Analysis of Insulating Characteristics of Cl₂-He Mixture Gases in Gas Discharges

Abstract

Insulating characteristics of Cl₂-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, density-normalized longitudinal diffusion coefficient, and density-normalized effective ionization coefficient, in Cl₂-He mixtures. A two-term 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 SF₆ gas.

1. Introduction

Chlorine (Cl2) has been selected as an available substitution candidate for the SF6 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 high-κ dielectrics and low-κ 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 Cl2 gas with the rare and conventional gases have been scarce so far. To the best of our knowledge, the electron transport coefficients in Cl2-He mixture gases with the whole Cl2 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, density-normalized longitudinal diffusion coefficient, and density-normalized effective ionization coefficient) in a wide E/N range (ratio of the electric field E to the neutral number density N) in the Cl2-He mixtures were analysed and calculated by using a two-term approximation of the Boltzmann equation for energy. The calculated electron transport coefficients were also compared with those of pure SF6 gas and the (E/N)lim values in those mixtures were also compared respectively with those of SF6-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 two-term 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 qm(ε) is the momentum-transfer cross section.

The density-normalized longitudinal diffusion coefficient is defined as [12]

where V1 is the speed of the electron, qT is the total cross section; Fn and ϖn (n=0, 1, 2) are, respectively, the electron energy distributions of various orders and their eigenvalues. V1, ϖn, ϖ0n, and An are given by

where qi(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 qa(ε) is the attachment cross section.

The electron collision cross sections for Cl2 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 two-term 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.

Fig. 1.Electron drift velocity, W, as functions of E/N for the Cl2-He mixtures with 10%, 30%, 50%, 70%, and 90% Cl2. The solid line and symbols show present W values calculated using a two-term approximation of the Boltzmann equation for the Cl2-He mixtures

Fig. 2.Density-normalized longitudinal diffusion coefficient, NDL, as functions of E/N for the Cl2-He mixtures with 10%, 30%, 50%, 70%, and 90% Cl2. The solid line and symbols show present NDL values calculated using a two-term approximation of the Boltzmann equation for the Cl2-He mixtures

Fig. 3.Density normalized effective ionization coefficient, (α-η)/N, as functions of E/N for the Cl2-He mixtures with 10%, 30%, 50%, 70%, and 90% Cl2 The solid line and symbols show present (α - η)/N values calculated using a two-term approximation of the Boltzmann equation for the Cl2-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 Cl2-He mixtures calculated in the E/N range 10 < E/N < 1000 Td (1 Td = 10−17 V.cm2 ) by a two-term 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 SF6 gas is shown in Fig. 1. The values of W in Cl2-He with concentration of Cl2 greater than 70% are lower than those of SF6 gas.

3.1.2 Density-normalized longitudinal diffusion coefficients

The results for the density-normalized longitudinal diffusion coefficients, NDL, as functions of E/N for Cl2-He mixtures calculated in the E/N range 10 < E/N < 1000 Td by a two-term approximation of the Boltzmann equation are shown in Fig. 2. In these binary mixtures, the values of NDL are suggested to be between those of the pure gases over E/N> 200 Td, respectively. In these figures, on the other hand, these NDL 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 SF6 is also shown in Fig. 2 for the aim of comparison. The NDL values of the pure SF6 are greater than those of these binary mixtures.

3.1.3. Density-normalized effective ionization coefficients

The results for the density-normalized effective ionization coefficients, (α-η)/N, as functions of E/N for Cl2-He mixtures calculated by a two-term approximation of the Boltzmann equation are shown in Fig. 3. In these binary mixtures, the values of (α-η)/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 [15] for the pure SF6 gas is also shown in Fig. 3. The (α-η)/N values in the Cl2-He mixture gases are greater than those of SF6 gas.

To the best of our knowledge, again, the electron transport coefficients in the Cl2-He mixtures with the entire concentration range of Cl2 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 Cl2 gas in binary mixtures increases, the values of the electron transport coefficients increase progressively to those of the pure Cl2.

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 Cl2-He mixtures are derived at 133.322 Pa and shown in Fig. 4. These values are respectively compared with those of the SF6-He mixture [16] shown in Fig. 4. The (E/N)lim value calculated for the pure CF3I gas is equal to 437 Td greater than the (E/N)lim of the pure SF6 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.

Fig. 4.Limiting field strength values of E/N, (E/N)lim, as functions of the percentage of Cl2 gas for the Cl2-He mixtures

Those binary mixtures can be considered as a prospective substitute for the SF6 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, density-normalized longitudinal diffusion coefficient, and density-normalized effective ionization coefficient in the Cl2-He mixture gases are calculated using a two-term 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 SF6 gas in experiments. Moreover, the limiting field strengths, (E/N)lim, for the Cl2-He mixtures are compared with those of the SF6-He mixture gases. The insulating characteristics of Cl2-He mixture gases are lower than those of the SF6-He mixture gases. These binary mixtures, therefore, are considered as a prospective substitute for the SF6 gas and binary mixture gases of SF6 with buffer gases in medium voltage and many industries.