Verification methods for one-dimensional particle-in-cell/Monte Carlo collisional simulations

One-dimensional particle-in-cell/Monte Carlo collisional (PIC/MCC) simulations are are widely applied to gain knowledge of the workings of capacitive discharges. Despite being powerful tools to reveal the physics of the plasma discharge, including electron power absorption mechanisms, and to provide essential information such as ion and electron energy distribution, the electron density is commonly underestimated while the average electron energy is overestimated, as the simulations results are compared to experimental findings [1,2]. Verification of the numerical PIC/MCC simulations is an essential step in the development of the physical models describing the plasma discharge as it demonstrates the correctness of the code and the underlying physical model description. In the past few years the description of the plasma chemistry of the argon discharge has been improved to include also the excited argon states (metastable levels, resonance levels, and the 4p manifold) modeled self-consistently with the particle dynamics as space and time-varying fluids [3]. There have also been improvements that involve including in the discharge model secondary electron emission due to neutral (including excited species), ion, electron, and resonant photon impact on the electrodes [3,4]. When all of these features are included in the discharge model the PIC/MCC simulation results show good agreement with recent experimental measurements in the low pressure range (1 - 10 Pa) [5,6] that is commonly used for etching in the semiconductor industry. Similar approach when modeling a capacitive chlorine discharge will be discussed briefly [7].