A rigorous method for fundamentally eliminating the low-frequency breakdown in full-wave finite-element-based analysis: Combined dielectric-conductor case

Abstract

It has been observed that a finite-element based solution of full-wave Maxwell's equations breaks down at low frequencies. Existing approaches have not rigorously solved the problem yet since they rely on low-frequency approximations. Moreover, little work has been reported for overcoming the low-frequency breakdown for realistic circuit problems in which dielectrics and non-ideal conductors coexist. In this work, we develop a rigorous method to fundamentally eliminate the low-frequency breakdown for the analysis of general problems involving both dielectrics and conductors. Its rigor has been validated by the analysis of realistic on-chip VLSI circuits at frequencies as low as DC. Furthermore, the proposed method is applicable to any frequency, hence constituting a universal solution of Maxwell's equations in a full electromagnetic spectrum. In addition, given an arbitrary integrated circuit and package structure, the proposed method can be used to quantitatively and rigorously answer critical design questions such as at which frequency full-wave effects become important and etc.