­­­­­Simulation benchmarks of the PIC-MCC codes XPDP1 and VSim for helium capacitively coupled plasma discharges with spatiotemporal analysis

The particle-in-cell Monte Carlo collision (PIC-MCC) method is essential for analyzing the kinetics of low-pressure, low-temperature capacitive discharges. Our prior work has showcased the effectiveness of the XPDP1 code, a PIC-MCC simulation tool, in aligning with the VSim simulation package for low-temperature helium capacitively coupled plasma (CCP) discharges. Expanding upon these efforts, this work focuses on providing spatiotemporal insights into plasma dynamics under varying operating conditions. Four benchmark cases, characterized by distinct gas pressures, were simulated to evaluate plasma properties, including charge density, electric potential, electric field, and electron energy probability distributions. Detailed spatiotemporal two-dimensional plots highlight the evolution of key plasma parameters across RF cycles. Results indicate that increasing gas pressure leads to ionization and energy transfer becoming more localized in sheath regions, emphasizing the influence of collisional processes on plasma behavior. The dynamic interaction between charged particles and the electric field was observed to govern sheath formation, energy dissipation, and ion acceleration, offering new insights into the mechanisms driving low-pressure plasma systems. Furthermore, the study incorporates improved cross-section data by replacing the original functional cross-sections in XPDP1 with experimentally validated data from the LXCat database. This refinement enhances the accuracy of collision modeling, resulting in more precise simulation outcomes. By combining rigorous benchmarking with spatiotemporal analysis, this work establishes PIC-MCC codes as a reliable computational tool for investigating low-pressure plasma systems and provides valuable insights applicable to plasma processing and semiconductor manufacturing.