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We propose an efficient method to accurately compute the frequency-dependent impedance of VLSI interconnects in the presence of multilayer conductive substrates. The resulting accuracy (errors less than 3%) and CPU time reduction (more than an order of magnitude) emerge from three different ingredients: a 2-D Green's function approach with the correct quasi-static limit, a modified discrete complex images approximation to the Green's function, and a continuous dipole expansion to evaluate the magnetic vector potential at the short distances that are relevant to VLSI interconnects. This approach permits the evaluation of the self-impedance and mutual-impedance of multi-conductor current loops, including substrate effects, in terms of easily computable analytical expressions that involve their relative separations and the electromagnetic parameters of the multilayer substrate.
Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on (Volume:28 , Issue: 7 )
Date of Publication: July 2009