Application of Embedded Stress Sensors for Third-Generation Reliability of Electronic Systems: Validation and Calibration of Mechanical Models in Fan-Out Wafer-Level Packaging

This article pioneers in-situ monitoring of stress evolution in operational advanced packaging structures through embedded silicon-based piezoresistive sensors. During four-point bending fatigue tests, we discovered a counterintuitive phenomenon: instead of exhibiting cyclic variations, the substrate stress progressively accumulated with loading cycles, eventually reaching saturation. To decipher this anomalous behavior, we developed an enhanced unified creep-plasticity constitutive model that concurrently captures nonlinear deformation mechanisms in solder joints, including simultaneous isotropic/kinematic hardening and strain-rate sensitivity. The model, validated through iterative finite element method (FEM)-sensor data convergence, revealed strain hardening in SAC305 solder joints as the dominant driver of substrate stress accumulation, with <8% deviation from experimental measurements—significantly outperforming conventional Anand models. Microstructural evidence from SEM/EDS further linked Pb particle fragmentation to accumulated inelastic deformation, bridging macro-mechanical responses to microscopic evolution. This article establishes a paradigm for reliability-by-design in next-gen packaging by synergizing embedded sensing with physics-aware constitutive modeling, addressing the critical gap in traditional approaches relying on ex-situ characterization.