Explainable integration of process and optical parameters for plasma etch depth prediction

Accurate prediction and understanding of plasma etch depth are crucial for process stability and yield in semiconductor manufacturing. While conventional machine learning approaches demonstrate the feasibility of noncontact prediction, they often lack physical interpretability and struggle with complex feature dependencies. In this study, we develop an explainable machine learning framework that integrates plasma process parameters and optical features from digital image colorimetry (DIC) to predict the remaining SiO2 thickness after plasma etching. To account for limited experimental data and measurement variability, a probabilistic treatment was applied by introducing spatial/parametric variations and input noise. Multiple regression models were systematically compared; the ensemble-based Random Forest Model (RFM) demonstrated superior performance (RMSE 1.4 nm) and greater robustness against multicollinearity than linear approaches. To interpret model behavior, SHapley Additive exPlanations (SHAP) analysis was applied, bridging the gap between data-driven predictions and plasma physics. Our analysis reveals that radio frequency power is the most influential parameter, while the low importance of gas flow rate indicates a surface-reaction-rate limited regime. Furthermore, DIC-derived features act as a high-resolution physical proxy for thin-film interference, providing complementary information to process parameters. Beyond accuracy, this framework establishes a physically meaningful correspondence between model-derived importance and underlying etching mechanisms. This approach provides a foundation for noninvasive, interpretable, and real-time process monitoring, enhancing transparency and control in semiconductor fabrication. To facilitate reproducibility, the experimental dataset is made publicly available.