Skip to main content
Log in

Time-dependent solution of Boltzmann equation in rf plasmas: A comparison with the effective field approximation

  • Published:
Plasma Chemistry and Plasma Processing Aims and scope Submit manuscript

Abstract

Electron isotropic distribution function (idf) and related quantities in rf plasmas (CO, H2, Ne), calculated by solving the time-dependent Boltzmann equation, are compared with the corresponding values obtained by using the effective field approximation (efa). We show that the agreement between the two methods depends on the ratio between the applied field frequency and the lumped frequencies for impulse and energy dissipation. In fact, only at moderately high field frequencies are results obtained according to efa comparable with the corresponding ones obtained by the time-dependent solution and subsequent time averaging, while in the other cases differences up to two orders of magnitude are observed.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Winkler, H. Deutsch, J. Wilhelm, and Ch. Wilke,Beitr. Plasmaphys. 24, 285 (1984).

    Google Scholar 

  2. R. Winkler, J. Wilhelm, and A. Hess,Ann. Phys. 42, 537 (1985).

    Google Scholar 

  3. R. Winkler, M. Capitelli, M. Dilonardo, C. Gorse, and J. Wilhelm,Plasma Chem. Plasma Process. in press.

  4. R. Winkler, H. Deutsch, J. Wilhelm, and Ch. Wilke,Beitr. Plasmaphys. 24, 303 (1984).

    Google Scholar 

  5. H. Margenau,Phys. Rev. 69, 508 (1946);73, 297 (1948); H. Margenau and L. M. Hartmann,Phys. Rev. 73, 309 (1948).

    Google Scholar 

  6. T. Holstein,Phys. Rev. 70, 367 (1946).

    Google Scholar 

  7. S. C. Brown,Encyclopedia of Physics, Vol. 22, Springer, Berlin (1956), p. 531.

    Google Scholar 

  8. W. P. Allis,Encyclopedia of Physics, Vol. 21, Springer, Berlin (1956), p. 383.

    Google Scholar 

  9. C. M. Ferreira and J. Loureiro,J. Phys. D: Appl. Phys. 16, 2471 (1983).

    Google Scholar 

  10. S. Veprek and P. Kocian,Helv. Phys. Acta 46, 447 (1973);Pure Appl. Chem. 48, 163 (1976).

    Google Scholar 

  11. R. A. Gottscho, R. H. Burton, D. L. Flamm, V. M. Donnelly, and G. P. Davis,J. Appl. Phys. 55, 2707 (1984).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Winkler, R., Dilonardo, M., Capitelli, M. et al. Time-dependent solution of Boltzmann equation in rf plasmas: A comparison with the effective field approximation. Plasma Chem Plasma Process 7, 125–137 (1987). https://doi.org/10.1007/BF01016003

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01016003

Key Words

Navigation