Plasma-enhanced atomic layer deposition (PEALD) has received increasing attention in thin films for laser applications. However, owing to the diversity and wide range of process parameters, the improvement of thin film properties often requires extensive, expensive and time-consuming experiments. Back-propagation neural networks (BPNNs) with shallow structure (single or double hidden layers) have shown potential for mapping between experimental parameters and material properties, but there has yet to employ BPNNs to construct the relationship between process parameters and PEALD thin film properties. In the paper, the BPNNs with the different numbers of hidden layers are used to establish the relationship between the annealing process parameters and the properties of HfO₂ thin films (refractive index, film thickness, O/Hf ratio).

The corresponding research results about progress on the process analysis of thin films based on deep neural networks are published in High Power Laser Science and Engineering, vol. 12, Issue 2 (Min Gao, Chaoyi Yin, Jianda Shao, Meiping Zhu. Neural network modeling and prediction of HfO₂ thin film properties tuned by thermal annealing[J]. High Power Laser Science and Engineering, 2024, 12(2): 02000e21).

Figure 1. THL-BPNN model with all neurons in adjacent layers connected

Figure 1 shows the structure of the THL-BPNN network model, which includes an input layer, an implicit layer, and an output layer. The number of neurons in the input layer and output layer is determined by the number of input and output variables of the dataset, respectively, while the number of neurons in the hidden layer is preliminarily determined by the empirical formula, and then the optimal number of neurons corresponding to the current dataset is found through global traversal search.

Figure 2. 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, middle, and right 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 a perfect prediction.

For modeling, the annealing parameters, including the annealing atmosphere and temperature, are used as inputs, and measured thin film properties, including the refractive index, layer thickness, and O/Hf ratio, are used as outputs. The data is split into two categories: training set and validation set. And the THL-BPNN model obtains both the fitting accuracy and model stability. Then the performance of the THL-BPNN model is compared with that of the LR and SVR models. The poor performance of the LR model on most datasets indicates that the effect of the two input features on the dependent output variable is nonlinear. The THL-BPNN model achieves a high accuracy of no less than 0.90 on all training and validation datasets, confirming that the THL-BPNN model outperforms the SVR model, which also belongs to the category of nonlinear regression fitting. Finally, the THL-BPNN model is used to predict the LIDT of PEALD-HfO₂ and PEALD-SiO₂ thin films, and the mapping relationship between deposition parameters and PEALD-SiO₂ thin film properties is constructed. The modeling results show that the predicted values are consistent with the measured values, proving that the THL-BPNN model is a reliable predictive learning-based model. We believe that the THL-BPNN model can be used to predict the properties of different types of thin films, thereby reducing the experimental cost of process optimization.