A pre-corrected FFT algorithm for fast electromagnetic modeling of three-dimensional integrated passives in multilayered substrates

A novel fast algorithm for accurate broadband electromagnetic analysis of 3-D passives embedded in multilayered media is presented. The electromagnetic boundary-value-problem for the interconnect layout embedded in silicon substrates is formulated in terms of Michalski-Zhang´s formulation C for the Mixed-Potential-Integral-Equation (MPIE). The MPIE is discretized using the Rao-Wilton-Glisson (RWG) basis. The numerical solution of the discretized MPIE is accelerated using a novel 3-D pre-corrected FFT (PFFT) algorithm. Unlike previously known 2.5-D versions of the algorithm that ignore vertical currents the proposed methodology accounts for 3-D features of the interconnect layout such as conductor sidewalls and vias. The low-frequency instability of MPIE is eliminated through loop-tree decomposition of the RWG basis allowing for full-wave 3D modeling from DC to multi-GHz frequencies in layered media.