Numerical Solution of Plasma Fluid Equations Using Locally Refined Grids

Journal of Computational Physics

Volumn 152, Issue 2, 1999, Pages 550-583

  Colella, Phillip ^a   Dorr, Milo R ^a   Wake, Daniel D ^a  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COLLISIONAL PLASMAS; DIFFUSION IN LIQUIDS; ELECTRIC FIELDS; NUMERICAL METHODS;

BLOCK STRUCTURED; DRIFT-DIFFUSION MODEL; ELECTRIC SOURCES; ENERGY EQUATION; EULER'S EQUATION; FLUID EQUATIONS; GOVERNING EQUATIONS; ION SPECIES; NUMERICAL SOLUTION; PLASMA FLUIDS;

POISSON EQUATION;

EID: 0000370341     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1999.6245     Document Type: Article

References (33)

1. A. S. Almgren, J. B. Bell, P. Colella, L. H. Howell, and M. L. Welcome, A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations, J. Comput. Phys. 142, 1 (1998).
2. M. J. Berger and P. Colella, Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys. 82, No. 1, 64 (1989).
3. M. J. Berger and J. Oliger, Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys. 53, 484 (1984).
4. J. D. Bukowski, D. B. Graves, and P. Vitello, Two-dimensional fluid model of an inductively coupled plasma with comparison to experimental spatial profiles, J. Appl. Phys. 80 (September 1996).
5. J. D. Bukowski, R. A. Stewart, D. B. Graves, and P. Vitello, Modeling inductively coupled plasma tools with chlorine chemistry, in Proceedings, Electrochemical Society Meeting, May 1994.
6. S. D. Cohen and A. C. Hindmarsh, CVODE User Guide, Technical Report UCRL-MA-118618, Lawrence Livermore National Laboratory, September 1994.
7. S. D. Cohen and A. C. Hindmarsh, CVODE, a stiff/nonstiff ODE solver in C, Comput. Phys. 10, No. 2, 138 (1996).
8. P. Colella, Multidimensional upwind methods for hyperbolic conservation laws, J. Comput. Phys. 87, 171 (1990).
9. P. Colella, M. R. Dorr, and D. D. Wake, A conservative finite difference method for the numerical solution of plasma fluid equations, J. Comput. Phys. 149, 168 (1999).
10. W. Y. Crutchfield and M. L. Welcome, Object Oriented Implementation of Adaptive Mesh Refinement Algorithms, Technical Report UCRL-JC-113502, Lawrence Livermore National Laboratory, Livermore, CA, April 1993.
11. G. W. Hedstrom, G. H. Rodrigue, M. Berger, and J. Oliger, Adaptive mesh refinement for 1-dimensional gas dynamics, in IMACS (North-Holland, Amsterdam, 1983), p. 43.
12. R. J. Hoekstra and M. J. Kushner, The effect of subwafer dielectrics on plasma properties in plasma etching reactors, J. Appl. Phys. 77, No. 8, 3668 (1995).
13. R. J. Hoekstra and M. J. Kushner, Predictions of ion energy distributions and radical fluxes in radio frequency biased inductively coupled plasma etching reactors, J. Appl. Phys. 79, No. 5, 2275 (1996).
14. L. H. Howell, R. B. Pember, P. Colella, J. P. Jessee, and W. A. Fiveland, A conservative adaptive-mesh algorithm for unsteady, combined-mode heat transfer using the discrete ordinates method, Numer. Heat Transfer, Part B, in press.
15. J. H. Ingold, Two-fluid theory of the positive column of a gas discharge, Phys. Fluids 15, No. 1, 75 (January 1972).
16. A. E. Koniges, G. G. Craddock, D. D. Schnack, and H. R. Strauss (Eds.), Proceedings, the Workshop on Adaptive Grid Methods for Fusion Plasmas, Lawrence Livermore National Laboratory, Technical Report CONE-941279, July 1995.
17. M. J. Kushner, W. Z. Collison, M. J. Grapperhaus, J. P. Holland, and M. S. Barnes, A three-dimensional model for inductively coupled plasma etching reactors: Azimuthal symmetry, coil properties, and comparison to experiments, J. Appl. Phys. 80, No. 3, 1337 (1996).
18. M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing (Wiley, New York, 1994).
19. D. M. Manos and D. L. Flamm, Plasma Etching: An Introduction (Academic Press, San Diego, 1989).
20. D. F. Martin, An Adaptive Cell-Centered Projection Method for the Incompressible Euler Equations, Ph.D. thesis, University of California at Berkeley, December 1998.
21. S. F. McCormick, MultiLevel Adaptive Methods for Partial Differential Equations, Frontiers in Applied Mathematics, Vol. 6 (SIAM, Philadelphia, 1989).
22. R. B. Pember, L. H. Howell, J. B. Bell, P. Colella, W. Y. Crutchfield, W. A. Fiveland, and J. P. Jesse, An adaptive projection method for the modeling of unsteady, low-mach number combustion, in Proceedings, Fall Meeting of the Western States Section of the Combustion Institute, 1997.
23. I. Peres and M. J. Kushner, Spatial distributions of power and ion densities in rf excited remote plasma reactors, Plasma Sources Sci. Technol. 5, 499 (1996).
24. 4 radio-frequency discharges for plasma etching, J. Vacuum Sci. Technol. B 10, No. 5, 2179 (1992).
25. O. Steiner, M. Knolker, and M. Schussler, Solar Surface Magnetism (Kluwer Academic, Dordrecht/Norwell, MA, 1994), p. 441.
26. R. A. Stewart, P. Vitello, and D. B. Graves, Two-dimensional fluid model of high density inductively coupled plasma sources, J. Vacuum Sci. Technol. B 12 (January 1994).
27. R. A. Stewart, P. Vitello, D. B. Graves, E. F. Jaeger, and L. A. Berry, Plasma uniformity in high-density inductively coupled plasma tools, Plasma Sources Sci. Technol. 4 (1995).
28. W. Tan, R. J. Hoekstra, and M. J. Kushner, A time dependent propagator method for long mean free path transport of neutral particles in plasma processing reactors, J. Appl. Phys. 79, No. 7, 3423 (1996).
29. P. L. G. Ventzek, M. Grapperhaus, and M. J. Kushner, Investigation of electron source and ion flux uniformity in high plasma density inductively coupled etching tools using two-dimensional modeling, J. Vacuum Sci. Technol. B 12, No. 6, 3118 (1994).
30. P. L. G. Ventzek, R. J, Hoekstra, and M. J. Kushner, Two-dimensional modeling of high density inductively coupled sources for materials processing, J. Vacuum Sci. Technol. B 12, No. 1, 461 (1994).
31. P. Wainman, R. A. Stewart, M. A. Lieberman, D. B. Graves, and P. Vitello, Comparison of langmuir probe characterization and model predictions in a high density ICP source, Bull. Am. Phys. Soc. 39, No. 6 (1994).
32. D. D. Wake, Simulation of Plasma Based Semiconductor Manufacturing Using Block Structured Locally Refined Grids, Ph.D. thesis, University of California at Davis, 1998.
33. H. Wu, B. W Yu, M. L. Li, and Y Yang, Two-dimensional fluid model simulation of bell jar top inductively coupled plasma, IEEE Trans. Plasma Sci. 25, No. 1, 1 (February 1997).