Insulating characteristics of Cl
_{2}
He mixture gases in gas discharges were analysed to evaluate ability of these gases for using in medium voltage and many industries. These are electron transport coefficients, which are the electron drift velocity, densitynormalized longitudinal diffusion coefficient, and densitynormalized effective ionization coefficient, in Cl
_{2}
He mixtures. A twoterm approximation of the Boltzmann equation was used to calculate the electron transport coefficients for the first time over a wide range of E/N (ratio of the electric field E to the neutral number density N). The limiting field strength values of E/N, (E/N)
_{lim}
, for these binary gas mixtures were also derived and compared with those of the pure SF
_{6}
gas.
1. Introduction
Chlorine (Cl
_{2}
) has been selected as an available substitution candidate for the SF
_{6}
gas in the published patent of Luly and Richard
[1]
because of low global warming potential (GWP) and high dielectric strength (i.e., a GWP less than approximately 22,200, and a dielectric strength greater than air). Moreover, this gas and its mixtures have been widely used in plasma etching of semiconductors, metals, and gate stacks with highκ dielectrics and lowκ dielectric films
[2

6]
.
The insulating characteristics, which are electron transport coefficients for not only pure atoms and pure molecules but also for the binary gas mixtures, are necessary to understand quantitatively plasma discharges and to evaluate ability of gases for using in high voltage and many industries. On the other hand, the electron transport coefficients of the binary mixtures of Cl
_{2}
gas with the rare and conventional gases have been scarce so far. To the best of our knowledge, the electron transport coefficients in Cl
_{2}
He mixture gases with the whole Cl
_{2}
concentration ranges have not been previously performed in not only measurements but also calculations.
In the present study, therefore, in order to gain more insight into the electron transport coefficients, the electron transport coefficients (electron drift velocity, densitynormalized longitudinal diffusion coefficient, and densitynormalized effective ionization coefficient) in a wide E/N range (ratio of the electric field E to the neutral number density N) in the Cl
_{2}
He mixtures were analysed and calculated by using a twoterm approximation of the Boltzmann equation for energy. The calculated electron transport coefficients were also compared with those of pure SF
_{6}
gas and the (E/N)
_{lim}
values in those mixtures were also compared respectively with those of SF
_{6}
He mixtures in the experiments. These binary gas mixtures are considered to use in medium voltage and many industries depending on mixture ratios and particular applications of gas and electrical equipment.
2. Analysis
The electron transport coefficients were calculated by sets of electron collision cross sections for gases and a twoterm approximation of the Boltzmann equation for the energy. In the present study, this calculating method, which was previously used
[6

10]
, was also briefly represented below. The electron drift velocity calculated from the solution of electron energy distribution function, f(ε, E/N), of the Boltzmann equation is defined as
[11]
where ε is the electron energy, m is the electron mass, e is the elementary charge and q
_{m}
(ε) is the momentumtransfer cross section.
The densitynormalized longitudinal diffusion coefficient is defined as
[12]
where V
_{1}
is the speed of the electron, q
_{T}
is the total cross section;
F
_{n}
and
ϖ
_{n}
(n=0, 1, 2) are, respectively, the electron energy distributions of various orders and their eigenvalues. V
_{1}
,
ϖ_{n}
,
ϖ
_{0n}
, and A
_{n}
are given by
where q
_{i}
(ε) is the ionization cross section.
The Townsend first ionization coefficient is defined as
[13]
where I is the ionization onset energy.
The electron attachment coefficient is defined as
[13]
where q
_{a}
(ε) is the attachment cross section.
The electron collision cross sections for Cl
_{2}
molecule determined by Tuan and Jeon
[7]
, He atom determined by Hayashi
[14]
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. For the sake of comparison and justification the validity of the sets of collision cross sections and that of twoterm approximation of the Boltzmann equation, the measured electron transport coefficients in each gas have been showed in
Figs. 1

3
. The calculated electron transport coefficients in each pure gas are in good agreement with the measurements over the wide E/N range.
Electron drift velocity, W, as functions of E/N for the Cl_{2}He mixtures with 10%, 30%, 50%, 70%, and 90% Cl_{2}. The solid line and symbols show present W values calculated using a twoterm approximation of the Boltzmann equation for the Cl_{2}He mixtures
Densitynormalized longitudinal diffusion coefficient, ND_{L}, as functions of E/N for the Cl_{2}He mixtures with 10%, 30%, 50%, 70%, and 90% Cl_{2}. The solid line and symbols show present ND_{L} values calculated using a twoterm approximation of the Boltzmann equation for the Cl_{2}He mixtures
Density normalized effective ionization coefficient, (αη)/N, as functions of E/N for the Cl_{2}He mixtures with 10%, 30%, 50%, 70%, and 90% Cl_{2} The solid line and symbols show present (α  η)/N values calculated using a twoterm approximation of the Boltzmann equation for the Cl_{2}He mixtures
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 Cl
_{2}
He mixtures calculated in the E/N range 10 < E/N < 1000 Td (1 Td = 10
^{−17}
V.cm
^{2}
) by a twoterm approximation of the Boltzmann equation are shown in
Fig. 1
. In these binary mixtures, the values of W are suggested to be between those of the pure gases over 100 Td < E/N < 700 Td and these values grow linearly over 10 Td < E/N < 40 Td. For the sake of comparison, the experimental electron drift velocity
[15]
for the pure SF
_{6}
gas is shown in
Fig. 1
. The values of W in Cl
_{2}
He with concentration of Cl
_{2}
greater than 70% are lower than those of SF
_{6}
gas.
 3.1.2 Densitynormalized longitudinal diffusion coefficients
The results for the densitynormalized longitudinal diffusion coefficients, ND
_{L}
, as functions of E/N for Cl
_{2}
He mixtures calculated in the E/N range 10 < E/N < 1000 Td by a twoterm approximation of the Boltzmann equation are shown in
Fig. 2
. In these binary mixtures, the values of ND
_{L}
are suggested to be between those of the pure gases over E/N> 200 Td, respectively. In these figures, on the other hand, these ND
_{L}
curves have minima in the E/N range of 15  170 Td for these binary mixtures. The same process responsible for the NDC region in the electron drift velocity curves in these binary mixtures caused the occurrence of these minima. The experimental densitynormalized longitudinal diffusion coefficient
[15]
for the pure SF
_{6}
is also shown in
Fig. 2
for the aim of comparison. The ND
_{L}
values of the pure SF
_{6}
are greater than those of these binary mixtures.
 3.1.3. Densitynormalized effective ionization coefficients
The results for the densitynormalized effective ionization coefficients, (αη)/N, as functions of E/N for Cl
_{2}
He mixtures calculated by a twoterm approximation of the Boltzmann equation are shown in
Fig. 3
. In these binary mixtures, the values of (αη)/N are also suggested to be between those of the pure gases, respectively. For the sake of comparison, the experimental densitynormalized effective ionization coefficient
[15]
for the pure SF
_{6}
gas is also shown in
Fig. 3
. The (αη)/N values in the Cl
_{2}
He mixture gases are greater than those of SF
_{6}
gas.
To the best of our knowledge, again, the electron transport coefficients in the Cl
_{2}
He mixtures with the entire concentration range of Cl
_{2}
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 Boltzmann equation, the present results calculated are reliable. More experiments of the electron transport coefficients for these binary mixtures need to be performed over the wide range of E/N in the future. In general, when the percentage ratio of the Cl
_{2}
gas in binary mixtures increases, the values of the electron transport coefficients increase progressively to those of the pure Cl
_{2}
.
 3.2 Limiting field strength values of E/N
The limiting field strength values of E/N, (E/N)
_{lim}
, at which α = η for the Cl
_{2}
He mixtures are derived at 133.322 Pa and shown in
Fig. 4
. These values are respectively compared with those of the SF
_{6}
He mixture
[16]
shown in
Fig. 4
. The (E/N)
_{lim}
value calculated for the pure CF
_{3}
I gas is equal to 437 Td greater than the (E/N)
_{lim}
of the pure SF
_{6}
gas (361 Td)
[15]
. It is considered to use in medium voltage and many industries if other chemical, physical, electrical, thermal, and economical studies are considered thoroughly.
Limiting field strength values of E/N, (E/N)_{lim}, as functions of the percentage of Cl_{2} gas for the Cl_{2}He mixtures
Those binary mixtures can be considered as a prospective substitute for the SF
_{6}
gas. The mixture ratio of those binary gas mixtures vary depending on the particular application of the gas and electrical equipment.
4. Conclusions
The electron drift velocity, densitynormalized longitudinal diffusion coefficient, and densitynormalized effective ionization coefficient in the Cl
_{2}
He mixture gases are calculated using a twoterm approximation of the Boltzmann equation for the energy in the wide E/N range. The electron transport coefficients calculated are also compared with those of the pure SF
_{6}
gas in experiments. Moreover, the limiting field strengths, (E/N)
_{lim}
, for the Cl
_{2}
He mixtures are compared with those of the SF
_{6}
He mixture gases. The insulating characteristics of Cl
_{2}
He mixture gases are lower than those of the SF
_{6}
He mixture gases. These binary mixtures, therefore, are considered as a prospective substitute for the SF
_{6}
gas and binary mixture gases of SF
_{6}
with buffer gases in medium voltage and many industries.
BIO
Do Anh Tuan He received the B.S and M.Sc. degrees in electrical engineering from Hanoi University of Science and Technology, Vietnam in 2004 and 2008, respectively. He received the Ph.D. degree in electrical engineering from Dongguk University, Korea in 2012. He is the Lecturer at the Faculty of Electronics and Electrical Engineering of Hung Yen University of Technology and Education, Vietnam from 2008. His research interests include electron swarm study, discharges and high voltage, and plasma applications.
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