Fig. 1. THL-BPNN model with all neurons in adjacent layers connected, where x = [x₁; x₂], y₁ and h_ij represent the input, output and intermediate processing signals, respectively.

Fig. 2. Accuracy of BPNNs with one to four hidden layers based on (a) the refractive index (at 355 nm), (b) layer thickness and (c) O/Hf ratio of PEALD-HfO₂. The four columns in each subgraph represent the R² values of the model in the training and validation sets and the RMSE values in the training and validation sets, respectively. The table indicates the number of neurons in each hidden layer of each model.

Fig. 3. Measured and predicted (a)–(c) refractive index, (d)–(f) layer thickness and (g)–(i) O/Hf ratio of HfO₂ thin films. The data in the left-hand, middle and right-hand columns are predicted by the LR model, SVR model and THL-BPNN model, respectively. The blue line (with a slope of 1) serves as a guideline for perfect prediction.

Fig. 4. Correlations between properties of HfO₂ thin films used in this section. Blue indicates a negative correlation, whereas red indicates a positive correlation. Darker colors and larger circles indicate higher correlations. The numbers inside the circles indicate the corresponding correlation coefficients of the two features.

Fig. 5. Comparison of measured and predicted LIDT values on the (a) training set and (b) validation set.

Fig. 6. Comparison of measured and predicted values of (a) the refractive index (at 355 nm), (b) the layer thickness and (c) the O/Si ratio for SiO₂ thin films in the validation set.

Table 1. Datasets for property prediction of HfO₂ and SiO₂ thin films.

Table 2. Datasets for LIDT prediction of HfO₂ and SiO₂ thin films.

Table 3. Evaluation of the LR, SVR and THL-BPNN models.

Table 4. Evaluation of the THL-BPNN model for SiO₂ thin film properties.