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

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 ( Δ W bump ), C4 bump ( Δ W C 4 ), and BGA ( Δ W 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 Δ W bump and Δ W C 4 ) 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.