Purpose The surface tension of Sn-based lead-free solders plays a critical role in determining their service performance in electronic packaging. Traditional experimental measurements are constrained by high cost, complex procedures and large data variability, while conventional theoretical models cannot fully characterize the complex nonlinear relationships between surface tension and its influencing factors. This study aims to develop a machine learning-based prediction method for the surface tension of Sn-based lead-free solders, providing reliable support for alloy composition optimization and industrial application. Design/methodology/approach A data set containing 169 groups of experimentally measured surface tension values was established from published literature. After preprocessing, the data set showed no missing values or outliers despite relatively uneven distribution, indicating satisfactory integrity suitable for small-sample machine learning modeling. Three machine learning algorithms, random forest (RF), support vector regression (SVR) and neural network (NN) were adopted and compared for surface tension prediction. Furthermore, an integrated hybrid model combining the three algorithms was constructed. Model performance was evaluated using mean squared error, root mean squared error, mean absolute error, coefficient of determination (R²) and analysis of variance. Findings Among the individual models, RF outperformed both SVR and NN. The proposed integrated hybrid model achieved significantly improved prediction accuracy, with a coefficient of determination R² up to 0.9437. Feature importance analysis and Pearson correlation coefficient analysis revealed that atomic volume and alloy composition are the dominant factors affecting the surface tension of liquid solders. Meanwhile, synergistic effects, including temperature, composition interactions and the correlation between atomic volume and electron density, exert notable influences on surface tension. Additionally, a simple and practical prediction equation was derived for convenient estimation of the surface tension of Sn-based solders. Originality/value This study systematically investigates the machine learning-based prediction of surface tension for Sn-based lead-free solders, proposing effective prediction models and a practical empirical equation. It provides important theoretical guidance for the compositional design of lead-free solders and the optimization of soldering processes, thereby promoting the development and industrial application of high-performance lead-free solder materials.
Min Wu (Tue,) studied this question.