Novel closed-form resistance formulae for rectangular interconnects

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.