A Rigorous Solution to the Low-Frequency Breakdown in Full-Wave Finite-Element-Based Analysis of General Problems Involving Inhomogeneous Lossless/Lossy Dielectrics and Nonideal Conductors

Existing methods for solving the low-frequency breakdown problem associated with full-wave solvers rely on low-frequency approximations, which has left a number of research questions to be answered. The conductors are also generally treated as perfect conductors and the dielectric loss is not considered. In this work, a rigorous method that does not utilize low-frequency approximations is developed to eliminate the low frequency breakdown problem for the full-wave finite-element based analysis of general 3-D problems involving inhomogeneous lossless and/or lossy dielectrics and nonideal conductors. This method has been validated by the analysis of realistic on-chip circuits at frequencies as low as dc. Furthermore, it is applicable to both low and high frequencies. In this method, the frequency dependence of the solution to Maxwell´s equations is explicitly and rigorously derived from dc to high frequencies. In addition to eliminating the low-frequency breakdown, such a theoretical model of the frequency dependence can be used to understand how the field solution, in a complicated 3-D problem with both lossless/lossy inhomogeneous dielectrics and nonideal conductors, should scale with frequency and at which frequency full-wave effects become important.