High-Frequency Mutual Impedance Extraction of VLSI Interconnects In the Presence of a Multi-layer Conducting Substrate

We propose a computationally efficient method to calculate, with high accuracy, the mutual impedance between two wires in the presence of multilayer substrates, as needed for high frequency CAD applications. The resulting accuracy (errors smaller than 2%) and CPU time reduction (factors of seven) emerge from three different ingredients: a two dimensional Green's function approach with the correct quasi-static limit, a modified discrete complex image approximation to the Green's function, and a novel discrete dipole approximation to evaluate the magnetic vector potential. This approach permits the evaluation of the mutual impedance between two loops in terms of easily computable analytical expressions that involve the relative separations and the electromagnetic parameters of the multi-layer substrate. The results are valid for long wires, for any separation, and for frequencies up to 100 GHz.