Exploring Electromagnetic Effects in High Frequency Helium Capacitively Coupled Plasma Discharges Using 1-D EM PIC-MCC Simulations

Capacitively coupled plasma (CCP) discharges are commonly analyzed using the electrostatic (ES) particle-in-cell (PIC) Monte Carlo collision (MCC) method due to its capability to accurately capture kinetic effects. Historically, CCPs and other plasma devices have been investigated with XPDP1, an ES PIC-MCC code developed by the Plasma Theory and Simulation Group at Michigan State University. XPDP1 enables the self-consistent solution of the Poisson equation and a general RLC circuit equation, modeling a plasma system connected to an external power supply. With the increasing demand for fabricating smaller features on larger wafers, the significance of electromagnetic (EM) effects in CCPs has risen considerably. This study aims to develop EM PIC-MCC simulations to study CCP discharges, aiming to better understand plasma physics and explore EM effects. In the EM simulations, Maxwell's equations are solved explicitly by updating Faraday and Ampere laws within the leapfrog scheme at each time step, instead of solving Poisson's equation in the ES case. The EM PIC-MCC simulations have been compared to ES PIC-MCC simulations and show good agreement for helium CCP discharges at 13.56 MHz. It is expected that the EM effects in CCP discharges become more significant when operating at a higher frequency, e.g., 27 MHz, 40MHz, and 60 MHz. The verification of the simulation method and a comparative analysis to understand the EM effects on helium CCP discharges will be presented and discussed. The outcomes are expected to offer valuable insights into the behavior of CCPs under varying operational frequencies, enhancing the precision of plasma processing applications in semiconductor industries.