Machine learning-driven hardness modeling and interpretable analysis of constitutive characteristics for thin copper films

Purpose Copper (Cu) thin films have been widely studied and applied in microelectronic devices due to their low resistivity, high melting point, good adhesion to various substrates and low electron mobility. In this paper, a complete workflow for machine learning (ML)-based hardness prediction of Cu thin films is proposed. This work effectively captures the nonlinear relationships between the physical properties such as elastic modulus, externally applied pressure, displacement and grain size of Cu thin films. Design/methodology/approach Four models – random forest (RF), extreme gradient boosting (XGBoost), K-nearest neighbors and gradient boosting decision tree – were established. In order to improve the prediction accuracy of the models, the particle swarm optimization algorithm was employed. Findings The R2 of all four models was greater than 0.85, the mean absolute error (MAE) was less than 0.16 and the root mean square error (RMSE) was less than 0.1. The XGBoost model after optimization demonstrated the best performance, attaining a 91% hit rate on the independent test set, with MAE and RMSE values of 0.0743 and 0.1227, respectively. Research limitations/implications The conventional approach for fabricating Cu thin films relies on traditional experimental methods, which often entail prolonged experimental periods and elevated time costs. Practical implications ML methods can simultaneously learn from existing data and predict the hardness of Cu thin films, thereby reducing experimental and time costs while maintaining predictive accuracy. Originality/value Leveraging advanced ML techniques, we developed a novel PSO-XGBoost hybrid framework to unravel complex nonlinear interactions among physicochemical properties of Cu thin films. This integrated approach achieved exceptional predictive performance, yielding 91% classification accuracy on an independent test dataset with MAE of 0.0743 and RMSE of 0.1227. These metrics demonstrate significant performance improvements over conventional statistical models, underscoring the model's capability to capture intricate material behavior patterns.