Integration of Short-Range Interaction into Pre-Trained Graph Neural Network Potential for Molecular Dynamics Simulations for Semiconductor Process

Plasma etching is crucial in semiconductor manufacturing for achieving higher bit density devices. Energetic ions from the plasma facilitate anisotropic etching and selective reactions on the substrate, enabling the creation of high aspect ratio structures. However, the complex nature of surface-plasma interactions necessitates atomistic simulations such as molecular dynamics (MD) to investigate detailed mechanism. While classical potentials are commonly employed in MD, their scarcity and challenging parameterization limit their utility. Machine learning potentials (MLPs), trained on density functional theory (DFT) data, offer an alternative for developing suitable interatomic potentials. Nevertheless, generating training datasets via DFT calculations remains a major bottleneck in MLP development. Alternatively, pre-trained models using graph-based neural networks (GNNs), trained on materials databases, are emerging as they can represent multiple elements within a single potential and bypass extensive data set for given simulations. These models can reproduce the surface energies and reaction energies in catalytic processes, suggesting their potential for predicting etching properties. However, these machine learning–based models, unlike physics-based models, do not ensure repulsion during high-energy collisions in etching. Indeed, the absence of repulsion in dimers and between adsorbates and substrates was observed in our tests
In this study, we propose a method to integrate short-range interactions using the Ziegler-Biersack-Littmark (ZBL) potential into the pre-trained SevenNet-0 model in the SevenNet package.² We incorporated ZBL interactions into the pre-trained model by adding a ZBL potential layer and gradually reducing the contribution of the Graph Neural Network (GNN) to zero at short ranges. We adopt reduced distance coordinate to replace element-dependent cutoff distances in the smooth transition of GNN. This approach avoids the need for retraining the pre-trained model. The energy conservation of the MLP is ensured by leveraging the autograd feature of PyTorch.
We validate the ZBL-integrated pre-trained model of SevenNet-0 (SevenNet-0-ZBL) by confirming that it reproduces the short-range behavior in dimers and in the structures between CF and Si₃N₄, SiO₂ substrates well with DFT calculations. When SevenNet-0-ZBL applied to implantation simulations of amorphous Si₃N₄ with C, F, and Ar atoms at 100 eV and 500 eV, the distribution of penetration depth closely matches results from Stopping and Range of Ions in Materials (SRIM), the widely used Monte Carlo simulation code for simulating ion implantation. Furthermore, MD simulations of plasma etching Si₃N₄ and SiO₂ with CH_xF_y ions in a small cell demonstrated that the energies of structures and reactions are consistent with DFT calculations. We also present results of etching yield, surface profile, and byproduct distributions, showing that the pre-trained model is suitable for etching simulations when compared to those from an in-house MLP.³ By eliminating the need for extensive dataset development, this integration of physical principles with the pre-trained model facilitates the broader adoption of MD simulations, enabling a more detailed understanding of plasma etching processes, the exploration of new systems, and the optimization of these processes.

1. Hong, Changho, et al. "Atomistic simulation of HF etching process of amorphous Si₃N₄ using machine learning potential." ACS Applied Materials & Interfaces 16.36 (2024)
2. Park, Yutack, et al. "Scalable Parallel Algorithm for Graph Neural Network Interatomic Potentials in Molecular Dynamics Simulations." J. Chem. Theory Comput. (2024)
3. In preparation