Comparative analysis on Gaussian process regression and numerical model for accurate Si ₃ N ₄ wet etching rate prediction under small training data condition

Abstract This paper proposes a method for predicting the single-wafer wet etching results of Si 3 N 4 using diluted hydrofluoric acid based on Gaussian process regression (GPR) with a limited set of measured data. The GPR model achieves high predictive accuracy even under conditions not included in the training data by optimizing both the hyperparameters and the kernel function that characterizes input correlations. The experimental data are categorized into two groups according to the observed etching-rate patterns, and multiple training datasets were constructed. Models are then trained on each dataset, and their predictive stability is evaluated using two metrics: mean square error and negative log predictive density. Also, the comparison of the prediction accuracy using different types of kernel function in the model is shown. Furthermore, the proposed GPR approach is compared with conventional explicit mathematical modeling methods, thereby demonstrating the superiority of the data-driven approach in capturing the complex dependencies among etching conditions.