• Title/Summary/Keyword: two-term approximation of the Boltzmann equation

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The analysis of electrons drift velocity in $SF_6+O_2$ mixture gas by Boltzmann-Equation (볼츠만 방정식을 이용한 $SF_6+O_2$ 혼합가스의 전자이동속도)

  • Song, Byoung-Doo;Ha, Sung-Chul;Jeon, Byung-Hoon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2002.05c
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    • pp.185-188
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    • 2002
  • This paper describes the information for quantitative simulation of weakly ionized plasma. We should grasp the meaning of the plasma state condition to utilize engineering application and to understand materials of plasma state. In this paper, the drift velocity of electron in $SF_6+O_2$ mixture gas calculated for range E/N values l~900[Td] at the temperature is 300[$^{\circ}K$] and pressure is 1[Torr], using a set of electron collision cross sections determined by the authors and the values of drift velocity of electrons are obtained for TOF, PT, SST sampling method of Backward Prolongation by two term approximation Boltzmann equation method. It has also been used to predict swarm parameter using the values of cross section as input. The result of Boltzmann equation, the drift velocity of electrons, has been compared with pure $SF_6$, pure $O_2$ and mixture gas.

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Ionization and Attachment Coefficients in CF4 (CF4 기체에서의 전리와 부착계수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.60 no.1
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    • pp.27-31
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    • 2011
  • In this paper, the electron transport characteristics in $CF_4$ has been analysed over the E/N range 1~300[Td] by a two-term approximation Boltzmann equation method and by a Monte Carlo simulation. The motion has been calculated to give swarm parameters for the electron drift velocity, longitudinal diffusion coefficient, the ratio of the diffusion coefficient to the mobility, electron ionization and attachment coefficients, effective ionization coefficient, mean energy, collision frequency and the electron energy distribution function. The electron energy distribution function has been analysed in $CF_4$ at E/N=5, 10, 100, 200 and 300[Td] for a case of the equilibrium region in the mean electron energy and respective set of electron collision cross sections. The results of Boltzmann equation and Monte Carlo simulation have been compared with experimental data by Y. Nakamura and M. Hayashi. The swarm parameter from the swarm study are expected to serve as a critical test of current theories of low energy electron scattering by atoms and molecules, in particular, as well as crucial information for quantitative simulations of weakly ionized plasmas.

Electron Collision Cross Sections for the TRIES Molecule and Electron Transport Coefficients in TRIES-Ar and TRIES-O2 Mixtures

  • Tuoi, Phan Thi;Tuan, Do Anh;Hien, Pham Xuan
    • Journal of the Korean Physical Society
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    • v.73 no.12
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    • pp.1855-1862
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    • 2018
  • A reliable set of low-energy electron collision cross sections for the triethoxysilane (TRIES) molecule was derived based on the measured electron transport coefficients for a pure TRIES molecule by using an electron swarm method and a two-term approximation of the Boltzmann equation. The electron transport coefficients calculated using the derived set are in good agreement with experimental value over a wide range of E/N values (ratio of the electric field E to the neutral number density N). The present electron collision cross section set for the TRIES molecule, therefore, is the most reliable so far for plasma discharges and for materials processing using the TRIES molecule. Moreover, the electron transport coefficients for the TRIES-Ar and the $TRIES-O_2$ mixtures were also calculated and analyzed over a wide range of E/N for the first time.

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

  • Tuan, Do Anh
    • Journal of Electrical Engineering and Technology
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    • v.10 no.4
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    • pp.1734-1737
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    • 2015
  • 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.

Analysis of electron transport properties of $CF_4+Ar$ mixtures gas by the TOF method (TOF법에 의한 $CF_4+Ar$ 혼합기체의 전자수송특성 해석)

  • 서상현;하성철;유회영
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1998.06a
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    • pp.279-283
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    • 1998
  • The electron swarm parameters in the$CF_4$(O.l%, 5%)+Ar mixtures are measured by time of flight method over the E/N(Td) range from 10 to 300LTdl. A two-term approximation of the Boltzmann equation analysis and Monte Carlo simulation have been also used to study electron transport coefficients. We have calculated W, NDL, NDT, $\alpha$ and the limiting breakdown electric field to gas mixtures ratio in pure $CF_4$ gas and$CF_4+Ar$ mixtures. The measured results and the calculated results have been compared each other paper.

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Basic study on the gas discharge panel for LCD and PDP (PDP와 LCD에서의 가스방전 페널에 대한 기초연구)

  • Song, Byoung-Doo;Ha, Sung-Chul;Jeon, Byung-Hoon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2003.11a
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    • pp.554-557
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    • 2003
  • This paper describes the information for quantitative simulation of weakly ionized plasma. We should grasp the meaning of the plasma state condition to utilize engineering application and to understand materials of plasma state. In this paper, electron swarm parameter in He+Xe and Ar+He mixture gas calculated for range E/N values $0.01{\sim}500$ [Td] at the temperature is 300 [K] and pressure is 1 [Torr], using a set of electron collision cross sections determined by the authors, and using a method of Backward Prolongation by two term approximation Boltzmann equation method, for basic study on the gas discharge panel.

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Characteristics of Electron Transport in $SiH_4$ Gas used by MCS-BEq Algorithm (MCS-BEq 알고리즘에 의한 $SiH_4$ 기체의 전자수송특성)

  • Kim, Sang-Nam;Seong, Nak-Jin
    • Proceedings of the KIEE Conference
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    • 2006.10b
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    • pp.159-162
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    • 2006
  • In this paper energy distribution function in $SiH_4$ has been analysed over the E/N range 0.5${\sim}$300Td and Pressure value 0.5, 1.0, 2.5 Torr by a two-term approximation Boltzmann equation method and by a Monte Carlo simulation. The motion has been calculated to give swarm parameters for the electron drift velocity, diffusion coefficient, electron ionization, mean energy and the electron energy distribution function. The electron energy distribution function has been analysed in $SiH_4$ at E/N=30, 50Td for a case of the equilibrium region in the mean electron energy and respective set of electron collision cross sections. The results show that the deduced electron drift velocities, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients and mean energy agree reasonably well with theoretical for a rang of E/N values.

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Electron Energy Distribution Function in $CF_4$ Gas used by MCS-BE Algorithm ($CF_4$ 기체의 MCS-BEq 알고리즘에 의한 전자에너지 분포함수)

  • Park, Jae-Sae;Kim, Sang-Nam;Kim, Il-Nam
    • Proceedings of the KIEE Conference
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    • 2002.06a
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    • pp.102-105
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    • 2002
  • In this paper, the electron transport characteristics in $CF_4$ has been analysed over the E/N range 1${\sim}$300 [Td] by a two-term approximation Boltzmann equation method and by a Monte Carlo simulation. The motion has been calculated to give swarm parameters for the electron drift velocity, longitudinal diffusion coefficient, the ratio of the diffusion coefficient to the mobility, electron ionization and attachment coefficients, effective ionization coefficient, mean energy, collision frequency and the electron energy distribution function. The swarm parameter from the swarm study are expected to serve as a critical test of current theories of low energy electron scattering by atoms and molecules, in particular, as well as crucial information for quantitative simulations of weakly ionized plasmas.

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A Study on the Electron Energy Distribution Function in $SF_6+Ar$ Mixtures Gas used by MCS-BE Algorithm ($SF_6+Ar$ 혼합기체의 MCS-BE 알고리즘에 의한 전자에너지 분포함수)

  • Kim, Sang-Nam;Ha, Sung-Chul
    • Proceedings of the KIEE Conference
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    • 2000.07e
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    • pp.17-21
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    • 2000
  • A Study on the electron energy distribution function in $SF_6+Ar$ mixtures gas used by MCS-BE algorithm, the electron swam parameters in the 0.5% and 0.2% $SF_6+Ar$ mixtures are measured by time of flight method over the E/N(Td) range from 30 to 300(Td). A two-term approximation of the Boltzmann equation analysis and Monte Carlo simulation have been also used to study electron transport coefficients. The electron energy distribution function has been analysed in $SF_6$ gas and $SF_6+Ar$ mixtures at E/N : 200(Td) for a case of the equilibrium region in the mean electron energy. The measured results and the calculated results have been compared each other.

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A Study on Characteristics of The $CF_3I$-Xe Mixtures gases in a Plasma Discharge Simulation (플라즈마 방전 시뮬레이션에 의한 $CF_3I$-Xe 혼합 가스에서의 물성 특성 연구)

  • Shim, Eung-Won;Tuan, Do Anh;Jeon, Byung-Hoon
    • Proceedings of the KIEE Conference
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    • 2011.07a
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    • pp.1582-1583
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    • 2011
  • Recently, it has been found that trifluoroiodomethane ( $CF_3I$) gas can replace $SF_6$ gas as a prospective substitute gas. For quantitative understanding of gas discharge phenomena, we should know electron collision cross sections and electron transport coefficients. Using electron collision cross sections of $CF_3I$ and Xe, we calculated elecron drift velocity, longitudinal coefficient, effective ionization coefficient in $CF_3I$-Xe mixtures using a two-term approximation of the Boltzmann equation. We also compared the electron transport coefficients in pure gas and those of 10%, 20%, 50%, and 70% $CF_3I$-Xe mixture gases. The present data may be showed appropriate ratios of $CF_3I$-Xe mixture gas for replacing the $SF_6$ gas.

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