New closed-form formula for frequency-dependent resistance and inductance of IC interconnects on silicon substrate

A highly accurate closed-form approximation of frequency-dependent mutual impedance per unit length of lossy silicon substrate coplanar-strip IC interconnects is developed. The derivation is based on a quasi-stationary full-wave analysis and Fourier integral transformation. The derivation shows the mathematical approximations needed to obtain the desired expressions. As a result, for the first time, we present a new, simple, yet surprisingly accurate, closed-form expression which yields accurate estimates of frequency-dependent mutual resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulae describe the mutual line impedance behaviour over the whole frequency range (i.e. also in the transition region between the skin effect, slow-wave and dielectric quasi-TEM modes). The results have been compared with reported data obtained by the modified quasi-static spectral domain approach and new CAD-oriented equivalent-circuit model procedure.