The Application of Regression Analysis in Modeling Interconnect Resistance

Abstract

As clock frequencies exceed giga-Hertz, the skin depth in analog and digital circuits decreases heavily. The technology scaling have lead to complications that pose significant challenges to on-chip interconnect design, such as the distortion of signal pulses. One of the most important causes of pulse distortion is the frequency-dependence of conductor loss, which can be incorporated into circuit models for interconnects as frequency-dependent resistance per-unit-length. This makes accurate resistance necessary in simulation. In order to achieve high simulation efficiency, closed-form formulae are often used to represent frequencydependent resistance of interconnects. In this letter, two closed-form formulae for the frequency-dependent per-unitlength resistance of rectangular cross-sectional interconnects are presented. The frequency-dependent per-unit-length resistance of a rectangular interconnect line or an interconnect line with a ground plane structure is first obtained by the method of moments (MOM). Based on this strict numerical MOM results, the novel closed-form formulae for a rectangular interconnect are fitted out using the regression analysis. The formulae can be widely used for analyzing on-chip power grid IR-drop when the frequency is changing. Compared to the previously published formulae for an interconnect, the formula provided here is more accurate during the frequency transition range. Keywordsinterconnect; resistance;Regression analysis;MOM;IC