae for rectangular interconnects

Abstract

Two closed-form formulae for the frequency-dependent resistance of rectangular cross-sectional interconnects are presented. The frequency-dependent resistance R(f) of a rectangular interconnect line or a interconnect line with a ground plane structure is first obtained by a numerical method. Based on the strict numerical results, a novel closed-form formula R (f) for a rectangular interconnect alone is fitted out using the Levenberg—Marquardt method. This R(f) can be widely used for analyzing on-chip power grid IR-drop when the frequency is changing. Compared to the previously published R(f) formula for an interconnect, the formula provided here is more accurate during the frequency transition range. Also for a bigger width to thickness ratio, this formula shows greater accuracy and robustness. In addition, this paper fits out the closed-form R(f) formula for a micro-strip-like interconnect (an interconnect with a ground plane), which is a typical structure in the on-chip or package power delivery system.