Electron Mean Energy in CF4, CH4, Ar mixtures

CF4, CH4, Ar 혼합기체의 전자 평균에너지

  • Kim, Sang-Nam (Dept. of Electrical Engineering, Incheon National University)
  • Received : 2015.10.06
  • Accepted : 2015.11.19
  • Published : 2015.12.01


Energy Distribution Function in pure $CH_4$, $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The calculations of electron swarm parameters require the knowledge of several collision cross-sections of electron beam. Thus, published momentum transfer, ionization, vibration, attachment, electronic excitation, and dissociation cross-sections of electrons for $CH_4$, $CF_4$ and Ar, were used. The differences of the transport coefficients of electrons in $CH_4$, mixtures of $CH_4$ and Ar, have been explained by the deduced energy distribution functions for electrons and the complete collision cross-sections for electrons. The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4$-Ar mixtures shows the Maxwellian distribution for energy. That is, $f({\varepsilon})$ has the symmetrical shape whose axis of symmetry is a most probably energy.


Monte Carlo simulation(MCS);Boltzmann equation(BEq);Mean energy;Tetrafluoro methane


  1. Flamm D. L., "Plasma Processing of Semiconductors" Williams P F, NATO ASI series, pp.1-22. 1997.
  2. H. Itoh, T. Matsumura, K. Satoh, Y. Nakao and H. Tagashira, "Development of electrons swarms in $CF_{4}$", Proc. 21st int. Conf. on Phenomena in Ionized Gases, (ICPIG) (Bochum : Germany) 1, pp. 245-6, 1993.
  3. R. W. L. Thomas, and W. R. L. Thomas, "Monte Carlo Simulation of electrical discharge in gases", J. Phys. B. Vol.2, pp.562-570, 1969.
  4. E. W. Mc Daniel and E. A. Mason "The Mobility and Diffusion off Ions in Gases" John Wiley and Sons. Inc. pp. 3-82, 1973
  5. S. A. J. Al-Amin and J. Lucas, "Electron swarm parameters in oxygen and methane", J. Phys. D:Appl.
  6. Y. Nakamura and M. Kurachi "Electron Transport Parameters in Argon and its momentum transfer cross section" J.Phys.21, pp.718-723, 1988
  7. L. G. H. Huxley & R. W. Cormpton. "The Diffusion and Drift of Electrons in Gases" John Wiley and Sons. Inc 1974
  8. A. Gilardini, "Low Energy Electron Collisions in Gases" John Wiley and Sons. lnc. pp.127-162. 1972
  9. K. L. Bell, N. S. Scott and M. A. Lennon, "The Scattering of low-energy electrons by Argon atoms" J. Phys. B: At. Mol. Phys. 17, pp. 4757-4765, 1984
  10. K. L. Bell, N. S. Scott and M. A. Lennon, "The Scattering of low-energy electrons by Argon atoms" J. Phys. B: At. Mol. Phys. 17, pp. 4757-4765, 1984
  11. W. C. Fon, K. A. Berrington, P. G. Burke, "The elastic Scattering of electrons from inert gases:
  12. M. Hayashi, "Swarm Studies and Inelastic Electron-Molecule Collisions", L. C. Pitchford, Springer-Verlag, 1986.
  13. S. N Kim, "Ionization and Attachment Coefficients in $CF_{4}$, $CH_{4}$, Ar Mixtures Gas" 61P-1-4, KIEE, pp13-18, 2012
  14. S. N. Kim, "Electron Energy Distribution function in $CF_{4}$ gas by MCSBEq" 62P-1-4, KIEE, pp. 18-22, 2013
  15. S. N. Kim, "Diffusion coefficients for electrons in $SF_{6}$-Ar Gas Mixtures by MCS-BEq" 64P-3-6, KIEE, pp. 125-129, 2015