Accurate analytic expressions for frequency-dependent inductance and resistance of single on-chip interconnects on conductive silicon substrate

Abstract

Simple and accurate closed-form expressions to calculate frequency-dependent distributed inductance and associated distributed series resistance per-unit-length of single on-chip interconnects on a lossy silicon substrate are presented. The analytic formulas for the frequency-dependent series impedance parameters are obtained using a closed-form integration method and the vector magnetic potential equation. It is shown that the calculated frequency-dependent inductance L( f) and resistance R( f) per-unit-length are in good agreement with the results obtained from rigorous full wave solutions and CAD-oriented equivalent-circuit modeling approach.