Closed-form expressions for the line parameters of co-planar on-chip interconnects on lossy silicon substrates

This paper describes a complete modeling methodology for obtaining closed-form expressions for the frequency-dependent R, L, G, C line parameters of coplanar-type on-chip interconnects on lossy silicon substrates. The frequency-dependent series impedance parameters are obtained using a complex image method to take into account the effects of eddy-currents in the substrate. The frequency-dependent shunt admittance parameters are derived in terms of low- and high-frequency asymptotic static solutions of the equivalent circuit model combined with the complex image method. The proposed closed-from expressions are shown to be in good agreement with full-wave electromagnetic solutions and measurement data.