Simulation of substrate currents

Recently a new approach was presented to determine the high-frequency response of on-chip passive components and interconnects. The method solves the electric scalar and magnetic vector potentials in a prescribed gauge. The latter one is included by introducing an additional independent scalar field, whose field equation needs to be solved. This additional field is a mathematical aid that allows for the construction of a gauge-conditioned, regular matrix representation of the curl-curl operator acting on edge elements. This paper reports on the convergence properties of the new method and shows the first results of this new calculation scheme for VLSI-based structures at high frequencies. The high-frequent behavior of the substrate current, the skin effect and current crowding is evaluated.