Analytical Expressions for High-Frequency VLSI Interconnect Impedance Extraction in the Presence of a Multilayer Conductive Substrate
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.
vlsi interconnect impedance substrate green's function high frequency magnetic dipole parasitic extraction