• Title/Summary/Keyword: Boltzmann Equilibrium

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Numerical Analysis on Heat Transfer Characteristics in Silicon Boated by Picosecond-to-Femtosecond Ultra-Short Pulse Laser (펨토초급 극초단 펄스레이저에 의해 가열된 실리콘 내의 열전달 특성에 관한 수치해석)

  • 이성혁;이준식;박승호;최영기
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.26 no.10
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    • pp.1427-1435
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    • 2002
  • The main aim of the present article is numerically to investigate the micro-scale heat transfer phenomena in a silicon microstructure irradiated by picosecond-to-femtosecond ultra-short laser pulses. Carrier-lattice non-equilibrium phenomena are simulated with a self-consistent numerical model based on Boltzmann transport theory to obtain the spatial and temporal evolutions of the lattice temperature, the carrier number density and its temperature. Especially, an equilibration time, after which carrier and lattice are in equilibrium, is newly introduced to quantify the time duration of non-equilibrium state. Significant increase in carrier temperature is observed for a few picosecond pulse laser, while the lattice temperature rise is relatively small with decreasing laser pulse width. It is also found that the laser fluence significantly affects the N 3 decaying rate of Auger recombination, the carrier temperature exhibits two peaks as a function of time due to Auger heating as well as direct laser heating of the carriers, and finally both laser fluence and pulse width play an important role in controlling the duration time of non-equilibrium between carrier and lattice.

Iterative Cumulant Moment Method for solution of Boltzmann Equation and its Application to Shock Wave Structure (반복적 Cumulant 모멘트 방법에 의한 Boltzmann 방정식의 해법과 충격파구조에 관한 연구)

  • Ohr, Young Gie
    • Journal of the Korean Chemical Society
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    • v.42 no.4
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    • pp.398-410
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    • 1998
  • For non-linear solution of the Boltzmann equation, the cumulant moment method has been studied. To apply the method to the normal shock wave problem, we restricted ourselves to the monatomic Maxwell molecular gases. The method is based on the iterative approach developed by Maxwell-Ikenberry-Truesdell (MIT). The original MIT approach employs the equilibrium distribution function for the initial values in beginning the iteration. In the present work, we use the Mott-Smith bimodal distribution function to calculate the initial values and follow the MIT iteration procedure. Calculations have been carried out up to the second iteration for the profiles of density, temperature, stress, heat flux, and shock thickness of strong shocks, including the weak shock thickness of Mach range less than 1.4. The first iteration gives a simple analytic expression for the shock profile, and the weak shock thickness limiting law which is in exact accord with the Navier-Stokes theory. The second iteration shows that the calculated strong shock profiles are consistent with the Monte Carlo values quantitatively.

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A study on the electron energy diffusion function of the sulphur hexaflouride ($SF_6$ 가스의 전자에너지 분포함수에 관한 연구)

  • 김상남;유회영;서상현;박동화;하성철
    • Proceedings of the Korean Institute of IIIuminating and Electrical Installation Engineers Conference
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    • 1996.11a
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    • pp.134-139
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    • 1996
  • The electron energy distributions function were analysed in sulphur hexaflouride at E/N : 500~800(Td) for a case of non-equilibrium ion in the mean electron energy. This paper describes the electron transport characteristics in SF$_{6}$ gas calculated for range of E/N values from 150~800(Td) by the Monte Carlo simulation and Boltzmann equation method using a set of electron collision cross sections determined by the authors and the values of electron swarm parameters. The results gained that the value of an electron swarm parameter such as the electron drift velocity, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients agree with the experimental and theoretical for a range of E/N. The properties of electron avalanches in an electron energy non-equilibrium region.n.

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A Study on the electron energy diffusion function of the sulphur hexaflouride (SF_6 가스의 전자에너지 분포함수에 관한 연구)

  • ;金相南
    • The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.13 no.2
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    • pp.227-227
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    • 1999
  • The electron energy distributions function were analysed in sulphur hexaflouride at E/N : 500~800(Td) for a case of non-equilibrium region in the mean electron energy. This paper describes the electron transport characteristics in $SF_6$ gas calculated for range of E/N values from 150~800(Td) by the Monte Carlo simulation and Boltzmann equation method using a set of electron collision cross sections determined by the authors and the values of electron swarm parameters. The results gained that the value of ane1ctron swarm parameter such as the e1ectron drift velocity, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients agree with the experimental and theoretical for a range of E/N. The properties of electron avalanches in an electron energy non-equilibrium region.

Emission spectroscopic diagnostics of argon arc Plasma in Plasma focus device for advanced lithography light source (차세대 리소그래피 빛샘 발생을 위한 플라스마 집속장치의 아르곤 아크 플라스마의 방출 스펙트럼 진단)

  • Hong, Y.J.;Moon, M.W.;Lee, S.B.;Oh, P.Y.;Song, K.B.;Hong, B.H.;Seo, Y.H.;Yi, W.J.;Shin, H.M.;Choi, E.H.
    • Journal of the Korean Vacuum Society
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    • v.15 no.6
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    • pp.581-586
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    • 2006
  • We have generated the argon plasma in the diode chamber based on the established coaxial electrode type and investigated the emitted visible light for emission spectroscopy. We applied various voltages $2\sim3.5kV$ to the device by 0.5kV, and obtained the emission spectrum data for the focused plasma in the diode chamber on the argon pressure of 330 mTorr. The Ar I and Ar II emission line are observed. The electron temperature and ion density have been measured by the Boltzmann plot and Saha equation from assumption of local thermodynamic equilibrium (LTE) The Ar I and Ar II ion densities have been calculated to be $\sim10^{15}/cc\;and\;~10^{13}/cc$, respectively, from Saha equation.

Nano Particle Charging Characteristics of Aerosol Charge Neutralizers (에어로졸 중화기의 나노 입자 하전 특성)

  • Ji, Jun-Ho;Bae, Swi-Nam;Hwang, Jung-Ho
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.27 no.10
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    • pp.1489-1497
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    • 2003
  • Aerosol charge neutralizers with various radioactive sources have been used to apply an equilibrium charge distribution to aerosols of unknown charge distribution. However, the performance of aerosol charge neutralizers is not well known, especially for highly charged particles. Measurements of highly charged particles are needed in air cleaning devices, e.g. electrostatic precipitator, bag filter with a pre-charger, and electrical cyclone. In this study, the particle charging characteristics of two different aerosol charge neutralizers were experimentally investigated for singly charged monodisperse particles and highly charged polydisperse particles. One has radioactive source of $^{85}$ Kr (beta source, 2 mCi) and the other has $^{210}$ Po (alpha source, 0,5 mCi). The air flow rate passing through each aerosol charge neutralizer was changed from 0.2 to 2.5 L/min. The results show that the charge distribution of singly charged monodisperse particles passing through the $^{85}$ Kr aerosol charge neutralizer is well agreed with the Boltzmann equilibrium charge distribution at an air flow rate of 0.3 L/min, However, it deviates from the equilibrium charge distribution when the air flow rates are 0.6, 1,0, and 1,5 L/min, On the other hands, the effect of air flow rate is insignificant for the $^{210}$ Po aerosol charge neutralizer. The non-equilibrium character in charge distribution of highly charged polydisperse particles passing through the $^{85}$ Kr aerosol charge neutralizer greatly depends on the air flow rate, however it is insensitive to the air flow rate for the $^{210}$ Po aerosol charge neutralizer.

Recent Advance in High Pressure Induction Plasma Source

  • Sakuta, T.
    • Journal of the Korean institute of surface engineering
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    • v.34 no.5
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    • pp.395-402
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    • 2001
  • An induction thermal plasma system have been newly designed for advanced operation with a pulse modulated mode to control the plasma power in time domain and to create non-equilibrium effects such as fast quenching of the plasma to produce new functional materials in high rate. The system consists of MOSFET power supply with a maximum power of 50 kW with a frequency of 460 kHz, an induction plasma torch with a 10-turns coil of 80 mm diameter and 150 mm length and a vacuum chamber. The pulse modulated plasma was successfully generated at a plasma power of 30 kW and a high pressure of 100 kPa, with taking the on and off time as 10 ms, respectively. Measurements were carried out on the time-dependent spectral lines emitted from Ar species. The dynamic behavior of plasma temperature in a pulse cycle was estimated by the Boltzmann plot and the excitation temperature of Ar atom was found to be changed periodically from around 0.5 to 1.7 eV during the cycle. Two application regions of the induction thermal plasma newly generated were introduced to material processing with high rate synthesis based on non equilibrium effects, and to the finding of new arc quenching gases coming necessary for power circuit breaker, which is friendly with earth circumstance alternative to SF6 gas.

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A Study on the electron energy diffusion function of the sulphur hexaflouride ($ SF_6$가스의 전자에너지 분포함수에 관한 연구)

  • 김상남;하성철
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.13 no.2
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    • pp.95-101
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    • 1999
  • The electron energy distributions function were analysed in sulIitur hexaflowide at E/N : 500~800(Td) for a case of non-equilibrium region in the nran electron energy. This papa- describes the electron transport characteristics in $ SF_6$ gas calculated for range of E/N values from 150~800(Td) by the Monte Carlo simulation and Boltzmann equation Irethod using a set of electron collision cross sectioos determined by the authors and the values of electron swarm parameters. The results gained that the value of an electron swarm parameter such as the electron drift velocity, the electron ionization or attachment coefficients, longitudinal and transverse diffusion coefficients agree with the experimental and theoretical for a range of E/N. The properties of electron avalanches in an electron energy non-equilibrium region.region.

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Analysis on particle deposition onto a heated, horizontal free-standing wafer with electrostatic effect (정전효과가 있는 가열 수평웨이퍼로의 입자침착에 관한 해석)

  • Yoo, Kyung-Hoon;Oh, Myung-Do;Myong, Hyon-Kook
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.21 no.10
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    • pp.1284-1293
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    • 1997
  • The electrostatic effect on particle deposition onto a heated, Horizontal free-standing wafer surface was investigated numerically. The deposition mechanisms considered were convection, Brownian and turbulent diffusion, sedimentation, thermophoresis and electrostatic force. The electric charge on particle needed to calculate the electrostatic migration velocity induced by the local electric field was assumed to be the Boltzmann equilibrium charge. The electrostatic forces acted upon the particle included the Coulombic, image, dielectrophoretic and dipole-dipole forces based on the assumption that the particle and wafer surface are conducting. The electric potential distribution needed to calculate the local electric field around the wafer was calculated from the Laplace equation. The averaged and local deposition velocities were obtained for a temperature difference of 0-10 K and an applied voltage of 0-1000 v.The numerical results were then compared with those of the present suggested approximate model and the available experimental data. The comparison showed relatively good agreement between them.