An Efficient Electromagnetic Computation Method for High-Density Multilayer Interconnects in Integrated Chips

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An improved method of moments (MoM) based on the augmented electric-field integral equation (A-EFIE) is proposed for efficient electromagnetic (EM) simulation of multilayer interconnects. The A-EFIE overcomes the low-frequency breakdown problem of the electric-field integral equation (EFIE), meeting the EM simulation requirements for interconnects from DC to sub-THz frequencies. The layered medium Green's function (LMGF) is integrated into the A-EFIE formulation, extending the proposed method to the electromagnetic simulation of high-density multilayer interconnects embedded in dielectric substrates. This work proposes a novel integration of the LMGF into the A-EFIE formulation for lossy conductors, in which both exterior and interior problems are considered. By accurately characterizing conductor losses and skin effects, the proposed method is well-suited for broadband EM simulation of multilayer interconnects in advanced packaging. Compared with the FEM implementation in the HFSS software, the proposed LMGF-based method eliminates the need for meshing stratified dielectric structures in integrated circuits, achieving at least two orders of magnitude reduction in mesh elements. Numerical examples are conducted on different chip-level multilayer interconnects to validate the effectiveness and efficiencies of the proposed method.