Thermo-mechanical co-design of 2.5D flip-chip packages with silicon and glass interposers via finite element analysis and machine learning

By Mohammad Rafiee ^a, Farough Agin ^b , Kuldeep Kumar ^c , Ezhilan Murali ^c
a Department of Mechanical Engineering, University of Ottawa, Canada 
^b Department of Chemical and Biological Engineering, University of Ottawa, Canada 
^c School of Electrical Engineering and Computer Science, University of Ottawa, Canada

Abstract

Advanced 2.5D flip-chip packages with silicon/glass interposers may pose tightly coupled thermo-mechanical trade-offs. This work presents a simulation-driven, machine-learning-assisted co-design framework that links high-fidelity finite-element analysis (FEA) with surrogate modeling, multi-objective optimization, and decision analysis. A 3D FEA model generates 500 Latin Hypercube design points for type of analysis (thermal and reliability), spanning geometry, materials, and thermal-path variables. Four minimized objectives are considered: junction-to-ambient thermal resistance (Θ_JA) and cycle-averaged plastic strain-energy density at the corner flip- chip cu-pillar bump (ΔW_bump), C4 bump (ΔW_C4 ), and BGA (ΔW_BGA ). Tree-based regressors (Random Forest, XGBoost) achieve high test-set fidelity and drive NSGA-II to enumerate the Pareto domain. A Net Flow multi-criteria decision method (MCDM) ranks Pareto candidates to identify a champion design with balanced thermo-mechanical performance. Re-simulation of the champion in FEA confirms surrogate accuracy for dominant responses (≈4–5 % deviation for ΔW_bump and ΔW_C4) and exact agreement for Θ_JA , while revealing weak coupling between thermal and mechanical objectives—enabling partial decoupling of heat-path optimization from interconnect reliability.

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