Accurate Substrate Analysis Based on a Novel Finite Difference Method via Synchronization Method on Layered and Adaptive Meshing

In this paper, we present a finite difference method (FDM) based on layered and adaptive meshing to extract substrate resistance. To allow adaptive meshing, a novel synchronization method is introduced which expresses the potential at other points than the centroids of panels by modifying the finite difference equations. This method makes it possible to overcome the high computational cost of the FDM due to tight uniform meshing requirements while enjoying a straightforward implementation and easy handling of irregular/arbitrary substrate structures to extract the substrate coupling of integrated circuits.