A unified finite-element solution from zero frequency to microwave frequencies for full-wave modeling of large-scale three-dimensional on-chip interconnect structures

It has been observed that a full-wave finite-element-based solution breaks down at low frequencies. This hinders its application to on-chip problems in which broadband modeling from DC to microwave frequencies is required. Although a static formulation and a full-wave formulation can be stitched together to solve this problem, it is cumbersome to implement both static and full-wave solvers and make transitions between these two when necessary. In this work, a unified finite-element solution from zero frequency to microwave frequencies is developed for full-wave modeling of large-scale three-dimensional on-chip interconnect structures. In this solution, a single full-wave formulation is used. No switching to a static formulation is needed at low frequencies. Numerical and experimental results demonstrate its validity.