Calculation of Electron Swarm Parameters in Tetrafluoromethane
The electron swarm parameters and electron energy distribution function (EEDF) are necessary, especially on
understanding quantitatively plasma phenomena and ionized gases. The EEDF and electron swarm parameters including the reduce effective ionization coefficient (α-η)/N (α and η are the ionization and attachment coefficient, respectively), electron drift velocity, electron mean energy, characteristic energy, density normalized longitudinal diffusion coefficient, and density normalized electron mobility in tetrafluoromethane (CF4) which was analyzed and calculated using the two-term approximation of the Boltzmann equation method at room temperature, over a range of the reduced electric field strength (E/N) between 0.1 and 1000 Td
(1Td=10-17 V.cm2), where E is the electric field and N is the gas density of the gas. The calculations required cross-sections of the electron beam, thus published momentum transfer, vibration, electronic excitation, ionization, and attachment cross-sections for CF4 were used, the results of the Boltzmann equation in a good agreement with experimental and theoretical values over the entire range of E/N. In all cases, negative differential conductivity regions were found. It is found that the calculated EEDF closes to Maxwellian distribution and decreases sharply at low E/N. The low energy part of EEDF flats and the high-energy tail of EEDF increases with increase E/N. The EEDF found to be non-Maxwellian when the E/N> 10Td, having
energy variations which reflect electron/molecule energy exchange processes. In addition, limiting field strength (E/N)limit has been calculated from the plots of (α-η)/N, for which the ionization exactly
balances the electron attachment, which is valid for the analysis of insulation characteristics and application to power equipment.
Bordage, M.C., and Segur, P., 1999. Boltzmann analysis of electron swarm parameters in CF4 using independently assessed electron-collision cross sections. Journal of Applied Physics, 86(7), pp.3558-3566.
Bordage, M.C., Segur, P., and Chouki, A., 1996. Determination of a set of electron impact cross sections in tetrafluoromethane consistent with experimental determination of swarm parameters. Journal Applied Physics, 80(3), pp. 1325- 1336.
Christophorou, L.G., and Olthoff, J.K., 2004. Fundamental Electron Interactions with Plasma Processing Gases. Kluwer Academic/Plenum Publisher, New York, pp.135-218.
Colonna, G., and D’Angelo A., 2016. The Two-term Boltzmann Equation. Plasma Modeling Methods and Applications. Ch. 2., IOP Publishing Ltd., United Kingdom, pp.2-34.
Cox, T.I., Deshmukh, V.G.I., and Armour, D.G., 1989. Reactive ion beam etching studies of tungsten with CF4/argon mixtures using ion scattering spectroscopy and SIMS. Vacuum, 39(11-12), pp.1171-1173.
Curtis, M.G., Isobel, C.W., and Mathieson, K.J., 1988. Electron swarm characteristic energies (Dr/µ) in tetrafluoromethane (CF4) at low E/N. Journal of Physics D: Applied Physics, 21(8), pp.1271-1274.
Do, A.T., 2016. Analysis of electron transport coefficients in binary mixtures of TEOS gas with Kr, Xe, He, and Ne gases for using in plasma assisted thin film deposition. Journal of Electrical Engineering and Technology, 11(2), pp.455-462.
Duzkaya, H., and Tezcan, S.S., 2017. Measurement and calculation of breakdown voltage in CF4 gas mixtures. Gazi Üniversitesi Journal Science Part C, 5(3), pp.185-195.
Duzkaya, H., and Tezcan, S.S., 2019. Boltzmann analysis of electron swarm parameters in CHF3+CF4 mixtures. Turkish Journal of Electrical Engineering and Computer Sciences, 27, pp.615-622.
Frost, L.S., and Phelps, A.V., 1962. Rotational excitation and momentum transfer cross sections for electrons in H2 and N2 from transfer coefficients. Physical Review, 127(5), pp.1621-1633.
Gassman, M., 1974. Freon-14 in high-grade krypton and in the atmosphere. Geophysics Research Letter, 6, pp.609-612.
Hagelaar, G.J.M., and Pitchford, L.C., 2005. Solving the Boltzmann equation to obtain electron transport coefficients and rate coefficients for fluid models. Plasma Sources Science and Technology, 14(4), pp.722-733.
Hioki, K., Hirata, H., Nakano, N., Petrovic, Z.L., and Makabe, T., 2000. Diagnostics of an inductively coupled CF4/Ar plasma. Journal of Vacuum Science Technology A Vacuum Surfaces and Films, 18(3), pp.864-872.
Holstein, T., 1946. Energy distribution of electrons in high frequency gas discharges. Physical Review, 70(5-6), pp.367-384.
Hunter, S.E., Carter, J.G., and Christophorou, L.G., 1988. Electron motion in the gases CF4, C3F8 and n-C4F10. Physical Review A General Physics, 38(1), pp.58-69.
Hunter, S.R., Carter, J.G., and Christophorou, L.G., 1985. Electron transport studies of gas mixtures for use in e-beam controlled diffuse discharge switches. Journal Applied Physics, 58(8), pp.3001-3015.
Jiang, P., and Economou, D.J., 1993. Temporal evolution of the electron energy distribution functions in oxygen and chlorine gases under dc and ac fields. Journal of Applied Physics, 73(12), pp.8151-8160.
Kitajima, T., Takeo, Y., Petrovic, Z.L., and Makabe, T., 2000. Functional separation of biasing and sustaining voltages in two-frequency capacitively coupled plasma. Applied Physics Letters, 77(4), pp.489-491.
Kurihara, M., Petrovic, Z.L., and Makabe, T., 2000. Transport coefficients and scattering cross-sections for plasma modeling in CF4-Ar mixtures: A swarm analysis. Journal of Physics D: Applied Physics, 33(7), pp.2146-2153.
Lee, Y.T., and More, R.M., 1984. An electron conductivity model for dense plasmas. Physics of Fluids, 27(5), pp.1273-1286.
Li, X., Zhao, H., and Jia, S., 2012. Dielectric breakdown properties of SF6-N2 mixtures in the temperature range 300-3000K. Journal Physics D: Applied Physics, 45(44), p.445202.
Liu, X., and Xiao, D., 2007. Monte Carlo simulation of electron swarm parameters in the SF6/CF4 gas mixtures. The Japan Society of Applied Physics. 46(4A), pp.1664-1667.
Mašek, K., Láska, L., D’Agostino, R., and Cramarossa, F., 1987. Boltzmann equation analysis of the electron gas in CF 4 discharges plasma. Contributions to Plasma Physics, 27(1), pp.15-21.
Michele, R., 2018. A Monte-Carlo software tools for the characterization of gas mixtures in various detector. Romanian Journal of Physics, 63, pp.8-10.
Muhle, J., Ganesan, A.L., Miller, B.R., Salameh, P.K., Harth, C.M., Greally, B.R., Rigby, M., Porter, L.W., Steele, L.P., Trudinger, C.M., Krummel, P.B., O’Doherty, S., Fraser, P.J., Simmonds, P.G., Prinn, R.G., and Weiss, R.F., 2010. Perfluorocarbons in the global atmosphere: Tetrafluoromethane, hexafluoroethane, and octafluoropropane. Atmospheric Chemistry and Physics, 10(11), pp.5145-5164.
Nakamura, Y., 1996. Electron Swarm Parameters in Pure CF4 and its Electron Collision Cross Sections. Imaging Detectors in High Energy, Astroparticle and Medical Physics: Proceedings of the UCLA International Conference. World Scientific Publishing Co Inc., Singapore, pp.75-79.
Pinheiro, M.J., and Loureiro, J., 2002. Effective ionization coefficients and electron drift velocities in gas mixtures of SF6 with He, Xe, CO2 and N2 from Boltzmann analysis. Journal of Physics D: Applied Physics, 35(23), pp.3077- 3084.
Proshina, O.V., Rakhimova, T.V., Lopaev, D.V., Samara, V., Baklanov, M.R., and de Marneff, J.F., 2015. Experimental and theoretical study of RF capacitively coupled plasma in Ar-CF4-CF3I mixtures. Plasma Sources Science and Technology, 25, p.055006.
Reinking, G.F., Christophorou, L.G., and Hunter, S.R., 1986. Studies of total ionization in gases/mixtures of interest to pulsed power applications. Journal Applied Physics, 60(2), pp.499-508.
Sang-Nam, K., 2011. The drift velocity of electron in CF4, CH4, Ar mixtures gas. The Transactions of the Korean Institute of Electrical Engineers P, 60(3), pp.105-109.
Sang-Nam, K., 2012. Ionization and attachment coefficients in CF4, CH4, Ar mixtures gas. The Transactions of the Korean Institute of Electrical Engineers P, 61(1), pp.13-17.
Sang-Nam, K., 2015. Electron mean energy in CF4, CH4, Ar mixtures. The Transactions of the Korean Institute of Electrical Engineers P, 64(4), pp.241-245.
Smith, K., and Thomson, R.M., 1978. Computer Modeling of Gas Lasers. Plenum Press, New York.
Stefanov, B., and Pirgov, P., 1993. Semiempirical method for extracting electron molecule cross sections from experimental data: CF4 as an example. Plasma Chemistry and Plasma Processing, 13(4), pp.655-671.
Tezcan, S.S., Dincer, M.S. and Bektas, S., 2016. Effective ionization coefficients, limiting electric fields, and electron energy distributions in CF3I+CF4+Ar ternary gas mixtures. Physics of Plasma, 23(7), p.073507.
Tezcan, S.S., Dincer, M.S., Bektas, S., and Hiziroglu, H.R., 2013. Boltzmann analysis of electron swarm parameters in binary CF4+Ar mixtures. IEEE Transactions on Dielectrics and Electrical Insulation, 20(1), pp.98-103.
Tezcan, S.S., Duzkaya, H., Dincer, M.S., and Hiziroglu, H.R., 2016. Assessment of electron swarm parameters and limiting electric fields in SF6+CF4+Ar gas mixtures. IEEE Transactions on Dielectrics and Electrical Insulation, 23(4), pp.1996-2005.
Vasenkov, A.V., 1999. Electron swarm parameters in carbon tetrafluoride. Journal of Applied Physics, 85(2), pp.1222-1224.
Wu, B.T., Xiao, D.M., and Zhang, L.C., 2006. Electron swarm coefficients in SF6 and CF4 gas mixtures from Monte Carlo method. The European Physical Journal Applied Physics, 35(1), pp.57-60.
Xiao, D.M., and Deng, Y., 2013. Determination of electron swarm parameters in pure CHF3 and CF4 by a time-resolved method. Plasma Science and Technology, 15(1), pp.25-29.
Xiao, D.M., Yang, J.L., and Xu, X., 2004. Electron swarm parameters in SF6 and CF4 gas mixtures. Japanese Journal of Applied Physics, 43(3A), pp.L369-L371.
Xueli, L., and Xiao, D.M., 2007. Monte Carlo simulation of electron swarm parameters in the SF6/CF4 gas mixtures. Japanese Journal of Applied Physics, 46(4A), pp.1663-1667.
Copyright (c) 2020 Idris H. Salih, Mohammad M. Othman, Sherzad A. Taha
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY-NC-SA 4.0] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).