Extraction of VLSI multiconductor transmission line parameters by complementarity

Solving lossy multiconductor transmission line (MTL) equations is of fundamental importance for the design and signal integrity verification of interconnections in VLSI systems. It is well established that the critical issue is the efficient and accurate electrical characterization of the MTLs through the determination of their per-unit-length parameters. In this respect, the so-called complementarity has the potential to become a fast and accurate method for the extraction of these parameters. Besides the value of the parameters, in fact, complementarity provides rigorous error bounds for them. Despite this important feature, commercial software do not use complementarity yet, due to the fact that there are unsolved theoretical issues related to the nonstandard formulation based on the electric vector potential. Some attempts to fill this gap have been already reported. The aim of this paper is to fill this gap by introducing a general formulation based on the electric vector potential highlighting the advantages of complementarity with respect to the standard first- and second-order finite element formulations.