1-D Electromagnetic Particle-In-Cell Simulations on Helium Capacitively Coupled Plasma Discharges

Electrostatic (ES) particle-in-cell (PIC) Monte Carlo collision (MCC) method is widely used for modeling capacitively coupled plasma (CCP) discharges especially when kinetic effects are important and concerned. XPDP1 as one of the ES PIC-MCC codes developed by Plasma Theory and Simulation Group (PTSG) at Michigan State University (formerly at UC Berkeley) has been employed to study CCPs as well as other plasma devices for several decades. The XPDP1 code can self-consistently solve the Poisson equation and a general RLC circuit equation for a plasma system coupled with an external power supply [1] so that the effects of impedance match can be considered. Recently, the electromagnetic (EM) effects in CCPs have attracted a lot of attention due to the needs for fabricating smaller features on larger wafers uniformly. In this work, we propose a development of EM PIC-MCC simulations for studying helium CCP discharges in order to investigate EM effects and gain more physics insight. Instead of solving Poisson's equation, the Maxwell equations are solved by updating Faraday's and Ampere's laws within the leapfrog scheme for each time step. The superposition and decomposition method is employed to couple the RLC circuit equation with the EM PIC-MCC simulations [2]. The developed EM PIC-MCC method is used to study helium CCP discharges and compared to the results from the ES PIC-MCC counterpart. The verification of the simulation methodology and the comparison for understanding the EM effects on the helium CCP discharges will be presented and discussed.