Analytic model for self and mutual frequency-dependent impedance of multiconductor interconnects on lossy silicon substrates

A highly accurate closed-form expressions for self and mutual frequency-dependent impedance (resistance and inductance per unit length) of a 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 which are needed in obtaining the desired expressions. As the result, for first time, we presents a new simple, yet surprisingly accurate closed-form. expressions which yield accurate estimates of self and mutual frequency-dependent resistance and inductance per unit length of coupled interconnects for a wide range of geometrical and technological parameters. The developed formulas describe the line impedance matrix 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.