Comparison of a one-dimensional particle-in-cell–Monte Carlo model and a one-dimensional fluid model for a CH4/H2 capacitively coupled radio frequency discharge

Abstract

A one-dimensional particle-in-cell-Monte Carlo ͑PIC-MC͒ model was developed for a capacitively coupled rf discharge in a mixture of CH 4 and H 2 . The electron behavior is kinetically simulated by solving Newton's equations and treating the electron collisions with the Monte Carlo algorithm, whereas the behavior of the ions and radicals is treated by a set of continuity equations. The distinctive feature of this model is its self-consistency, i.e., the motion of the electrons is considered in the real electric field calculated from the Poisson equation, and not in the time-averaged electric field. The PIC-MC results were compared with the data calculated by means of a pure fluid model. In both models, exactly the same type of species, reactions, and cross sections are used. The results of both models, such as the electron energy distribution function, the average electron energy, and the densities of the various plasma species, are compared at a gas pressure of 0.14 Torr and a discharge frequency of 13.56 MHz, for the power ranging from 0.5 to 25 W. The nonstationary and nonlocal features of the electron energy distribution function are shown in the PIC-MC calculations. The effect of accumulation of low-energy electrons in the center of the discharge at higher input power Pϭ25 W is observed in the PIC-MC model, in contrast with the fluid model. The mechanisms causing the accumulation of low-energy electrons, and the processes defining the stationary state of the discharge are analyzed. The applicability of the fluid model for the calculation of the density of different hydrocarbon radicals is discussed.

A reaction model for plasma coating of nanoparticles by amorphous carbon layers

“…Following Ref. 28, we disregard the vibration excitation electronneutral reactions in order to limit the number of the species. To account for the electron-neutral reactions, the rate constants k i , i = 1 , .…”

Particle in Cell Simulation of Low Temperature Laboratory Plasmas

“…Recently PIC MCC models have been successfully applied for the simulation of RF discharges with increasingly complex plasma-chemistry [12][13][14][15][16][17][18][19]. PIC simulations are useful not only for getting quantitative description for the system of interest, but also for understanding the basic physics of the discharge, helping to validate existing analytical models and to build new ones.…”

Two-dimensional PIC–MCC simulations of a capacitively coupled radio frequency discharge in methane

“…The developed PIC-MCC approach is two-dimensional in space and threedimensional for particles motion (2D3V). In Monte-Carlo collisions simulations of electron kinetics, besides the elastic scattering, six electron-methane reactions were considered (listed in table 1), with the same cross sections as in [11] and [15]. Electron-electron Coulomb scattering, secondary electron emission and wall reflection were neglected so all particles reaching the chamber walls were eliminated.…”

“…Besides, the electron-impact vibrational excitation reactions, which affect the electron energy distribution, were not considered. Another approach is presented in work [15], where the PIC-MCC simulations were proceeded only for electrons with accounting of 18 electron-neutral reactions, thus providing the reaction rates, while the kinetics of ions and neutral species (with total number of 20) was treated using diffusion-drift approximation and mass balance.…”