Accurate Electromagnetic Modeling for Multiscale Interconnect Structures Based on Volume-Surface Integral Equations

Electromagnetic modeling and analysis of interconnect structures of chips can be described by integral equation approach. Traditionally, the surface integral equations (SIEs) are used to describe both the conducting part (interconnects and ground) and penetrable substrate part, but they may not be suitable for the substrate part if it includes inhomogeneous materials. The volume integral equations (VIEs) are needed for such inhomogeneous substrate and the volume-surface integral equations (VSIEs) are formed when the VIEs are coupled with the SIEs of conducting part. The VSIEs are usually solved by the method of moments (MoM) with Rao-Wilton-Glisson (RWG) basis function and Schaubert-Wilton-Glisson (SWG) basis function, but it may not be convenient when the multiscale feature of the interconnect structures is considered. This paper proposes a hybrid scheme to solve the VSIEs where the MoM is used to discretize the SIEs for the conducting part while the Nyström method is employed to discretize the VIEs for the penetrable part. The scheme has shown some merits as demonstrated by a numerical example.