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 presented. The model includes the frequency-dependent distribution of the current on the silicon substrate (the substrate skin effect). From this model, simple formulas for accurate calculation of the frequency dependent distributed mutual inductance and the associated series mutual resistance of coupled interconnects on a silicon substrate are derived. The validity of the proposed formulas has been checked by comparison with 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 be well modeled for accurate prediction of the resistance and inductance over the whole frequency range.