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

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A Simulation of the Energy Distribution Function for Electron in $CF_4$-Ar Mixtures Gas ($CF_4$ 혼합기체(混合氣體)에서 전자(電子)에너지분포함수)

  • Kim, Sang-Nam;Seong, Nak-Jin
    • Proceedings of the KIEE Conference
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    • 2004.07e
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    • pp.37-40
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    • 2004
  • Electron swarm parameters in pure $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation(BEq.) method and the Monte Carlo simulation(MCS) The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4$-Ar mixtures shows the Maxwellian distribution for energy. That is, f(${\varepsilon}$) has the symmetrical shape whose axis of symmetry is a most probably energy

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Electron Swarm Drift Velocity and Characteristic Energy in e$^{[-10]}$ -CF$_4$Scattering (e ̄-CF$_4$산란의 전자이동속도 및 특성에너지 연구)

  • 임상원;유회영;김상남;하성철
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 1996.11a
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    • pp.169-174
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    • 1996
  • In this paper, the electron transport characteristic 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 alteration of cross sections from the literature is avoided as much as possible in the analysis. The motion has been calculated to give swarm parameters for the electron drift velocity(W), diffusion coefficient(D$_{L}$), the ratio of the diffusion coefficient to the mobility(D$_{L}$/$\mu$), mean energy($\varepsilon$), the electron energy distribution function. The electron energy distribution function has been analysed in CF$_4$at E/N=50, 100 and 200(Td) for a case of the equilibrium region in the mean electron energy. The results of Boltzmann equation and Monte Carlo simulation have been compared with experimental data by Y. Nakamura and M. Hayashi.shi.

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Electron swarm parameter in $CH_4$ by MCS-BE simulation (시뮬레이션에 의한 $CH_4$ 전자군 파라미터)

  • Kim, Sang-Nam;Seong, Nak-Jin
    • Proceedings of the KIEE Conference
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    • 2005.10a
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    • pp.89-92
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    • 2005
  • Using quantitative simulations of weakly ionized plasma, we can analyze gas characteristic. In this paper, the electron transport characteristic in $CH_4$ has been analysed over the E/N range 0.1${\sim}$ 300(Td), at the 300($_{\circ}$ K) by the two term approximation Boltzmann equation method and Monte Carlo Simulation. The electron energy distribution function has been analysed in $CH_4$ at E/N=10, 100 for a case of the equilibrium region in the mean energy. The result of Boltzmann equation and Monte Carlo Simulation has been compared with experimental data by Ohmori, $Lucas^{[18]}$ and Carter. The swarm parameter from the swarm study are expected to sever as a critical test of current theories of low energy scattering by atoms and molecules.

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The Analysis of Electron Transport Characteristics in $SiH_4$ Plasma ($SiH_4$ 플라즈마중의 전자수송특성 해석)

  • Lee, Hyoung-Yoon;Ha, Sung-Chul;Kim, Dae-Yeon
    • Proceedings of the KIEE Conference
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    • 1998.11c
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    • pp.925-928
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    • 1998
  • In this paper, the electron transport characteristics in $SiH_4$ has been analysed over the E/N range $0.5{\sim}300[Td]$ and Pressure value 0.5, 1, 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, 50[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 Pollock, Ohmori, cottrell and Walker.

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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

  • Tuan, Do Anh
    • Journal of Electrical Engineering and Technology
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    • v.11 no.2
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    • pp.455-462
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    • 2016
  • The electron transport coefficients in not only pure atoms and molecules but also in the binary gas mixtures are necessary, especially on understanding quantitatively plasma phenomena and ionized gases. Electron transport coefficients (electron drift velocity, density-normalized longitudinal diffusion coefficient, and density-normalized effective ionization coefficient) in binary mixtures of TEOS gas with buffer gases such as Kr, Xe, He, and Ne gases, therefore, was analyzed and calculated by a two-term approximation of the Boltzmann equation in the E/N range (ratio of the electric field E to the neutral number density N) of 0.1 - 1000 Td (1 Td = 10−17 V.cm2). These binary gas mixtures can be considered to use as the silicon sources in many industrial applications depending on mixture ratio and particular application of gas, especially on plasma assisted thin-film deposition.

Electron Transport Characteristics in $SiH_4$ by MCS-BEq (MCS-BEq에 의한 $SiH_4$ 전자수송특성(電子輸送特性))

  • Seong, Nak-Jin;Kim, Sang-Nam
    • Proceedings of the KIEE Conference
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    • 2005.10a
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    • pp.97-100
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    • 2005
  • This paper describes the electron transport characteristics in SiH4 has been analysed over the E/N range 0.5${\sim}$300[Td] and Pressure value 0.5, 1, 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, 50[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 Pollock, Ohmori, cottrell and Walker.

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Analysis of the Mean Energy in $SiH_4-Ar$ Mixture Gases ($SiH_4-Ar$ 혼합기체의 평균 에너지에 관한 연구)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.55 no.2
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    • pp.57-61
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    • 2006
  • This paper calculates and gives the analysis of mean energy in pure $SiH_4,\;Ar-SiH_4$ mixture gases ($SiH_4-0.5[%],\;5[%]$) over the range of $E/N =0.01{\sim}300[Td]$, p = 0.1, 1, 5.0 [Torr] by Monte Carlo the Backward prolongation method of the Boltzmann equation using computer simulation without using expensive equipment. The results have been obtained by using the electron collision cross sections by TOF, PT, SST sampling, compared with the experimental data determined by the other author. It also proved the reliability of the electron collision cross sections and shows the practical values of computer simulation. The calculations of electron swarm parameters require the knowledge of several collision cross-sections of electron beam. Thus, published momentum transfer, ionization, vibration, attachment, electronic excitation, and dissociation cross-sections of electrons for $SiH_4$ and Ar, were used. The differences of the transport coefficients of electrons in $SiH_4$, mixtures of $SiH_4$ and Ar, have been explained by the deduced energy distribution functions for electrons and the complete collision cross-sections for electrons. A two-term approximation of the Boltzmann equation analysis and Monte Carlo simulation have been used to study electron transport coefficients.

Electron Mean Energy in CF4, CH4, Ar mixtures (CF4, CH4, Ar 혼합기체의 전자 평균에너지)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.64 no.4
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    • pp.241-245
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    • 2015
  • Energy Distribution Function in pure $CH_4$, $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The calculations of electron swarm parameters require the knowledge of several collision cross-sections of electron beam. Thus, published momentum transfer, ionization, vibration, attachment, electronic excitation, and dissociation cross-sections of electrons for $CH_4$, $CF_4$ and Ar, were used. The differences of the transport coefficients of electrons in $CH_4$, mixtures of $CH_4$ and Ar, have been explained by the deduced energy distribution functions for electrons and the complete collision cross-sections for electrons. The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4$-Ar mixtures shows the Maxwellian distribution for energy. That is, $f({\varepsilon})$ has the symmetrical shape whose axis of symmetry is a most probably energy.

Ionization and Attachment Coefficients in CF4, CH4, Ar Mixtures Gas (CF4, CH4, Ar 혼합기체의 전리와 부착계수)

  • Kim, Sang-Nam
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.61 no.1
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    • pp.13-17
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    • 2012
  • Ionization and Attachment Coefficients in pure $CH_4$, $CF_4$ and mixtures of $CF_4$ and Ar, have been analyzed over a range of the reduced electric field strength between 0.1 and 350[Td] by the two-term approximation of the Boltzmann equation (BEq.) method and the Monte Carlo simulation (MCS). The calculations of electron swarm parameters require the knowledge of several collision cross-sections of electron beam. Thus, published momentum transfer, ionization, vibration, attachment, electronic excitation, and dissociation cross-sections of electrons for $CH_4$, $CF_4$ and Ar, were used. The results of the Boltzmann equation and the Monte Carlo simulation have been compared with the data presented by several workers. The deduced transport coefficients for electrons agree reasonably well with the experimental and simulation data obtained by Nakamura and Hayashi. The energy distribution function of electrons in $CF_4$-Ar mixtures shows the Maxwellian distribution for energy. That is, f(${\varepsilon}$) has the symmetrical shape whose axis of symmetry is a most probably energy. The proposed theoretical simulation techniques in this work will be useful to predict the fundamental process of charged particles and the breakdown properties of gas mixtures.

The analysis of the electron drift velocity of Xenon gas by Boltzmann-equation (볼츠만 방정식을 이용한 Xe 가스의 전자 이동속도 해석)

  • Song, Byoung-Doo;Ha, Sung-Chul;Jeon, Byoung-Hoon
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.05c
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    • pp.201-203
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    • 2001
  • This paper describes the information for quantitative simulation of weakly ionized plasma. We must 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 Xenon gas calculated for range of E/N values from 0.01~500[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 experimental data by L. S. Frost and A. V. Phelps for a range of E/N. The swarm parameter from the study are expected to server as a critical test of current theories of low energy scattering by atoms and molecules.

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