Electromagnetic Modeling and Simulation for Interconnect Structures Based on Volume-surface Integral Equations

摘要

Electromagnetic (EM) analysis for interconnect and packaging structures usually relies on the solutions of surface integral equations (SIEs) in integral equation solvers. Though the SIEs are necessary for the conductors in the structures, one has to assume a homogeneity of material for each layer of substrate if SIEs are used for the substrate. When the inhomogeneity of materials in the substrate has to be taken into account, then volume integral equations (VIEs) are indispensable. In this work, we consider the inhomogeneous materials of substrate and replace the SIEs with the VIEs to form volume-surface integral equations (VSIEs) for the entire structures. The VSIEs are solved with the method of moments (MoM) by using the Rao-Wilton-Glisson (RWG) basis function to represent the surface current on the conductors and Schaubert-Wilton-Glisson (SWG) basis function to expand the volume current inside the substrate. A numerical example is presented to demonstrate the effectiveness of the approach.