Characterization and modeling of multiple coupled on-chip interconnects onsilicon substrate

A quasi-magnetostatic integral formulation approach is applied to compute t he frequency-dependent series resistance and inductance parameters for coup led microstrip on-chip interconnects on silicon. The method is based on the simultaneous discretization of interconnect conductors and silicon substra te, and takes into account the substrate skin effect (eddy currents), as we ll as the conductor skin and proximity effects. An efficient equivalent-cir cuit model based on "effective substrate current loops" is extracted from t he frequency-dependent R and L parameters for a class of coupled microstrip -type on-chip interconnects. The frequency response of the proposed model c onsisting of only passive R, L elements agrees well with the broad-band cha racteristics of the distributed resistance and inductance parameters of the interconnect obtained by electromagnetic simulation. Model extraction resu lts are presented for asymmetric coupled interconnects to demonstrate the p roposed method.