Parallel layered-medium integral-equation methods for electromagnetic analysis of high-fidelity full-size electronic package models

A parallel iterative layered-medium integral-equation solver is presented for fast and scalable network parameter extraction of high-fidelity full-size electronic package models. The solver relies on a 2-D fast-Fourier-transform (FFT)-based acceleration method, a sparse preconditioner, and a scalable parallelization method to reduce the computational costs as well as advanced lumped-port models to improve the accuracy of network parameter extraction. To be able to analyze full-size electronic package models, the solver is integrated to a reduced-domain layered-medium integral-equation formulation that models large portions of planar conductors using layered medium Green’s functions. To demonstrate the method’s efficiency and applicability to complex electronic packaging problems, various package models with increasingly higher fidelities and larger sizes are analyzed, their numerical results are validated, and the costs are quantified. The studied models include a full-size package model with 304 differential-pair traces that fan out on two different routing layers that carry signals from the chip to the board through 10 metallization layers; the model contains 3127 plated-through-hole core-layer vias, 1216 stacked microvias connected to the traces, and ~3×10⁴ single-layer microvias that stitch metallization layers. The proposed parallel layered-medium integral-equation methods reduced the number of unknowns for the full-wave analysis of this model to only ~4.9×10⁶; using 1536 processes on a petascale cluster, the methods required a wall clock time of ̃ 0.58 seconds per iteration, ~28 minutes per excitation, and ~560 hours per frequency to extract the 1216-port network parameters.