RF Hollow Cathode Discharge Characterization using PIC-MCC Simulation and Reduced Order Model Development

Radio-frequency (RF) hollow cathode discharges (HCD) at low to moderate pressures have gained significance for advanced plasma processes in the semiconductor industry. HCDs form in cylindrical cavities in the cathode, and one can use an array of such cavities to create large area HCDs. The plasma in the hollow cavities can become more intense due to the hollow cathode effect (HCE) under certain conditions. A single hollow cathode hole is modeled using Particle-in-Cell/Monte Carlo Collision simulation. In this model, using charge density of particles, Poisson equation is solved for electric potential, which yields the electric field. Using the electric field, all charged particles are moved. The PIC code considers particle collisions using a Monte Carlo model. Statistics of these collisions are used to determine electron energy dissipation in the plasma. RF hollow cathode behavior is simulated for different hole size, pressure and RF voltage. The plasma penetrates inside the hollow cathode hole with increase in pressure. With increase in hole size, plasma penetrates further into the hole. At high RF voltage, plasma density enhancement is limited as plasma spreads over larger volume. With increase in frequency RF sheath heating, hence plasma density increases. A higher secondary electron emission coefficient increases plasma density as well. The synergistic effect of RF sheath heating and secondary electron acceleration on HCD has been explored. Additionally, a reduced order modeling framework is developed based on neural network using plasma model parameters from a RF parallel plate reactor. Different methodologies have been explored in selecting and preprocessing physical data to train and validate the neural network. The prediction of trained neural network compares well with that of the underlying physical model. The neural network framework is applied to RF HCD to determine the collective behavior of an array of hollow cathode holes.