Electromagnetic Modeling of Packaging Structures With Lossy Interconnects Based on Two-Region Surface Integral Equations

Abstract

Accurate electromagnetic (EM) modeling for packaging structures with lossy interconnects requires to consider the finite conductivity of the conducting interconnects. In the integral equation approach, the conducting loss is usually accounted for through an approximate surface impedance when the skin depth of current is small, but this approximation may not be valid for large skin depth caused by low frequencies or small conductivities. In this paper, we treat the lossy interconnects as dielectric-like media and use the two-region electric field integral equations (EFIEs) to characterize the EM feature of the interconnects. The EFIEs are solved with the method of moments in which the Rao-Wilton-Glisson (RWG) basis function and dual basis function (DBF) are used to represent the electric and magnetic current densities, respectively. The joint use of RWG and DBF can remove the need of wisely formulating integral equations and selecting testing schemes and also alleviate the low-frequency effect in a wideband modeling for multiscale interconnect structures. Numerical examples are presented to demonstrate the approach and its robustness has been verified.