Plasma Physics Reports

, Volume 45, Issue 8, pp 786–797 | Cite as

Simulation of an Inductive Discharge in Argon with the Gas Flow and Inhomogeneous Gas Temperature

  • A. N. Kropotkin
  • D. G. VoloshinEmail author


With the purpose to create new methods for monitoring the parameters of low-temperature nonequilibrium plasma, a numerical drift-diffusion model of an inductive RF discharge in argon is developed and a study is made of ion transport onto the surface of the processed material. The model was tested against the available experimental and theoretical data. The calculations were performed for an inductive discharge in argon with parameters typical of modern plasmachemical reactors (a frequency of 13.56 MHz and a gas pressure in the chamber of 10 mTorr). The plasma density, electron temperature, and ion flux onto the processed surface are calculated; the gas temperature is found as a function of the input RF power; and the discharge parameters are determined as functions of the gas flow rate.



This study was supported by the Russian Science Foundation, project no. 18-72-00155.


  1. 1.
    J. Hopwood, Plasma Sources Sci. Technol. 1, 109 (1992).ADSCrossRefGoogle Scholar
  2. 2.
    M. Laroussi, Plasma Process. Polym. 2, 391 (2005).CrossRefGoogle Scholar
  3. 3.
    J. Lettry, D. Aguglia, J. Alessi, P. Andersson, S. Bertolo, S. Briefi, A. Butterworth, Y. Coutron, A. Dallocchio, N. David, E. Chaudetet, D. Faircloth, U. Fantz, D. A. Fink, M. Garlasche, et al., Rev. Sci. Instrum. 87, 02B139 (2016).Google Scholar
  4. 4.
    U. Fantz, B. Heinemann, D. Wunderlich, R. Riedl, W. Kraus, R. Nocentini, and F. Bonomo, Rev. Sci. Instrum. 87, 02B307 (2016).Google Scholar
  5. 5.
    V. M. Donnelly and A. Kornblit, J. Vac. Sci. Technol. A 31, 050825 (2013).CrossRefGoogle Scholar
  6. 6.
    S. D. Athavale and D. J. Economou, J. Vac. Sci. Technol. 14, 3702 (1996).CrossRefGoogle Scholar
  7. 7.
    H. Shin, W. Zhu, L. Xu, V. M. Donnelly, and D. J. Economou, Plasma Sources Sci. Technol. 20, 055001 (2011).ADSCrossRefGoogle Scholar
  8. 8.
    J. Meichsner and T. Wegner, Eur. Phys. J. D 72, 85 (2018).ADSCrossRefGoogle Scholar
  9. 9.
    I. Adamovich, S. D. Baalrud, A. Bogaerts, P. J. Bruggeman, M. Cappelli, V. Colombo, U. Czarnetzki, U. Ebert, J. G. Eden, P. Favia, D. B. Graves, S. Hamaguchi, G. Hieftje, M. Hori, I. D. Kaganovich, et al., J. Phys. D 50, 323001 (2017).CrossRefGoogle Scholar
  10. 10.
    A. F. Aleksandrov, K. V. Vavilin, E. A. Kral’kina, V. B. Pavlov, and A. A. Rukhadze, Plasma Phys. Rep. 33, 746 (2007).ADSCrossRefGoogle Scholar
  11. 11.
    D. V. Lopaev, T. V. Rakhimova, A. T. Rakhimov, A. I. Zotovich, S. M. Zyryanov, and M. R. Baklanov, J. Phys. D 51, 02LT02 (2018).Google Scholar
  12. 12.
    S. Uchida, S. Takashima, M. Hori, M. Fukasawa, K. Ohshima, K. Nagahata, and T. Tatsumi, J. Appl. Phys. 103, 073303 (2008).ADSCrossRefGoogle Scholar
  13. 13.
    M. R. Baklanov, J.-F. de Marneffe, D. Shamiryan, A. M. Urbanowicz, H. Shi, T. V. Rakhimova, Huai Huang, and P. S. Ho, J. Appl. Phys. 113, 041101 (2013).ADSCrossRefGoogle Scholar
  14. 14.
    K. Nishida, S. Mattei, S. Mochizuki, J. Lettry, and A. Hatayama, J. Appl. Phys. 119, 233302 (2016).ADSCrossRefGoogle Scholar
  15. 15.
    K. Nishida, M. Onai, J. Lettry, M. Q. Tran, and A. Hatayama, J. Comput. Phys. 350, 891 (2017).ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    E. Kawamura, C. K. Birdsall, and V. Vahedi, Plasma Sources Sci. Technol. 9, 413 (2000).ADSCrossRefGoogle Scholar
  17. 17.
    T. Makabe, Advances in Low Temperature RF Plasmas: Basis for Process Design (Elsevier, Amsterdam, 2002).Google Scholar
  18. 18.
    Ch. K. Birdsall and A. B. Langdon, Plasma Physics via Computer Simulation (McGraw-Hill, New York, 1985).Google Scholar
  19. 19.
    T. Tajima, Computational Plasma Physics (Addison-Wesley, Redwood City, CA, 1988).Google Scholar
  20. 20.
    J. Cheng, L. Ji, Y. Zhu, and Y. Shi, J. Semicond. 31, 032004 (2010).Google Scholar
  21. 21.
    E. Gogolides and H. H. Sawin, J. Appl. Phys. 72, 3971 (1992).ADSCrossRefGoogle Scholar
  22. 22.
    C.-C. Hsu, M. A. Nierode, J. W. Coburn, and D. V. Graves, J. Phys. D 39, 3272 (2006).ADSCrossRefGoogle Scholar
  23. 23.
    H. C. Kim, F. Iza, S. S. Yang, M. Radmilović-Radjenović, and J. K. Lee, J. Phys. D 38, R283 (2005).ADSCrossRefGoogle Scholar
  24. 24.
    A. O. Brezmes and C. Breitkopf, Vacuum 116, 65 (2015).ADSCrossRefGoogle Scholar
  25. 25.
    D. P. Lymberopoulos and D. J. Economou, J. Res. Nat. Inst. Stand. Technol. 100, 473 (1995).CrossRefGoogle Scholar
  26. 26.
    Yu. P. Raizer, Gas Discharge Physics (Nauka, Moscow, 1987; Springer-Verlag, Berlin, 1991).Google Scholar
  27. 27.
    G. J. M. Hagelaar and L. C. Pitchford, Solving the Boltzmann Equation to Obtain Electron Transport Coefficients and Rate Coefficients for Fluid Models (Centre de Physique des Plasmas et de leurs Applications de Toulouse Toulouse, 2005).Google Scholar
  28. 28.
    A. O. Brezmes and C. Breitkopf, Vacuum 109, 52 (2014).ADSCrossRefGoogle Scholar
  29. 29.
    H. Singh and D. B. Graves, J. Appl. Phys. 88, 3889 (2000).ADSCrossRefGoogle Scholar
  30. 30.
    V. A. Godyak, R. B. Piejak, and B. M. Alexandrovich, Plasma Sources Sci. Technol. 11, 525 (2002).ADSCrossRefGoogle Scholar
  31. 31.
    L. J. Mahoney, A. E. Wendt, E. Barrios, C. J. Richards, and J. L. Shohet, J. Appl. Phys. 76, 2041 (1994).ADSCrossRefGoogle Scholar
  32. 32.
    M. A. Lieberman and A. J. Lichtenberg, Principles of Plasma Discharges and Materials Processing (Wiley, New York, 2005).CrossRefGoogle Scholar
  33. 33.
    A. D. Richards, B. E. Thomson, and H. H. Sawin, Appl. Phys. Lett. 50, 492 (1987).ADSCrossRefGoogle Scholar
  34. 34.
    D. B. Graves, M. J. Kushner, J. W. Gallagher, A. Garscadden, G. S. Oehrlein, and A. V. Phelps, Database Needs for Modeling and Simulation of Plasma Processing. National Research Council, Panel of Database Needs in Plasma Processing (National Academy Press, Washington, DC, 1996).Google Scholar
  35. 35.
    A. V. Phelps and Z. Lj. Petrović, Plasma Sources Sci. Technol. 8, R21 (1999).ADSCrossRefGoogle Scholar
  36. 36.
    A. J. Dixon, M. F. A. Harrison, and A. C. H. Smith, J. Phys. B 9, 2617 (1976).ADSGoogle Scholar
  37. 37.
    C. Lee and M. A. Lieberman, J. Vacuum Sci. Technol. A 13, 368 (1995).ADSCrossRefGoogle Scholar
  38. 38.
    G. M. Grigor’yan, N. A. Dyatko, and I. V. Kochetov, Plasma Phys. Rep. 41, 434 (2015).ADSCrossRefGoogle Scholar
  39. 39.
    R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. II, Chaps. 15–29.zbMATHGoogle Scholar
  40. 40. Scholar
  41. 41. Scholar
  42. 42.
    A. V. Phelps, J. Appl. Phys. 76, 747 (1994).ADSCrossRefGoogle Scholar
  43. 43.
    V. A. Godyak, in Electron Kinetics and Applications of Glow Discharges, Ed. by U. Kortshagen and L. D. Tsendin (Plenum, New York, 1998), p. 241.Google Scholar
  44. 44.
    P. A. Miller, G. A. Hebner, K. E. Greenberg, P. D. Pochan, and B. P. Aragon, J. Res. Nat. Inst. Stand. Technol. 100, 427 (1995).CrossRefGoogle Scholar
  45. 45.
    A. Rezvanov, R. Chanson, L. Zhang, N. Hacker, K. A. Kurchikov, S. Klimin, S. M. Zyryanov, D. V. Lopaev, E. Gornev, I. Clemente, A. Miakonkikh, and K. I. Maslakov, J. Phys. D 51, 325202 (2018).CrossRefGoogle Scholar
  46. 46.
    R. W. Boswell and I. J. Morey, Appl. Phys. Lett. 52, 21 (1988).ADSCrossRefGoogle Scholar
  47. 47.
    K. H. A. Bogart and V. M. Donnelly, J. Appl. Phys. 86, 1822 (1999).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Skobeltsyn Institute of Nuclear Physics, Moscow State UniversityMoscowRussia

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