Edge-based smoothed finite element method for electro-thermo-mechanical simulation of TSV structures

With continuous advancements in manufacturing processes and increasing integration density, the adoption of efficient numerical methods for multi-physics coupling simulations has become critical to enhancing packaging reliability. The edge-based smoothed finite element method (ES-FEM), a prominent member of the smoothed finite element method (S-FEM) family, synergizes meshless concepts with traditional finite element method (FEM) frameworks. It is distinguished by superior accuracy, reduced sensitivity to mesh distortion, and a softer stiffness response. In this work, we extend the ES-FEM to multi-physics coupling applications and propose a novel algorithm for electro-thermo-mechanical simulation. The efficacy of this approach is validated through electro-thermo-mechanical simulations of through-silicon via (TSV) structures in advanced packaging, demonstrating both high accuracy and computational efficiency. This advancement provides a robust and innovative tool for addressing multi-physics coupling challenges in packaging design.