Efficient Electromagnetic Analysis for Interconnect and Packaging Structures Using Dual Basis Function in the Method of Moments

Abstract

Efficient electromagnetic analysis for interconnect and packaging structures is developed by solving surface integral equations (SIEs) with the method of moments. Since the SIEs include both electric and magnetic currents as unknowns on the interfaces of dielectric materials, two basis functions are needed to represent them. The robust Rao-Wilton-Glisson (RWG) basis function is a natural choice to represent the electric current, but how one represents the magnetic current is less obvious. One may employ n̂ × RWG basis function, where n̂ is a unit normal vector on the material interfaces or the RWG basis function again to represent the magnetic current, but both choices are not ideal. In this paper, we use the dual basis function proposed by Chen and Wilton in 1990 to represent the magnetic current, and find that it is robust though complicated in implementation. The interconnect and packaging analysis requires extra cares on numerical procedure because of the multiscale features and low-frequency effects of the structures. With the use of RWG and dual basis functions together, both electric and magnetic currents are well represented and the system matrix is well conditioned. Therefore, the low-frequency effects are alleviated and the poor mesh quality can be sustained without special treatment. Numerical examples for typical structures are presented to illustrate the merits of the scheme.