Closed-form expressions for the series impedance parameters of on-chip interconnects on multilayer silicon substrates

This paper presents accurate closed-form expressions for the frequency-dependent series impedance parameters of on-chip interconnects over general multilayer conductive silicon substrates. The closed-form expressions are obtained from a generalized complex image approach combined with a surface impedance formulation that takes into account the effects of the distributed eddy currents in the multilayer conductive substrate. Results for single and coupled microstrips on multilayer conductive substrates are shown over a broadband frequency range of 20 GHz and compared with full-wave electromagnetic solutions. It is demonstrated that a thin, heavily-doped channel-stop layer may contribute significantly to the series resistance at higher frequencies. The new approach is further validated for a coplanar waveguide interconnect by comparison with measurement data.