Interconnect analysis: From 3-D structures to circuit models

A combination of discretized integral formulations, sparsification techniques, and krylov-subspace based model-order reduction are described leading to robust tools for automatic generation of macromodels that represented the distributed RLC effects in 3-D interconnect. Three challenges are described based on these new method which include handling the non-ideal semiconductor substrate, picking the expansion points for model-order reduction, and handling the massively coupled problem. Computational results are presented to address the problems cited.