Novel closed-form resistance formulae for rectangular interconnects

Two closed-form formulae for the frequency-dependent resistance of rectangular cross-sectional inter- connects are presented. The frequency-dependent resistance R.f / of a rectangular interconnect line or a intercon- nect line with a ground plane structure is first obtained by a numerical method. Based on the strict numerical results, a novel closed-form formulaR.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 accu- rate 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 inter- connect (an interconnect with a ground plane), which is a typical structure in the on-chip or package power delivery system.