Particle and fluid simulations of low-temperature plasma discharges: benchmarks and kinetic effects

Fluid, particle-in-cell and hybrid models are the numerical simulation techniques commonly used for simulating low-temperature plasma discharges. Despite the complexity of plasma systems and the challenges in describing and modelling them, well-organized simulation methods can provide physical information often difficult to obtain from experiments. Simulation results can also be used to identify research guidelines, find optimum operating conditions or propose novel designs for performance improvements. In this paper, we present an overview of the principles, strengths and limitations of the three simulation models, including a brief history and the recent status of their development. The three modelling techniques are benchmarked by comparing simulation results in different plasma systems (plasma display panels, capacitively coupled plasmas and inductively coupled plasmas) with experimentally measured data. In addition, different aspects of the electron and ion kinetics in these systems are discussed based upon simulation results.

[1]  Nakano,et al.  Modeling and diagnostics of the structure of rf glow discharges in Ar at 13.56 MHz. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[2]  Liu Chen,et al.  I. Heating of Magnetized Plasmas by Large-Amplitude Electric Field. I. Reduction of the Grid Effects in Simulation Plasmas. , 1974 .

[3]  Z. Donkó,et al.  BRIEFCOMMUNICATION: Use of secondary-electron yields determined from breakdown data in cathode-fall models for Ar , 1999 .

[5]  Jae Koo Lee,et al.  TWO-DIMENSIONAL SELF-CONSISTENT RADIATION TRANSPORT MODEL FOR PLASMA DISPLAY PANELS , 2002 .

[6]  J. Boeuf,et al.  Numerical model of rf glow discharges. , 1987, Physical review. A, General physics.

[7]  R. M. Vaughan,et al.  Secondary emission formulas , 1993 .

[8]  Godyak,et al.  Abnormally low electron energy and heating-mode transition in a low-pressure argon rf discharge at 13.56 MHz. , 1990, Physical review letters.

[9]  A. Ellingboe,et al.  Analytical model of a dual frequency capacitive sheath , 2003 .

[10]  W. Williamson,et al.  A kinetic study of the local field approximation in simulations of AC plasma display panels , 1995 .

[11]  M. Surendra,et al.  Particle simulations of radio-frequency glow discharges , 1991 .

[12]  Particle-in-cell simulation of gas breakdown in microgaps , 2004, physics/0409131.

[13]  K. Jensen,et al.  A Continuum Model of DC and RF Discharges , 1986, IEEE Transactions on Plasma Science.

[14]  J. Evans,et al.  Nonlocal power deposition in inductively coupled plasmas. , 2001, Physical review letters.

[15]  Jae Koo Lee,et al.  Method to increase the simulation speed of particle-in-cell (PIC) code , 2001 .

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

[17]  V. Kolobov,et al.  Negative Power Absorption in Inductively Coupled Plasma , 1997 .

[18]  J. Vaughan,et al.  A new formula for secondary emission yield , 1989 .

[19]  A. Paranjpe Modeling an inductively coupled plasma source , 1994 .

[20]  V. Godyak,et al.  On nonlocal heating in inductively coupled plasmas , 2002 .

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

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

[23]  W. Goedheer,et al.  A two‐dimensional fluid model for an argon rf discharge , 1993 .

[24]  David B. Graves,et al.  Capacitively coupled glow discharges at frequencies above 13.56 MHz , 1991 .

[25]  A. Bruce Langdon,et al.  THEORY OF PLASMA SIMULATION USING FINITE-SIZE PARTICLES. , 1970 .

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

[27]  Mark J. Kushner,et al.  Modeling of microdischarge devices: Pyramidal structures , 2004 .

[28]  G. Wunner,et al.  Asynchronous cycling as a convergence acceleration method in particle simulation of direct current glow discharges , 1997 .

[29]  H. Kim,et al.  Mode transition induced by low-frequency current in dual-frequency capacitive discharges. , 2004, Physical review letters.

[30]  Pascal Colpo,et al.  Design of a magnetic-pole enhanced inductively coupled plasma source , 2001 .

[31]  N. Babaeva,et al.  Ion energy distribution control in single and dual frequency capacitive plasma sources , 2005 .

[32]  Jae Koo Lee,et al.  Analytic model for a dual frequency capacitive discharge , 2003 .

[33]  Mikhail N. Shneider,et al.  Radio-Frequency Capacitive Discharges , 1995 .

[34]  Vladimir Kolobov,et al.  Nonlocal electron kinetics in collisional gas discharge plasmas , 1995 .

[35]  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 .

[36]  Matthew N. O. Sadiku,et al.  Numerical Techniques in Electromagnetics , 2000 .

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

[38]  Jae Koo Lee,et al.  Velocity space ring‐plasma instability, magnetized, Part II: Simulation , 1979 .

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

[40]  Charles K. Birdsall,et al.  Physical and numerical methods of speeding up particle codes and paralleling as applied to RF discharges , 2000 .

[41]  A novel electrical model of nerve and muscle using Pspice , 2003 .

[42]  H. Kim,et al.  Dual radio-frequency discharges: Effective frequency concept and effective frequency transition , 2005 .

[43]  K. Tachibana,et al.  Three-dimensional diagnostics of dynamic behaviors of excited atoms in microplasma for plasma display panels , 2003 .

[44]  H. Murakami,et al.  A study of the secondary electron yield /spl gamma/ of insulator cathodes for plasma display panels , 2001 .

[45]  Jane P. Chang,et al.  Lecture Notes on Principles of Plasma Processing , 2003 .

[46]  S. Selberherr Analysis and simulation of semiconductor devices , 1984 .

[47]  W. Nicholas G. Hitchon Plasma Processes for Semiconductor Fabrication , 1999 .

[48]  Jae Koo Lee,et al.  Striation phenomenon in the plasma display panel , 2001 .

[49]  J. Verboncoeur Particle simulation of plasmas: review and advances , 2005 .

[50]  M. Kushner,et al.  Numerical investigation of the kinetics and chemistry of rf glow discharge plasmas sustained in He, N2, O2, He/N2/O2, He/CF4/O2, and SiH4/NH3 using a Monte Carlo-fluid hybrid model , 1992 .

[51]  Robert J. Hoekstra,et al.  Two‐dimensional modeling of high plasma density inductively coupled sources for materials processing , 1994 .

[52]  Tadahiro Ohmi,et al.  Dual excitation reactive ion etcher for low energy plasma processing , 1992 .

[53]  D. J. Economou,et al.  The anomalous skin effect in gas discharge plasmas , 1997 .

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

[55]  H. Sawin,et al.  Continuum modeling of radio‐frequency glow discharges. I. Theory and results for electropositive and electronegative gases , 1992 .

[56]  C. Punset,et al.  Addressing and sustaining in alternating current coplanar plasma display panels , 1999 .

[57]  John P. Verboncoeur,et al.  An object-oriented electromagnetic PIC code , 1995 .

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

[59]  Jae Koo Lee,et al.  Modeling of breakdown behavior in radio-frequency argon discharges with improved secondary emission model , 2005 .

[60]  W. Hitchon Plasma Processes for Semiconductor Fabrication: Introduction , 1999 .

[61]  G. Kroesen,et al.  Energy distribution of ions and fast neutrals in microdischarges for display technology , 2000 .

[62]  D. Graves Fluid model simulations of a 13.56‐MHz rf discharge: Time and space dependence of rates of electron impact excitation , 1987 .

[63]  P. Thieberger,et al.  Secondary-electron yields and their dependence on the angle of incidence on stainless-steel surfaces for three energetic ion beams , 2000 .

[64]  Three-dimensional fluid simulation of a plasma display panel cell , 2002 .

[65]  V. Yegorenkov,et al.  Low-pressure gas breakdown in combined fields , 1994 .

[66]  E. Choi,et al.  Striations in a coplanar ac-plasma display panel , 2000 .

[67]  Maheswaran Surendra,et al.  A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges , 1995 .

[68]  David B. Graves,et al.  Modeling and simulation of magnetically confined low-pressure plasmas in two dimensions , 1991 .

[69]  Alex V Vasenkov,et al.  Electron energy distributions and anomalous skin depth effects in high-plasma-density inductively coupled discharges. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  C. Guarnieri,et al.  Langmuir probe measurements of a radio frequency induction plasma , 1993 .

[71]  S. Rauf,et al.  Dynamics of a coplanar-electrode plasma display panel cell. I. Basic operation , 1999 .

[72]  A. Fridman,et al.  Non-thermal atmospheric pressure discharges , 2005 .

[73]  A. Bruce Langdon,et al.  EFFECTS OF THE SPATIAL GRID IN SIMULATION PLASMAS. , 1970 .

[74]  Vladimir Kolobov,et al.  EFFECT OF COLLISIONLESS HEATING ON ELECTRON ENERGY DISTRIBUTION IN AN INDUCTIVELY COUPLED PLASMA , 1998 .

[75]  V. Godyak,et al.  OBSERVATION OF SECOND HARMONIC CURRENTS IN INDUCTIVELY COUPLED PLASMAS , 1999 .

[76]  M. Sadiku Numerical Techniques in Electromagnetics , 2000 .

[77]  J Reece Roth,et al.  Industrial Plasma Engineering: Volume 2: Applications to Nonthermal Plasma Processing , 2001 .

[78]  R. Hoekstra,et al.  Predictions of ion energy distributions and radical fluxes in radio frequency biased inductively coupled plasma etching reactors , 1996 .

[79]  A self-consistent analytical model for non-collisional heating , 1997 .

[80]  Turner Collisionless electron heating in an inductively coupled discharge. , 1993, Physical review letters.

[81]  T. Makabe,et al.  SPATIOTEMPORAL CHARACTERISTICS DETERMINED BY A RELAXATION CONTINUUM MODEL OF AN INDUCTIVELY COUPLED PLASMA , 1994 .

[82]  R. Gottscho,et al.  Negative Ion Kinetics in RF Glow Discharges , 1986, IEEE Transactions on Plasma Science.

[83]  N. Babaeva,et al.  Oxygen ion energy distribution: Role of ionization, resonant, and nonresonant charge-exchange collisions , 2005 .

[84]  I. Kaganovich Anomalous capacitive sheath with deep radio-frequency electric-field penetration. , 2002, Physical review letters.

[85]  Hopkins,et al.  Anomalous sheath heating in a low pressure rf discharge in nitrogen. , 1992, Physical review letters.

[86]  Jae Koo Lee,et al.  Striation Mechanism and Triggered Striation in Dielectric Microdischarge Plasma. , 2001 .

[87]  M. Lieberman,et al.  The influence of antenna configuration and standing wave effects on density profile in a large-area inductive plasma source , 1999 .

[88]  H. Gummel,et al.  Large-signal analysis of a silicon Read diode oscillator , 1969 .

[89]  Jeffrey Hopwood,et al.  Review of inductively coupled plasmas for plasma processing , 1992 .

[90]  J. Boeuf Plasma display panels: physics, recent developments and key issues , 2003 .

[91]  John M. Dawson,et al.  One‐Dimensional Plasma Model , 1962 .

[92]  T. Makabe,et al.  Two-dimensional CT images of two-frequency capacitively coupled plasma , 1999 .

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

[94]  Hideo Okuda,et al.  Nonphysical noises and instabilities in plasma simulation due to a spatial grid , 1972 .

[95]  Jae Koo Lee,et al.  Dual-frequency capacitive discharges: Effect of low-frequency current on electron distribution function , 2005 .

[96]  Jae-Yong Lim,et al.  Secondary electron emission coefficient of a MgO single crystal , 1999 .

[97]  Toshiki Tajima Computational Plasma Physics , 1988 .

[98]  Jae Koo Lee,et al.  The voltage-pulsing effects in AC plasma display panel , 1999 .

[99]  P. Koidl,et al.  Ion and electron dynamics in the sheath of radio‐frequency glow discharges , 1991 .

[100]  D. J. Economou,et al.  Analysis of low pressure rf glow discharges using a continuum model , 1990 .

[101]  R. Cohen,et al.  Electron kinetics in radio-frequency magnetic fields of inductive plasma sources , 1996 .

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

[103]  O. Buneman,et al.  Dissipation of Currents in Ionized Media , 1959 .

[104]  J. Moshman,et al.  Monte Carlo Calculation of Noise Near the Potential Minimum of a High‐Frequency Diode , 1956 .

[105]  S. S. Yang,et al.  Application of two-dimensional numerical simulation for luminous efficiency improvement in plasma display panel cell , 2003 .

[106]  C. Birdsall,et al.  Space‐Charge Instabilities in Electron Diodes and Plasma Converters , 1961 .

[107]  M. Lieberman,et al.  Ion energy distributions in rf sheaths; review, analysis and simulation , 1999 .

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

[109]  S. S. Yang,et al.  Three-dimensional self-consistent radiation transport model for the fluid simulation of plasma display panel cell , 2003 .

[110]  S. S. Kim,et al.  Antenna configuration for uniform large-area inductively coupled plasma production , 2000 .