New analytic expressions for mutual inductance and resistance of coupled interconnects on lossy silicon substrate

A new analytic model for series mutual impedance of coupled interconnects on lossy silicon substrate is presenteded. The model includes the frequency-dependent distribution of the current on the silicon substrate (the substrate skin effect). From this model easy formulas for the accurate calculation of the frequency dependent distributed mutual inductance and the associated series mutual resistance of coupled interconnects on silicon substrate are derived. The validity of the proposed formulas has been checked by a comparison with the equivalent-circuit model data and corresponding full wave solutions. Through this work, it is found that the effect of the semiconducting substrate return path on the transmission behaviour of the interconnects must to be well modeled for the accurate prediction of the resistance and inductance over the whole frequency range.