Skip to main content

Fluid and Hybrid Models of Non Equilibrium Discharges

  • Chapter
Book cover Plasma Processing of Semiconductors

Part of the book series: NATO ASI Series ((NSSE,volume 336))

Abstract

In this paper we present a general discussion of fluid and hybrid models of non equilibrium discharge plasmas. We emphasize in particular the description of the charge particle — electric field submodel and do not consider the questions of plasma chemistry and plasma surface interaction. Assumptions implied by the fluid description, and some aspects of the numerical methods are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Birdsall, C.K., Plasma Processing of Semiconductors (Kluwer, Dordrecht, 1997).

    Google Scholar 

  2. Pitchford, L.C., Ouadoudi, N., Boeuf, J.P., Legendi, M., Puech, V., Thomaz, J.C., and Gundersen, M.A. (1995) Triggered breakdown in low-pressure hollow cathode (pseudospark) discharges, Journal of Applied Physics 78, 77–89.

    Article  Google Scholar 

  3. Boeuf, J.P., and Pitchford, L.C. (1991) Pseudo-spark discharges via computer simulation, IEEE Trans. Plasma Sci. 19, 286.

    Article  Google Scholar 

  4. Lieberman, M.A., and Lichtenberg, A.J., Principles of plasma discharges and material processing (John Wiley & sons, N.Y., 1994).

    Google Scholar 

  5. Nitschke, T.E, and Graves, D.B. (1994) A comparison of particle in cell and fluid model simulations of low-pressure radio frequency discharges, J. Appl. Phys. 76, 5646–5660.

    Article  Google Scholar 

  6. Turner, M.M. (1995) Pressure heating of electrons in capacitively coupled rf discharges, Phys. Rev. Lett. 75, 1312–1315.

    Article  Google Scholar 

  7. Turner, M.M. (1993) Collisionless heating in an inductively coupled discharge, Phys. Rev. Lett. 71, 1844–1847.

    Article  Google Scholar 

  8. Vahedi, V., Lieberman, M.A., Peso, G. Di, Rognlien, T.D., and Hewett, D. (1995) Analytic model of power deposition in inductively coupled plasma sources, J. Appl. Phys. 78, 14461458.

    Article  Google Scholar 

  9. Turner, M.M. (1996) Simulation of kinetic effects in inductive discharges, Plasma Sources Sci. Technol. 5, 159–165.

    Article  Google Scholar 

  10. Surendra, M., Graves, D.B., and Piano, L.S. (1992) Self-consistent dc glow discharge simulations applied to diamond film deposition reactors, J. Appl. Phys. 71, 5169–5198.

    Article  Google Scholar 

  11. Fiala, A, Pitchford, L.C, and Boeuf, J.P (1994) Two-dimensional, hybrid model of low-pressure glow discharges, Physical Review E 49, 5607–5622.

    Article  Google Scholar 

  12. Sommerer, T.J., and Kushner, M.J. (1992) Numerical Investigations of the Kinetics and Chemistry of rf Glow Discharges sustained in He, N2, O2, He/N2/O2, CF4/O2, and SiH4/NH3 using a Monte Carlo fluid hybrid model, J. Appl. Phys. 71, 1654–1673.

    Article  Google Scholar 

  13. Ventzek, P.L.G., Sommerer, T.J., Hoekstra, R.J., and Kushner, MJ. (1993) Two-dimensional hybrid model of inductively coupled plasma sources for etching, Appl. Phys. Lett. 63, 605–607.

    Article  Google Scholar 

  14. Ventzek, P.L.G., Hoekstra, R.J., and Kushner, MJ. (1994) Two-dimensional Modeling of high plasma density inductively coupled sources for plasma processing, J. Vac. Sci. Technol. B 12, 461.

    Google Scholar 

  15. Belenguer, Ph., and Boeuf, J.P. (1990) Transition between different regimes of rf glow discharges, Phys. rev. A 41, 4447–4459.

    Article  Google Scholar 

  16. Porteous, R.K., Wu, H.M., and Graves, D.B. (1993) A two-dimensional, axysymmetric model of a magnetized glow discharge plasma, Plasma Sources Sci. Technol. 3, 25–39.

    Article  Google Scholar 

  17. Boeuf, J.P., and Pitchford, L.C., Two-dimensional model of stationnary plasma thrusters, presented at the Proc. IEEE Int. Conf. on Plasma Sci.„ Santa Fe, New Mexico, USA, 1994 (unpublished).

    Google Scholar 

  18. Nitschke, T.E., and Graves, D.B. (1995) Matching an rf sheath model to a bulk plasma model, IEEE trans. Plasma Sci. 23, 717–727.

    Article  Google Scholar 

  19. Pérès, I., Fortin, M., and Margot, J. (1996) The radial structure of a magnetically confined surface-wave plasma column, Phys. Plasmas 3, 1754–1769.

    Article  Google Scholar 

  20. DiPeso, G., Vahedi, V., D.W. Hewett, and Rognlien, T.D. (1994) Two-dimensional self-consistent fluid simulation of radio frequency inductive sources, J. Vac. Sci. Technol. A 12, 1387–1396.

    Article  Google Scholar 

  21. Lymberopoulos, D.P., and Economou, D. (1995) Two-dimensional simulation of polysilicon etching with chlorine in a high density plasma reactor, IEEE Trans. Plasma Sci. 23, 573–580.

    Article  Google Scholar 

  22. Merad, A., and Boeuf, J.P. (1996) Unpublished.

    Google Scholar 

  23. Boeuf, J.P., and Pitchford, L.C., SIGLO-2D, a 2D user-friendly model for glow discharge simulation (Kinema Research, siglo@kinema.com, Monument, CO, 1996).

    Google Scholar 

  24. Greenberg, K.E., Hargis, P.J., Jr, and Miller, P.A., (1990) The GEC rf reference cell: diagnostics techniques and initial results, Sandia National Laboratories Report SETEC90-013

    Google Scholar 

  25. see also Hargis, P.J., Jr, et al. (1994) The Gaseous Electronics Conference radio-frequency reference cell: A defined parallel plate radio-frequency system for experimental and theoretical studies of plasma processing discharges, Rev. Sci. Instrum. 65, 140–154.

    Article  Google Scholar 

  26. Pitchford, L.C., Boeuf, J.P., and Morgan, W.L., BOLSIG, a 2 term, user-friendly solver for the electron Boltzmann equation (Kinema Research, siglo@kinema.com, Monument, CO, 1996).

    Google Scholar 

  27. Barnes, M.S., Colter, T.J., and Elta, M.E. (1988) A staggered-mesh finite-difference numerical method for solving the transport equations in low pressure rf discharges, J. Comp. Phys. 77, 53–72.

    Article  MATH  Google Scholar 

  28. Graves, D.B. (1986) A continuum model of dc and rf discharges, IEEE Trans. Plasma Sci. 14, 78–91.

    Article  Google Scholar 

  29. Richards, A.D., Thompson, B.E., and Sawin, H.H. (1987) Continuum modeling of argon radio frequency glow discharges, Appl. Phys. Lett. 50, 492–494.

    Article  Google Scholar 

  30. Gogolides, E., and Sawin, H.H. (1992) Continuum modeling of radio-frequency glow discharges. I. Theory and results for electropositive and electronegative gases, J. Appl. Phys. 72, 3971–3987.

    Article  Google Scholar 

  31. Passchier, J.D.P., and Goedheer, W.J. (1993) A two-dimensional fluid model for an argon rf discharge, J. Appl. Phys. 74, 3744–3751.

    Article  Google Scholar 

  32. Lymberopoulos, D.P., and Economou, D.J. (1994) Modeling and simulation of glow discharge plasma reactors, J. Vac. Sci. Technol. A 12, 1229–1236.

    Google Scholar 

  33. Lymberopoulos, D.P., and Economou, D.J. (1995) Two-dimensional self-consistent radio frequency plasma simulations relevant to the gaseous electronics conference if reference cell, J. Res. Natl. Inst. Stand. Technol. 100, 473–494.

    Article  Google Scholar 

  34. Meyyappan, M., and Govindan, T.R. (1993) Radio frequency discharge modeling: Moment equations approach, J. Appl. Phys. 74, 2250–2259.

    Article  Google Scholar 

  35. Boeuf, J.P., and Pitchford, I.C. (1995) Two-dimensional model of a capacitively coupled rf discharge and comparisons with experiments in the Gaseous Electronics Conference reference reactor, Phys. Rev. E 51, 1376–1390.

    Article  Google Scholar 

  36. Nakano, N., Shimura, N., Petrovic, Z. Lj., and Makabe, T. (1994) Simulations of rf glow discharges in SF6 by the relaxation continuum model, Phys. rev. E 49, 4455–4465.

    Article  Google Scholar 

  37. Boeuf, J.P., and Pitchford, L.C., SIGLO-RF, a 1D user-friendly model for rf discharge simulation (Kinema Research, siglo@kinema.com, Monument, CO, 1995).

    Google Scholar 

  38. Surendra, M. (1995) Radiofrequency discharge benchmark model comparison, Plasma Sources Sci. Technol. 4, 56–73.

    Article  Google Scholar 

  39. Gogolides, E., H.H. Sawin, and Brown, R.A. (1992) Direct calculations of time-periodic states of continuum models of radio-frequency plasmas, Chem. Eng. Sci. 47, 3839–3855.

    Article  Google Scholar 

  40. Wu, C.H.J., Meyyapan, M., and Economou, D.J. (1995) Special Issue on Modeling and Simulation of Collisional Low-Temperature Plasmas, IEEE Trans. Plasma Sci. 23.

    Google Scholar 

  41. Kushner, M.J., and Ruzik, D.N. (1996) Special Issue on Images in Plasma Science, IEEE Trans. Plasma Sci. 24.

    Google Scholar 

  42. (1995) J. Res. Natl. Inst. Stand. Technol. 100.

    Google Scholar 

  43. Boeuf, J.P., Belenguer, Ph., and Hbid, T. (1994) Plasma Particle Interactions, Plasma Sources Sci. Technol. 3, 407–417.

    Article  Google Scholar 

  44. Dalvie, M., Surendra, M., Selwyn, G.S., and Guarnieri, C.R. (1994) Detection and modeling of electrode topography effects on particle traps, Plasma Sources Sci. Technol. 3, 442–447.

    Article  Google Scholar 

  45. (1994) Special Issue on “Formation, Transport, and Consequences of Particles in Plasmas”, Plasma Sources Sci. Technol..

    Google Scholar 

  46. Dorier, J.L., Hollenstein, C., Howling, A.A., Courteille, C, Scwarzenbach, W., Merad, A., and Boeuf, J.P. (1996) Global visualization of powder trapping in capacitive if plasmas by two-dimensional laser scattering, IEEE Trans. Plasma Sci. 24, 101–102.

    Article  Google Scholar 

  47. Dorier, J.L., “Genese, croissance et consequences de particules dans les plasmas de silane à basse pression et basse temperature,”, Ecole Polytechnique Fédérale de Lausanne, 1996.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Boeuf, JP., Merad, A. (1997). Fluid and Hybrid Models of Non Equilibrium Discharges. In: Williams, P.F. (eds) Plasma Processing of Semiconductors. NATO ASI Series, vol 336. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5884-8_16

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-5884-8_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6486-6

  • Online ISBN: 978-94-011-5884-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics