Efficient electromagnetic analysis for interconnect and packaging structures based on volume-surface integral equations

Electromagnetic (EM) analysis for interconnect and packaging structures usually relies on the solutions of surface integral equations (SIEs) in integral equation approach. Though the SIEs are necessary for the conducting part, they require a homogeneity of material in each layer in the substrate. In this work, we use the volume integral equations (VIEs) to replace the SIEs in the substrate and combine the SIEs for the conducting parts to form volume-surface integral equations (VSIEs). The VIEs allow the inhomogeneity of materials in the substrate and provide more flexibility in EM modeling and analysis. A numerical example is presented to demonstrate the scheme.