PIC/MCC simulation of capacitively coupled discharges: Effect of particle management and integration

Abstract A PIC/MCC simulation model for the analysis of low-temperature discharge plasmas is represented which takes the common leapfrog and the velocity Verlet algorithm for the particle integration, adaptive particle management as well as parallel computing using MPI into account. Main features of the model including the impact of super particle numbers, adaptive particle management and the time step size for the different integration methods are represented. The investigations are performed for low-pressure capacitively coupled radio frequency discharges in helium and argon. Besides a code verification by comparison with benchmark simulation results in helium it is shown that an adaptive particle management is particularly suitable for the simulation of discharges at elevated pressures where boundary effects and processes in the sheath regions are important. Furthermore, it is pointed out that the velocity Verlet integration scheme allows to speed up the PIC/MCC simulations compared to the leapfrog method because it makes the use of larger time steps at the same accuracy possible.

[1]  A. Phelps,et al.  Cold-cathode discharges and breakdown in argon: surface and gas phase production of secondary electrons , 1999 .

[2]  H. Fehske,et al.  Radio-frequency discharges in oxygen: I. Particle-based modelling , 2007, 0705.0495.

[3]  Benjamin Alexandrovich,et al.  Measurement of electron energy distribution in low-pressure RF discharges , 1992 .

[4]  Jan S. Hesthaven,et al.  Implicit-explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning , 2009, Comput. Phys. Commun..

[5]  T. Makabe,et al.  Plasma Electronics: Applications in Microelectronic Device Fabrication , 2006 .

[6]  John P. Verboncoeur,et al.  Simultaneous potential and circuit solution for 1D bounded plasma particle simulation codes , 1990 .

[7]  Fabrice Deluzet,et al.  Asymptotic-Preserving Particle-In-Cell method for the Vlasov-Poisson system near quasineutrality , 2010, J. Comput. Phys..

[8]  Charles K. Birdsall,et al.  Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. I. Analysis of numerical techniques , 1993 .

[9]  U. Ebert,et al.  A time scale for electrical screening in pulsed gas discharges , 2014, 1405.7215.

[10]  Jürgen Geiser,et al.  Electrostatic Ion Thrusters - Towards Predictive Modeling , 2015 .

[11]  W. C. Swope,et al.  A computer simulation method for the calculation of equilibrium constants for the formation of physi , 1981 .

[12]  Jannis Teunissen,et al.  Controlling the weights of simulation particles: adaptive particle management using k-d trees , 2013, J. Comput. Phys..

[13]  Franck Assous,et al.  A new method for coalescing particles in PIC codes , 2003 .

[14]  Giovanni Lapenta,et al.  Control of the number of particles in fluid and MHD particle in cell methods , 1995 .

[15]  J. Booth,et al.  Frequency dependence of the electrical asymmetry effect in dual-frequency capacitively coupled discharges , 2013 .

[16]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[17]  J. Booth,et al.  Secondary electron induced asymmetry in capacitively coupled plasmas , 2013 .

[18]  David Tskhakaya,et al.  Particle in Cell Simulation of Low Temperature Laboratory Plasmas , 2007 .

[19]  U. Czarnetzki,et al.  The effect of the driving frequencies on the electrical asymmetry of dual-frequency capacitively coupled plasmas , 2012 .

[20]  J. Schulze,et al.  Coupling effects of driving frequencies on the electron heating in electronegative capacitive dual-frequency plasmas , 2013 .

[21]  J. Booth,et al.  Electron heating in capacitively coupled plasmas revisited , 2014 .

[22]  B. J. Muga,et al.  Particle-in-Cell Method , 1970 .

[23]  A. Hatayama Progress in modeling and numerical simulation of negative hydrogen ion sources. , 2008, The Review of scientific instruments.

[24]  Olivier Chanrion,et al.  A PIC-MCC code for simulation of streamer propagation in air , 2008, J. Comput. Phys..

[25]  Combined PIC MCC approach for fast simulation of a radio frequency discharge at a low gas pressure , 2003, physics/0308071.

[26]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[27]  Stephan Reuter,et al.  Plasmas for medicine , 2013 .

[28]  Z. Donkó Particle simulation methods for studies of low-pressure plasma sources , 2011 .

[29]  Michael P Eastwood,et al.  A common, avoidable source of error in molecular dynamics integrators. , 2007, The Journal of chemical physics.

[30]  J. Schulze,et al.  Effects of fast atoms and energy-dependent secondary electron emission yields in PIC/MCC simulations of capacitively coupled plasmas , 2014, 1411.2464.

[31]  M. Turner,et al.  Simulation benchmarks for low-pressure plasmas: Capacitive discharges , 2012, 1211.5246.

[32]  J. Meichsner,et al.  Dynamics and Electronegativity of Oxygen RF Plasmas , 2012 .

[33]  M. Lieberman,et al.  A benchmark study of a capacitively coupled oxygen discharge of the oopd1 particle-in-cell Monte Carlo code , 2013 .

[34]  Peter Arbenz,et al.  A novel adaptive time stepping variant of the Boris-Buneman integrator for the simulation of particle accelerators with space charge , 2012, J. Comput. Phys..

[35]  C. Birdsall,et al.  Plasma Physics via Computer Simulation , 2018 .

[36]  U. Ebert,et al.  The inception of pulsed discharges in air: simulations in background fields above and below breakdown , 2014, 1405.7216.

[37]  Patrick Verdonck,et al.  Plasma Etching , 2022 .

[38]  J. Booth,et al.  Control of the ion flux and ion energy in CCP discharges using non-sinusoidal voltage waveforms , 2012 .

[39]  I. Rafatov,et al.  Particle in Cell/Monte Carlo Collision Method for Simulation of RF Glow Discharges: Effect of Super Particle Weighting , 2014 .

[40]  J. Schulze,et al.  Ionization by bulk heating of electrons in capacitive radio frequency atmospheric pressure microplasmas , 2012, 1208.6519.

[41]  Dale R. Welch,et al.  Adaptive particle management in a particle-in-cell code , 2007, J. Comput. Phys..

[42]  M. Lieberman,et al.  Capacitive RF discharges modelled by particle-in-cell Monte Carlo simulation. II. Comparisons with laboratory measurements of electron energy distribution functions , 1993 .

[43]  A. Lichtenberg,et al.  Principles of Plasma Discharges and Materials Processing , 1994 .

[44]  Godyak,et al.  Evolution of the electron-energy-distribution function during rf discharge transition to the high-voltage mode. , 1992, Physical review letters.

[45]  F. Iza,et al.  Electron kinetics in radio-frequency atmospheric-pressure microplasmas. , 2007, Physical review letters.

[46]  New combined PIC-MCC approach for fast simulation of a radio frequency discharge at low gas pressure , 2003 .

[47]  A. V. Phelps,et al.  The application of scattering cross sections to ion flux models in discharge sheaths , 1994 .

[48]  K. Nanbu,et al.  Probability theory of electron-molecule, ion-molecule, molecule-molecule, and Coulomb collisions for particle modeling of materials processing plasmas and cases , 2000 .