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

Yazan Almaetah,Kamal Alalul,D. Santos

Published 2026 in 2026 Pan Pacific Strategic Electronics Symposium (Pan Pacific)

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 Arrheniusbased 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 $60-90^{\circ} \mathrm{C}$ 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 ($\Delta$ AIC $>3000$ vs. baseline). Parameters including an activation energy ($\sim 22 ~\text{kJ} / \text{mol}$, 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 PIML 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 temperaturehumidity 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 ($\mathrm{R}^{2} \approx 0.986$ in grouped cross-validation) and generalized well to external datasets at 175° C when anchored by the physicsbased 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.

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