Journal of Science & Technology 101 (2014) 087-091
Calculations of Electron Transport Coefficients and Limiting Field Strengths in Gas Discharges for CFsI-Ne and Cb-Ne mixtures
Do Anh Tuan
Hung Yen University of Technology and Education, Khoai Chau. Hung Yen, Viet Nam Received May 16, 2013, accepted April 22, 2014
Abstract
Electron transport coefficients in gas discharges for CFsl-Ne and Ck-Ne mixtures were analysed and calculated by a two-term approximation of the Boitzmann equation in a wide E/N range (ratio of the electric field E to the neutral number density N) The electron transport coefficients include the electron driff velocity, density-normalized longitudinal diffusion coefficient, and density-normalized effective ionization coefficient These results are calculated for the first time over a wide range of E/N values The limiting field strength values of E/N. (E/N)im, for these binary gas mixtures were also derived and compared with those of the pure SFe gas. The (E/N}i,m values of CFsl-Ne mixture gas were greater than those of the pure SFe gas with the CF3I concentration equal to approximately 70%. These binary gas mixtures, therefore, may be considered to use In high voltage and many industries depending on mixture ratios and particular applications of gas and electncal equipments.
Keywords. Limiting field strength values. Electron transport coefficients, CFal-Ne mixture gas
1. Introduction
Plasma discharges for processing procedures with materials containing flounne (F ) chlorine (CI) and oxygen (Oz) molecules have been a subject of great interest because of their applications in film etching and deposition in microele<,tronic device fabrication [1] Chlorine and its mixtures are widelv used in plasma etching of semiconductois metals and gate stacks w ith high K. dielectni-s ind low K dielecQic films [2 4] Concurrendy chlorme eas was also selected as an available substitution candidate for the SFfi gas m the published patent of Luly and Richard [^] who suggested dielectric gaseous compounds unique dielectnc gases and preferred dielectric compounds, which have low global warming potential (GWP) and high dielectnc strength (i.e., a GWP less than approximately 22,200, and a dielectnc strength greater than air), and which avoid the greenhouse problems related to SFe for use in electnc equipment applications
On the other hand, recently, much research has been concentrated on trifluoroiodomethane (CF3I) gas because of its low global warmuig potential, very short atmospheric lifetime and relatively low toxicity gas [6-7] It is a gas that is a substitudon candidate for the SFe gas and as a candidate to the replacement of potent greenhouse affects. The boiling point of CF3I gas is higher than that of the S¥e gas. At an absolute pressure of 0,5 MPa, CF3I becomes liquids at about 26''C [8],
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whereas the SFs gas becomes liquids at about -30 "C [9]. On the other hand, the SFe gas is used in gas circuit breakers at 0,5 to 0.6 MPa. Therefore, it is impossible to use CF3I gas, if this gas is used at this pressure level [2] However, in order to reduce the liquefaction temperature of CF3I gas, Taki el al. [2]
decreased partial pressure by mixing it with other gases such as N2 and CO2. For example, the boiling pomt can be reduced from about 26 "C (pure CF3I) to about -12 "C at 0,5 MPa by using a 30% CF3I-CO2 mixture [3], Therefore, it is necessary to mix the CF3I gas with different buffer gases.
Moreover, the accurate electron collision cross sections and electron transport coefficients, for not only pure atoms and pure molecules but also for the binary gas mixtures, are necessary to understand quantitatively plasma phenomena and ionized gases The collision processes and electron transport coefficients of the bmary mixtures of the rare and conventional gases with each of the CF3I and CU gas have been scarce so far. To the best of our knowledge, the electron transport coefficients m CFal-Ne and Cb-Ne mixtures with the whole CF3I and CI: concentration ranges have not been previously performed in not only measurements but also calculations.
In the present study, in order to gain more insight mto the electron transport coefficients, therefore, the electron transport coefficients (electron drift velocity, density-normalized longitudmal diffusion coefficient, and density-normalized effective ionization coefficient) in a wide E/N range (ratio of the electric field E to the neutral number
Journal of Science & Technology 101 (2014) 087-091 density N) in the CFjI-Ne and Cb-Ne mixtures,
respectively, were analysed and calculated by using a two-term approximation of the Boitzmann equation for energy. The negative differential conductivity (NDC) phenomena, that is, decreasmg electron drift velocity with increasing electnc field strength [10], in these binary gas mixtures were suggested. The electron transport coefficients calculated were also compared with those of pure SF^ gas and the (E/N)iim values in those mixtures were also compared respectively with those of SF^-Ne mixtures in the experiments. These binary gas mixtures are considered to use in high voltage and many industries depending on mixture ratios and particular applications of gas and electrical equipment.
2. Analysis
The present analysis used the electron swarm method This method was previously used for calculating the electron transport coefficients and determining the sets of electron collision cross sections for CFjl [9], Cb [11], and TEOS [12]
molecules The electron transport coefficients were calculated by sets of electron collision cross sections for gases and a two-term approximation of the Boitzmann equation for the energy.
The electron drift velocity calculated from the solufion of electron energy distribution function, f(e, E/N), of the Boitzmann equation is defined as [13]
--\±\ e^ r g df{£,E/N)
where e is the electron energy, m is the electron mass, e is the elementary charge and qn,(E) is the momennim-transfer cross section.
The density-normalized longitudinal diffusion coefficient is defined as [14]
-\^l^~-^(^:^~^')<^^ + £ — F^M
IT ^^-"A-
IT
^lA "^
(2) where Vi is the speed of the electron, qr is the total cross section, Fn andro^^ (n = 0, 1, 2) are, respectively, the electron energy distnbutions of various orders and their eigenvalues Vi, u? , n?
and An are given by
V = 2e ' (2 1)
ro„ =V^Nj\'^^qF^ds. (2.2)
-^/;^|,,.x,.,,„.,.„,.
(2.3) (2.4)
A_=£F_de. (2.5) where q, is the ionization cross section.
The Townsend first ionization coefficient is defined as [15]
" ' " " F H / / ( E . £ / A ' ) e " " ? , ( s ) d e (3) where 1 is the ionization onset energy and qi(E) is the ionization cross secfion
The electron attachment coefficient is defmed as [15]
" ' " ' i F m //fefi/wy"?.(6)* (4)
where qa(£) is the attachment cross section.
The electron collision cross sections for Cb molecule determined by Tuan and Jeon [11], CFjl molecule determined by Kimura and Nakamura [9], and Ne atom determined by Hayashi [16] have been used as initial sets. The accuracy of the electron collision cross section set for each gas was confirmed to be consistent with all electron transport coefficients in each pure gas. The calculated electron transport coefficients in each pure gas are in good agreement with the measurements over the wide E/N range.
3. Results and discussion 3.1. Electron transport coefficients 3.1.1. Electron drift velocities
The results for the electron drift velocities, W, as functions of E/N for CFjI-Ne and Cb-Ne mixtures calculated in the E/N range 10 < E/N < 1000 Td (I Td = 1 0 " V,cm^) by a two-term approximation of the Boitzmann equation are shown in Figs. 1 and 2, respectively. Slight regions of the NDC phenomena in these gas mixtures are observed in the E/N range 15 < E/N < 170 Td, The NDC is relatively shallow for all mixtures. The occunences of these phenomena are due to the Ramsauer-Townsend minimum (RTM)
Journal of Science & Technology 101 (2014) 087-091 of the elastic momentum transfer cross sections of the
Ne atom and the CFjI molecules. In these binary mixtures, the values of W are suggested to be between those of the pure gases over E/N > 100 Td and these values grow linearly over E/N > 200 Td.
For the sake of companson, the experimental electron drift velocity [9] for the pure SF* gas is shown m Figs. I and 2
31.2 Density-normalized longitudinal diffitsion coefficients
The results for the density-normalized longitudinal dtffusion coefficients, NDL, as funclions of E/N for CF3l-Ne and Cb-Ne mixtures calculated in the E/N range 10 < E/N < 1000 Td by a two-term approximation of the Boitzmann equation are shown in Figs. 3 and 4, respecnvely. In these binary mixtures, the values of NDL are suggested to be between those of the pure gases over E/N > 200 Td, respecnvely.
Fig. 1 Electron drift velocity, W, as ftinchons of E/N for the CFjl-Ne mixtures with 10%, 30%, 50%, 70%
and 90% CF3I, The solid line and symbols show present W values calculated using a two-term approximafion of the Boitzmann equation fortheCFjI- Ne mixtures
Fig, 2. Electron dnft velocity, W, as functions of E/N for the Cb-Ne mixtures with 10%, 30%, 50%, and 70% Cb- The solid line and symbols show present W values calculated usmg a two-term approximation of the Boitzmann equation for the Cb-Ne mixtures
Fig. 3. Density-normalized longitudinal diffiision coefficient, NDL, as functions of E/N for the CFjI-Ne mixUires with 10%, 30%, 50%, 70% and 90% CF3I.
The solid line and symbols show present NDL values calculated using a two-temi approximation of the Boitzmann equation for the CF^l-Ne mixtures.
Fig. 4. Density-normalized longitudinal diffusion coefficient, NDL, as fiinctions of E/N for the Cb-Ne mixftires with 10%, 30%, 50%, and 70% Cb- The solid Ime and symbols show present NDL values calculated using a two-term approximation of the Boitzmann equation for the Cb-Ne mixtures.
Journal of Science & Technology 101 (2014) 087-091 In these Fig.s, on the other hand, these NDL
curves have minima in the E/N range of 15 - 170 Td for these bmary mixtures. The same process responsible for the NDC region in the electron drift velocity curves in these binary mixtures caused the occunence of these minima. The experimental density-normalized longitudinal diffusion coefficient [9] for the pure SFh is also shown in Figs. 3 and 4 for the aim of companson. The NDL values of the pure SFft are greater than those of these binary mixmres.
The calculated NDL values in 50% CFjI-Ne in the E/N ranges of E/N < 700 Td are very close to those of the pure SFe gas.
3.1.3 Density-normalized effective ionization coefficients
The results for the density-normalized effective ionization coefficients, (a - TI)/N, as functions of E/N for CFgl-Ne and Cb-Ne mixtures calculated by a two-term approximation of the Boitzmann equation are shown in Figs. 5 and 6, respectively. In these binary mixtures, the values of (a - T5)/N are also suggested to be between those of the pure gases, respectively. For the sake of comparison, the experimental density-normalized effective ionization coefficient [9] for the pure SFe gas is also shown in Figs. 5 and 6.
To the best of our knowledge, again, the electron transport coefficients in the CFjl-Ne and Cb- Ne mixtures with the entire concentration range of CF3I and CI2 have not been previously performed in both theory and experiment. Because of the accuracy of the electron collision cross sections for the present
gases and the validity of the Boitzmann equation, the present resuhs calculated are reliable, MOR experiments of the electron transport coefficients for these binary mixtures need to be performed over ibe wide range of E/N in the future. In general, when the percentage ratio of the CF3I or Cb gases m binaiy mixtures increases, the values of the electron transport coefficients increase progressively to those of the pure CF3I or Cb, respectively, 3.2. Limiting field strength valuesofE/N
The limiting field strength values of E/N, (E/N)i,n,, at which a = 11 for the CFiI-Ne and Cb-Ne mixtures are derived at 133.322 Pa and shown in Fig, 7. These values are respectively compared with those of the SF6-Ne mixture [17] shown m Fig, 7, The (E/N)iim value calculated for the pure CF3I gas is equal to 437 Td greater than the (E/N);™ of the pure SFe gas (361 Td) [9]. It can be considered as a prospective substitute for the SFe gas. Concurrently, in Fig. 7, the CF3I concentration in the CFsI-Ne mixture equal to about 65 - 75%, is considered to use in high voltage and many industries if other chemical, physical, electrical, thermal, and economical studies are considered thoroughly.
Those bmary mixtures can be considered as a prospective substitute for the SFe gas The mixture ratio of those binary gas mixtures vary depending on (he particular application of the gas and electncal equipment.
E/N(Td|
Fig, 5. Density normahzed effective ionization coefficient, (a - TI)/N, as functions of E/N for the CF3I- Ne mixmres with 10%, 30%, 50%, 70% and 90%
CF3I The solid line and symbols show present (a - Ti)/N values calculated using a two-term approximation of the Boitzmann equation for the CF3I- Ne mixtures
Cl,-Na Mintures
j ™ ^ ^ / ^
r::^--^;^"^^
P U I B C I ,
,
•
^ '
p ^ C I ,
- « - 3 0 * C I , > l « •
- («eSF,ra
Fig, 6. Density normalized effective ionization coefficient, {a - TI)/N, as fiinctions of E/N for the CI2- Ne mixtures with 10%, 30%, 50%, and 70% Cb. The solid line and symbols show present (a - TI)/N values calculated using a two-term approximation of the Boitzmann equation for the Cb-Ne mixtures.
Journal of Science & Technology 101 (2014) 087-091
400
2 JOQ
1
0- SF.-Ne[l7]
/ •
P « C , M . , T d )
/ ' . _x
(CF,I, CI,, andSFJ%
Fig. 7. Limiting field strength values of E/N, (E/N)i,n„
as functions of the percentage of CF3I and Cb gases for the CF3l-Ne and Cb-Ne mixtures, respectively.
4. Conclusions
The electron drift velocity, density-normalized longitudinal diffiision coefficient, and density- normalized effective ionization coefficient in the CFsI-Ne and Cb-Ne mixtures are calculated using a two-term approximation of the Boitzmann equation for the energy in the E/N range of 10 - 1000 Td and 10 - 400 Td, respectively. The NDC phenomena in these binary gas mixtures are suggested. The electron transport coefficienis calculated are also compared with those of the pure SFe gas in expenments. The limiting field strength values of E/N for the binary mixtures of 70% CFjI-Ne gas are determined and essentially greater than those of the pure SFe gas These binary mixtures is considered to use in high voltage and many industries. For the purposes of justification of the accuracy of our results, more experimental data for electron transport coefficients for the binary mixtures of CF3I with these gases need to he performed over a wide range of E/N, References
[1) Y Li, O. Patten, D, Youn, and D, J. Wuebbles,
•'Potential impacts of CF3I on ozone as a replacement for CFsBr in aircraft app lie aliens," Atmos, Chem Phys., 6 (2006) 4559^568
[2] M, Taki, D, Maekawa, H Odaka, H. Mizoguchi, and S. Yanabu; "Interruption capability of CF3I gas as a Substitution candidate for SFe gas," IEEE Trans, DielecnHcs and Elec, Insulation, 14 (2007) 341-346, [3] H. Takagari, H. Kasuya, H Mizoguchi, and S
Yanabu; "Investigation of the performance of CF3I gas as a possible substitate for SFe," IEEE Trans.
Dielecmcs and Elec, Insulation, 15 (2008) 1424- 1429,
[4] H. Kasuya, Y Kawamura, H. Mizoguchi, Y, Nakamura, S. Yanabu, and N Nagasaki;
"Interruption capability and decomposed gas density
of CF3I as a substitute for SF* gas," IEEE Trans.
Dielectrics and Elec. Insulation, 17 (2010) 1196- 1203,
[5] M, H. Luly and R, G Richard; Gaseous Dielectric with Low Global Warming Potentials, U.S. Patent Application Publication (US 2010/0320428 Al), pp 1-20 {Dec. 2010).
[6] N Nakayama, E. E Ferrenz, D. R Oslling. A S.
Nichols, J. F. Faulk, and C, R. Arumainayagam;
"Surface chemistry and radiation chemistry of nifluoroiodomethane (CF3I) on Mo (110)," J, Phys Chem, B, 108 (2004) 4080-4085,
[7] J de Urquijo; "Is CF3I a good gaseous dielectnc? A comparative swarm study of CF3I and SFt," J Phys , Conf Ser., 86 (2007) 012008-1-10.
[8] 1. V Kocheiov, A. P, Napartovich, N. P Vagin, and N, N, Yuryshev, "Mechanism of pulse discharge production of iodine atoms from CF3I molecules for a chemical oxygen-iodine laser," J, Phys, D, 42 (2009) 0055201-1-8-
[9] M, Kimura and Y Nakamura, "Electron swarm parameters in CF3I and a set of electron collision cross sections for the CF3I molecule," J. Phys, D, 43 (2010)145202-1-6.
[10] R, E, Robson; "Generalized Einstein relation and negative differential conductivity in gases," Aust J Phys,, 37 (1984) 35^M,
[II] D,A.TuanandB H Jeon; "Electron collision cross sections for the Cb molecule from electron transport coefficients," J Phys. Soc, Jpn., 80 (2011) 084301-1- 5,
[12] D. A. Tuan and B H, Jeon; "Electron CoUision Cross Seelions for the Tetraethoxysilane Molecule and Electron Transport Coefficients in Tetraethoxysilane- O: and Tetraethoxysilane-Ar Mixtures," Joumal of the Physical Society of Japan, 81 (2012) 064301-1-8 [13) L. G. H, Huxley and R W. Crompton; The Diffusion
and Dnfl of Electrons in Gases. New York; John Wiley &. Sons, 1974, ch, 6 and ch, ! 3.
[14] B, H, Jeon; Determination of electron collision cross- sections for the oxygen molecule by using an electron swami study, J. Korean Phys, Soc, 43 (2003) 513- 525,
[15] L G. Christophorou and S, R Hunter; From basic research to application: in Electron-Molecule Interations and Their Applications, vol. 2, L. G.
Chnstophorou. Ed, Florida; Academic Press, pp 318-112, 1984,
[16] M Hayashi, Luminous layers in the prebreakdown region of low pressure noble gases, J. Phys. D. vol.
15,pp. 1411, 1982.
[17] D, M. Xiao, H. L, Liu, and Y. Z Chen; Electron swarm parameters in SFe/Ne mixmres determined by swarm expenment; J Appl Phys., Vol. 86, No. 11,1 December 1999.