Enhancement of the simulation speed of a particle-in-cell method combined with machine learning technology

Traditional fluid simulations rely on closure applied to the moment solutions of the Boltzmann equation. In contrast, the particle-in-cell (PIC) method tracks the motion of all charged particles to provide the advantage of computing spatiotemporal changes in the energy distribution function. However, PIC simulations suffer from relatively slow computational speeds to maintain numerical stability when coupling the particle mover and the field solver. This study aims to improve the computational efficiency of PIC simulations for plasma processing equipment in the semiconductor industry by integrating AI-based field prediction with GPU-accelerated parallelization of the particle mover. To this end, a large-scale dataset of spatiotemporal potential distributions, generated under various plasma process conditions, was constructed and used to train deep learning models. An AI-enhanced PIC simulation framework was developed to enable rapid prediction of electric potential distributions by varying RF frequencies, input powers, and gas pressures. Frequency-domain datasets were generated via fast Fourier transforms, and deep learning models predicted the corresponding steady-state potential distributions, which were subsequently reconstructed in the time domain to provide initial conditions for the PIC simulator. The proposed AI-assisted simulation approach was validated against conventional PIC models, demonstrating substantial improvements in computational speed while maintaining high accuracy.