@article{b413c759021041ceaa318be666a02167,
title = "Particle Simulations of Radio-Frequency Glow Discharges",
abstract = "Particle-in-cell simulations are used to study the structure of radio-frequency (RF) glow discharges in helium between parallel-plate electrodes. We have examined a range of conditions and report on a variety of observed phenomena. Comparisons to experiment and analytical models are made, when possible. The differences between discharges in which secondary electrons play a key role in sustaining the discharge and those in which secondary electrons are unimportant are examined in three cases which illustrate the importance of the discharge-sustaining mechanisms. Electron-energy distributions are found to be, in general, non-Maxwellian, with shapes that depend in complex ways on discharge conditions. In the absence of secondary electron emission, electron heating in the sheath regions of the discharge is enhanced at higher voltages compared to ohmic heating in the bulk of the plasma. Fast electrons accelerated by the advancing sheath can carry a substantial fraction of the conduction current in the bulk of the discharge, reducing the effective bulk ohmic heating of electrons. Ion-energy distributions at electrode surfaces have been predicted and are compared to experimental measurements. Simulations indicate that ion power deposition scales as the square of the applied voltage, while electron power deposition scales approximately linearly with applied voltage. Discharge power is dominated by ion losses at higher voltages. These results are in good agreement with predictions from analytical models of RF discharges.",
author = "M. Surendra and Graves, {David B.}",
note = "Funding Information: EAKLY ionized gas discharges between parallel-plate elec-W trodes sustained by application of voltages at radio frequencies (RF) are commonly used in the microelectronics industry for etching and deposition of thin films. Because of this important application and also because this configuration can be usefully studied under the assumption that quantities vary only with phase in the RF period and one spatial dimension, a considerable effort is now underway to model these discharges. A wide range of models have been put forward, including approximate analytical models [ 13- [3]; equivalent circuit models [4], [5]; models based on moment or fluid equations [6]-[17]; numerical solutions of the Boltzmann equation [18]; and particle models [19] - [22]. The latter two approaches have the advantage that kinetic information is obtained from the simulation: Velocity distribution functions are the result of the calculations. Until recently, solutions of the Boltzmann equation and related particle-simulation methods have not been conducted with simultaneous solution of Poisson{\textquoteright}s equation to obtain a self-consistent kinetic level solution. Particle-in-cell (or particle-mesh)/Monte Carlo models of RF glows provide kinetic information self-consistently by integrating the equations of motion of many superparticles representing electrons and ions with a simultaneous numerical solution of Poisson{\textquoteright}s equation on a spatially discretized mesh and with a Monte Carlo treatment of electron-neutral and ion- Manuscript received July 12, 1990; revised November 14, 1990. This work was supported by the National Science Foundation through Grant CTS-8957179 and the San Diego Supercomputer Center. The authors are with the Department of Chemical Engineering, University of California, Berkeley, Berkeley, CA 94720. IEEE Log Number 9042742.",
year = "1991",
month = apr,
doi = "10.1109/27.106808",
language = "English (US)",
volume = "19",
pages = "144--157",
journal = "IEEE Transactions on Plasma Science",
issn = "0093-3813",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",
}