Warpage prediction and optimization in ultra-thin fan-out panel-level packaging substrates via equivalent CTE correction and multi-layer shell element modeling

To address the critical challenge of insufficient prediction accuracy for thermal stress-induced warpage in ultra-thin fan-out panel-level packaging (FOPLP) substrates, this study proposes a composite simulation methodology integrating curing shrinkage effects and coefficient of thermal expansion (CTE) matching optimization. Through Finite Element Analysis combined with multi-layer shell element modeling, the influence of curing shrinkage on residual stress distribution was systematically investigated. A novel approach was developed by equivalently incorporating curing shrinkage as a CTE correction term, enabling the construction of a high-fidelity thermo-mechanical coupling simulation model. The results demonstrate that optimizing CTE match between BT/PP substrates and copper interconnections significantly mitigates interfacial thermal stress concentration, reducing warpage deformation. After incorporating curing shrinkage effects, the relative error between simulation and experimental measurements decreased from 27.6% to 10.6%. Further analysis reveals that the low-modulus characteristic of interlayer materials (e.g., PP) enables stress relaxation through localized plastic deformation, synergizing with CTE matching to achieve warpage control. This work establishes an efficient simulation framework of “Equivalent CTE Correction and Multi-layered Shell Element” for ultra-thin FOPLP substrates. The proposed CTE-modulus synergistic optimization strategy provides theoretical guidance for high-reliability packaging structural design, demonstrating significant engineering applicability.