Fluid simulations of glow discharges: Effect of metastable atoms in argon

A one‐dimensional fluid simulation of a 13.56 MHz argon glow discharge including metastable species was performed as an example of a coupled glow‐discharge/neutral‐transport‐reaction system. Due to the slow response time of metastables (∼10 ms) direct time integration of the coupled system requires ∼105 rf cycles to converge. This translates to prohibitively long computation time. An ‘‘acceleration’’ scheme was employed using the Newton–Raphson method to speed up convergence, thereby reducing the computation time by orders of magnitude. For a pressure of 1 Torr, metastables were found to play a major role in the discharge despite the fact that their mole fraction was less than 10−5. In particular, metastable (two‐step) ionization was the main mechanism for electron production to sustain the discharge. Bulk electric field and electron energy were lower, and a smaller fraction of power was dissipated in the bulk plasma when compared to the case without metastables. These results suggest that neutral transport and reaction must be considered in a self‐consistent manner in glow discharge simulations, even in noble gas discharges.

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

[2]  Yu. A. Lebedev,et al.  Computer simulation of microwave and DC plasmas: comparative characterisation of plasmas , 1992 .

[3]  A continuum model for low‐pressure radio‐frequency discharges , 1991 .

[4]  D. J. Economou,et al.  Theoretical and Experimental Investigations of Chlorine RF Glow Discharges I . Theoretical , 1992 .

[5]  H. Tagashira,et al.  A hybrid Monte Carlo/fluid model of RF plasmas in a SiH/sub 4//H/sub 2/ mixture , 1991 .

[6]  D. J. Economou,et al.  Numerical Simulation of a Single‐Wafer Isothermal Plasma Etching Reactor , 1990 .

[7]  Spatiotemporal evolution of a low‐pressure glow discharge , 1991 .

[8]  A. Ward.  Effect of Space Charge in Cold-Cathode Gas Discharges , 1958 .

[9]  Mark J. Kushner,et al.  Monte‐Carlo simulation of electron properties in rf parallel plate capacitively coupled discharges , 1983 .

[10]  V. A. Feoktistov,et al.  RF discharge modeling considering time dependence and spatial nonlocality of the electron energy spectrum , 1991 .

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

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

[13]  C. M. Ferreira,et al.  Populations in the metastable and the resonance levels of argon and stepwise ionization effects in a low‐pressure argon positive column , 1985 .

[14]  D. Choi,et al.  A numerical simulation of rf glow discharge containing an electronegative gas composition , 1990 .

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

[16]  R. Gottscho,et al.  Nonlinear excitation and dissociation kinetics in discharges through mixtures of rare and attaching gases , 1988 .

[17]  Analytic approach to glow discharge theory: result and analysis , 1992 .

[18]  J. Boeuf,et al.  Pseudospark discharges via computer simulation , 1991 .

[19]  Evangelos Gogolides,et al.  Comparison of experimental measurements and model predictions for radio‐frequency Ar and SF6 discharges , 1989 .

[20]  I. J. Morey,et al.  Self‐consistent simulation of a parallel‐plate rf discharge , 1988 .

[21]  J. McVittie,et al.  Scaling laws for radio frequency glow discharges for dry etching , 1990 .

[22]  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 .

[23]  J. Loureiro,et al.  Electron transport parameters and excitation rates in argon , 1983 .

[24]  R. Boswell,et al.  Simulation of pulsed electropositive and electronegative plasmas , 1991 .

[25]  M. Elta,et al.  A staggered-mesh finite-difference numerical method for solving the transport equations in low pressure RF glow discharges , 1988 .

[26]  H. Sawin,et al.  Continuum modeling of argon radio frequency glow discharges , 1987 .

[27]  Leon Lapidus,et al.  Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications , 1976 .

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

[29]  K. Jensen,et al.  The importance of free radical recombination reactions in CF4/O2 plasma etching of silicon , 1990 .

[30]  James E. Lawler,et al.  A self-consistent kinetic plasma model with rapid convergence , 1991 .

[31]  Michael A. Lieberman,et al.  Macroscopic modeling of radio‐frequency plasma discharges , 1989 .

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

[33]  H. Ruder,et al.  A one‐dimensional model of dc glow discharges , 1992 .

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

[35]  M. Kushner,et al.  Computer simulation of materials processing plasma discharges , 1989 .

[36]  J. Z. Zhu,et al.  The finite element method , 1977 .

[37]  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.

[38]  W. L. Engl,et al.  TNPT-an efficient method to simulate forced nonlinear RF networks in time domain , 1977 .

[39]  Ingrid Bonde.  VAT , 1992 .

[40]  K. Saraswat,et al.  Simulation of Mass Transport for Deposition in Via Holes and Trenches , 1991 .