AETHER: A simulation platform for inductively coupled plasma

Abstract An in-house code is developed to simulate the inductively coupled plasma (ICP). The model comprises the fluid, electromagnetic and transformer submodels. Fluid equations are solved to evaluate the plasma flow parameters, including the plasma and neutral densities, ion and neutral velocities, electron flux, electron temperature, and electric potential. The model relies on the ambipolar approximation and offers the evaluation of plasma parameters without solving the sheath region. The electromagnetic model handles the calculation of the electric and magnetic fields using the magnetic vector potential. The transformer model captures the effect of the matching circuit utilized in laboratory experiments for RF power deposition. The continuity and momentum equations are solved using finite volume method. The energy, electric potential, and magnetic vector potential equations are solved using finite difference method. The resulting linear systems of equations are solved with iterative solvers including Jacobi and GMRES. The code is written using the C++ programming language, it works in parallel and has graphical user interface. The model is applied to study ICP characteristics of a plasma confined within a cylindrical chamber with dielectric walls for two different power deposition cases. The results obtained from the developed model are verified using the plasma module of COMSOL Multiphysics. The model is also applied to a plasma source configuration, and it is demonstrated that there is an overall increase in the plasma potential when current is extracted from ICP with a biased wall electrode.

[1]  T. M. Antonsen,et al.  QUICKPIC: A highly efficient particle-in-cell code for modeling wakefield acceleration in plasmas , 2006, J. Comput. Phys..

[2]  Laurene V. Fausett,et al.  Applied Numerical Analysis Using MATLAB (2nd Edition) , 2007 .

[3]  N. Fisch,et al.  A Parametric Study of Electron Extraction from a Low Frequency Inductively Coupled RF-Plasma Source , 2009 .

[4]  F. Hwang,et al.  Parallel 2D Axisymmetric Fluid Modeling of CF4 Discharge in an Inductively Coupled Plasma Source During SiO2 Etching , 2014 .

[5]  Ute Dreher,et al.  Scientific Computing And Differential Equations An Introduction To Numerical Methods , 2016 .

[6]  L. Fausett.  Applied Numerical Analysis Using MATLAB , 1999 .

[7]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

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

[9]  Chia-Jung Hsu.  Numerical Heat Transfer and Fluid Flow , 1981 .

[10]  Giovanni Lapenta,et al.  DEMOCRITUS: An adaptive particle in cell (PIC) code for object-plasma interactions , 2011, J. Comput. Phys..

[11]  I. Katz,et al.  Fundamentals of Electric Propulsion: Ion and Hall Thrusters , 2008 .

[12]  Colin Campbell,et al.  Parallel Programming with Microsoft® .NET: Design Patterns for Decomposition and Coordination on Multicore Architectures , 2010 .

[13]  N. Hershkowitz,et al.  Global nonambipolar flow: Plasma confinement where all electrons are lost to one boundary and all positive ions to another boundary , 2007 .

[14]  Horst W. Loeb,et al.  Recent Work on Radio Frequency Ion Thrusters , 1970 .

[15]  Jong-Shinn Wu,et al.  Development of a parallel semi-implicit two-dimensional plasma fluid modeling code using finite-volume method , 2012, Comput. Phys. Commun..

[16]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[17]  김찬홍,et al.  다중물리 해석 프로그램 : COMSOL Multiphysics , 2006 .

[18]  Mikhail N. Shneider,et al.  Sheath governing equations in computational weakly-ionized plasmadynamics , 2013, J. Comput. Phys..

[19]  Charles K. Birdsall,et al.  Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms, PIC-MCC , 1991 .

[20]  Benjamin Alexandrovich,et al.  A simple analysis of an inductive RF discharge , 1992 .

[21]  Gul A. Agha,et al.  Concurrent object-oriented programming , 1993, CACM.

[22]  M. Lieberman,et al.  Fast 2D hybrid fluid-analytical simulation of inductive/capacitive discharges , 2011 .

[23]  Michael A. Lieberman,et al.  Magnetic induction and plasma impedance in a cylindrical inductive discharge , 1997 .

[24]  Julian Smart,et al.  Cross-Platform GUI Programming with wxWidgets , 2005 .

[25]  Y. Okuno,et al.  Numerical studies on the nonequilibrium inductively coupled plasma with metal vapor ionization , 1996 .

[26]  Y. Saad,et al.  GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems , 1986 .

[27]  Joel H. Ferziger,et al.  Computational methods for fluid dynamics , 1996 .

[28]  H. Fukumoto,et al.  Plasma chemical behaviour of reactants and reaction products during inductively coupled CF4 plasma etching of SiO2 , 2009 .

[30]  G. Golub,et al.  Scientific Computing and Differential Equations: An Introduction to Numerical Methods , 1991 .

[31]  P. B. Snyder,et al.  BOUT++: A framework for parallel plasma fluid simulations , 2008, Comput. Phys. Commun..

[32]  Pascal Colpo,et al.  Determination of the equivalent circuit of inductively coupled plasma sources , 1999 .

[33]  Kerstin Vogler,et al.  Table Of Integrals Series And Products , 2016 .

[34]  James M. Stone,et al.  Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics , 2013, J. Comput. Phys..

[35]  J. Meijerink,et al.  An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix , 1977 .

[37]  Emre Turkoz,et al.  2-D Electromagnetic and Fluid Models for Inductively Coupled Plasma for RF Ion Thruster Performance Evaluation , 2014, IEEE Transactions on Plasma Science.

[38]  Parallel 2 D Axisymmetric Fluid Modeling of CF 4 Discharge in an Inductively Coupled Plasma Source During SiO 2 Etching , 2014 .

[39]  Murat Celik,et al.  2D Axisymmetric Fluid and Electromagnetic Models for Inductively Coupled Plasma (ICP) in RF Ion Thrusters , 2013 .

[40]  Stephen Travis Pope,et al.  A Description of the Model-View-Controller User Interface Paradigm in the Smalltalk-80 System , 1998 .

[41]  Virginie Grandgirard,et al.  TOKAM-3D: A 3D fluid code for transport and turbulence in the edge plasma of Tokamaks , 2010, J. Comput. Phys..

[42]  Daniel E. Hastings,et al.  Computational modeling of expanding plasma plumes in space using a PIC-DSMC algorithm , 1996 .

[43]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[44]  Michael Meng-Tsuan Tsay.  Two-dimensional numerical modeling of Radio-Frequency ion engine discharge , 2010 .

[45]  John Michael Fife,et al.  Hybrid-PIC modeling and electrostatic probe survey of Hall thrusters , 1998 .

[46]  D. Goebel,et al.  Analytical Discharge Model for RF Ion Thrusters , 2008, IEEE Transactions on Plasma Science.

[47]  Mikhail N. Shneider,et al.  Electron and ion transport equations in computational weakly-ionized plasmadynamics , 2014, J. Comput. Phys..

[48]  J. Cary,et al.  VORPAL: a versatile plasma simulation code , 2004 .

[49]  A. Fridman,et al.  Plasma Physics and Engineering , 2021 .