Physics-Informed Machine Learning for Predicting IMC Growth in SAC305 Solder Joints Under Thermal-Humidity Stress

ABSTRACT The formation and growth of intermetallic compound (IMC) layers constitute a decisive factor governing the mechanical integrity and long-term reliability of solder joints in advanced electronic packaging. While temperature-driven IMC kinetics are well-characterized through classical Arrhenius-based diffusion models, the role of relative humidity (RH) as a co-accelerating stressor has remained largely underrepresented in predictive IMC growth models. In this work, we present a hybrid Physics-Informed Machine Learning (PI-ML) framework built on experimental data collected from controlled isothermal storage tests of SAC305/Cu solder joints aged under 60-90 °C and 60-100% RH to predict IMC thickness growth. Our baseline physics model augments the classical square-root-time growth law with a humidity correction term, yielding a statistically significant improvement in model fit (ΔAIC > 3000 vs. baseline). Parameters including an activation energy (~22 kJ/mol, reflecting effective diffusion under combined thermal-humidity stress) and RH sensitivity were fitted using nonlinear regression with bootstrapped confidence intervals. We then trained a Random Forest model on the residuals of the physics prediction using interaction terms (e.g., temperature × RH), forming the core of our PI-ML architecture. Model interpretation using SHAP revealed that the initial IMC thickness (IMC 0 ) was the most influential factor in the residual model, followed by the temperature-humidity interaction (TxRH). This highlights that deviations from ideal growth are primarily driven by the starting interfacial state and coupled environmental stressors. The combined PI-ML model achieved high predictive accuracy (R 2 ≈ 0.986 in grouped cross-validation) and generalized well to external datasets at 175 °C when anchored by the physics-based Arrhenius formulation. This work demonstrates that Physics-Informed ML enables enhanced accuracy, interpretability, and extrapolation in microstructural growth prediction. The proposed framework offers a novel path toward reliability-aware material modeling and is readily extendable to other thermomechanical degradation mechanisms.