• Title, Summary, Keyword: Charge transport equation

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Electric Discharge Analysis Using Nonlinarly-Coupled Equation of Electromagnetic Field and Charge Transport (방전현상 해석을 위한 전자장 및 전하이동 방정식의 비선형 결합 알고리즘)

  • Lee, Se-Yeon;Park, Il-Han;Lee, Se-Hee
    • Proceedings of the KIEE Conference
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    • pp.1494-1495
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    • 2006
  • A complete finite element analysis method for discharge onset process, which is governed and coupled by charge transport equation and electric field equation, was presented. The charge transport equation of first order was transformed into a second-order one by utilizing the artificial diffusion scheme. The two second-order equations were analyzed by the finite element formulation which is well-developed for second-order ones. The Fowler-Nordheim injection boundary condition was adopted for charge transport equation. After verifying the numerical results by comparing to the analytic solutions using parallel plane electrodes with one carrier system, we extended the result to blade-plane electrodes in 2D xy geometry with three carriers system. Radius of the sharp tip was taken to be 50 ${\mu}m$. When this sharp geometry was solved by utilizing the space discretizing methods, the very sharp tip was found to cause a singularity in electric field and space charge distribution around the tip. To avoid these numerical difficulties in the FEM, finer meshes, a higher order shape function, and artificial diffusion scheme were employed.

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FE Analysis of Plasma Discharge and Sheath Characterization in Dry Etching Reactor

  • Yu, Gwang Jun;Kim, Young Sun;Lee, Dong Yoon;Park, Jae Jun;Lee, Se Hee;Park, Il Han
    • Journal of Electrical Engineering and Technology
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    • v.9 no.1
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    • pp.307-312
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    • 2014
  • We present a full finite element analysis for plasma discharge in etching process of semiconductor circuit. The charge transport equations of hydrodynamic diffusion-drift model and the electric field equation were numerically solved in a fully coupled system by using a standard finite element procedure for transient analysis. The proposed method was applied to a real plasma reactor in order to characterize the plasma sheath that is closely related to the yield of the etching process. Throughout the plasma discharge analysis, the base electrode of reactor was tested and modified for improving the uniformity around the wafer edge. The experiment and numerical results were examined along with SEM data of etching quality. The feasibility and usefulness of the proposed method was shown by both numerical and experimental results.

Electrokinetic flow and electroviscous effect in a charged slit-like microfluidic channel with nonlinear Poisson-Boltzmann field

  • Chun, Myung-Suk;Kwak, Hyun-Wook
    • Korea-Australia Rheology Journal
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    • v.15 no.2
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    • pp.83-90
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    • 2003
  • In cases of the microfluidic channel, the electrokinetic influence on the transport behavior can be found. The externally applied body force originated from the electrostatic interaction between the nonlinear Poisson-Boltzmann field and the flow-induced electrical field is applied in the equation of motion. The electrostatic potential profile is computed a priori by applying the finite difference scheme, and an analytical solution to the Navier-Stokes equation of motion for slit-like microchannel is obtained via the Green's function. An explicit analytical expression for the induced electrokinetic potential is derived as functions of relevant physicochemical parameters. The effects of the electric double layer, the zeta potential of the solid surface, and the charge condition of the channel wall on the velocity profile as well as the electroviscous behavior are examined. With increases in either electric double layer or zeta potential, the average fluid velocity in the channel of same charge is entirely reduced, whereas the electroviscous effect becomes stronger. We observed an opposite behavior in the channel of opposite charge, where the attractive electrostatic interactions are presented.

SENSITIVITY ANALYSIS TO EVALUATE THE TRANSPORT PROPERTIES OF CdZnTe DETECTORS USING ALPHA PARTICLES AND LOW-ENERGY GAMMA-RAYS

  • Kim, Kyung-O;Ahn, Woo-Sang;Kwon, Tae-Je;Kim, Soon-Young;Kim, Jong-Kyung;Ha, Jang-Ho
    • Nuclear Engineering and Technology
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    • v.43 no.6
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    • pp.567-572
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    • 2011
  • A sensitivity analysis of the methods used to evaluate the transport properties of a CdZnTe detector was performed using two different radiations (${\alpha}$ particle and gamma-ray) emitted from an $^{241}Am$ source. The mobility-lifetime products of the electron-hole pair in a planar CZT detector ($5{\times}5{\times}2\;mm^3$) were determined by fitting the peak position as a function of biased voltage data to the Hecht equation. To verify the accuracy of these products derived from ${\alpha}$ particles and low-energy gamma-rays, an energy spectrum considering the transport property of the CZT detector was simulated through a combination of the deposited energy and the charge collection efficiency at a specific position. It was found that the shaping time of the amplifier module significantly affects the determination of the (${\mu}{\tau}$) products; the ${\alpha}$ particle method was stabilized with an increase in the shaping time and was less sensitive to this change compared to when the gamma-ray method was used. In the case of the simulated energy spectrum with transport properties evaluated by the ${\alpha}$ particle method, the peak position and tail were slightly different from the measured result, whereas the energy spectrum derived from the low-energy gamma-ray was in good agreement with the experimental results. From these results, it was confirmed that low-energy gamma-rays are more useful when seeking to obtain the transport properties of carriers than ${\alpha}$ particles because the methods that use gamma-rays are less influenced by the surface condition of the CZT detector. Furthermore, the analysis system employed in this study, which was configured by a combination of Monte Carlo simulation and the Hecht model, is expected to be highly applicable to the study of the characteristics of CZT detectors.

Modeling the electric transport of HCl and H3PO4 mixture through anion-exchange membranes

  • Koter, Stanislaw;Kultys, Monika;Gilewicz-Lukasik, Barbara
    • Membrane Water Treatment
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    • v.2 no.3
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    • pp.187-205
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    • 2011
  • The electric transport of the mixture of hydrochloric and phosphoric acids through strong base (Neosepta ACM) and weak base (Selemion AAV) anion-exchange membranes was investigated. The instantaneous efficiency of HCl removal from the cathode solution, $CE_{Cl}$, with and without $H_3PO_4$ was determined. It was found that $CE_{Cl}$ was 0.8-0.9 if the number of moles of elementary charge passed through the system, $n_F$, did not exceed ca. 80% of the initial number of HCl moles in the cathode solution, $n_{Cl,ca,0}$. The retention efficiency of $H_3PO_4$ in that range was close to one. The transport of acid mixtures was satisfactorily described by a model based on the extended Nernst-Planck and Donnan equations for $n_F$ not exceeding $n_{Cl,ca,0}$. Among the tested model parameters, most important were: concentration of fixed charges, the porosity-tortuosity coefficient, and the partition coefficient of an undissociated form of $H_3PO_4$. For the both membranes, the obtained optimal values of fixed charge concentration, $\bar{c}_m$, were up to 40% lower than the literature values of $\bar{c}_m$ obtained from the equilibrium measurements. Regarding the $H_3PO_4$ equilibria, it was sufficient to consider $H_3PO_4$ as a monoprotic acid.

ANALYSIS OF CHARGE COLLECTION EFFICIENCY FOR A PLANAR CdZnTe DETECTOR

  • Kim, Kyung-O;Kim, Jong-Kyung;Ha, Jang-Ho;Kim, Soon-Young
    • Nuclear Engineering and Technology
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    • v.41 no.5
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    • pp.723-728
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    • 2009
  • The response property of the CZT detector ($5{\times}5{\times}5\;mm^3$), widely used in photon spectroscopy, was evaluated by considering the charge collection efficiency, which depends on the interaction position of incident radiation, A quantitative analysis of the energy spectra obtained from the CZT detector was also performed to investigate the tail effect at the low energy side of the full energy peak. The collection efficiency of electrons and holes to the two electrodes (i.e., cathode and anode) was calculated from the Hecht equation, and radiation transport analysis was performed by two Monte Carlo codes, Geant4 and MCNPX. The radiation source was assumed to be 59.5 keV gamma rays emitted from a $^{241}Am$ source into the cathode surface of this detector, and the detector was assumed to be biased to 500 V between the two electrodes. Through the comparison of the results between the Geant4 calculation considering the charge collection efficiency and the ideal case from MCNPX, an pronounced difference of 4 keV was found in the full energy peak position. The tail effect at the low energy side of the full energy peak was confirmed to be caused by the collection efficiency of electrons and holes. In more detail, it was shown that the tail height caused by the charge collection efficiency went up to 1000 times the pulse height in the same energy bin at the calculation without considering the charge collection efficiency. It is, therefore, apparent that research considering the charge collection efficiency is necessary in order to properly analyze the characteristics of CZT detectors.

A Numerical Solution of Transport of Mono- and Tri-valent Cations during Steady Water Flow in a Binary Exchange System

  • Ro, Hee-Myong;Yoo, Sun-Ho
    • Journal of Applied Biological Chemistry
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    • v.43 no.1
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    • pp.18-24
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    • 2000
  • A one-dimensional transport of displacing monovalent ion, $A^+$, and a trivalent ion being displaced, $B^{3+}^ in a porous exchange system such as soil was approximated using the Crank-Nicolson implicit finite difference technique and the Thomas algorithm in tandem. The variations in the concentration profile were investigated by varying the ion-exchange equilibrium constant (k) of ion-exchange reactions, the influent concentrations, and the cation exchange capacity (CEC) of the exchanger, under constant flux condition of pore water and dispersion coefficient. A higher value of k resulted in a greater removal of the native ion, behind the sharper advancing front of displacing ion, while the magnitude of the penetration distance of $A^+$ was not great. As the CEC increased, the equivalent fraction of $B^{3+}^ initially in the soil was greater, thus indicating that a higher CEC adsorbed trivalent cations preferentially over monovalent ions. Mass balance error from simulation results was less than 1%, indicating this model accounted for instantaneous charge balance fairly well.

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Analysis on Particle Deposition onto a Heated Rotating Disk with Electrostatic Effect (정전효과가 있는 가열 회전원판으로의 입자침착 해석)

  • 유경훈
    • Korean Journal of Air-Conditioning and Refrigeration Engineering
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    • v.14 no.5
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    • pp.424-432
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    • 2002
  • Numerical analysis has been conducted to characterize deposition rates of aerosol particles onto a heated, rotating disk with electrostatic effect under the laminar flow field. The particle transport mechanisms considered were convection, Brownian diffusion, gravitational settling, thermophoresis and electrophoresis. The aerosol particles were assumed to have a Boltzmann charge distribution. The electric potential distribution needed to calculate local electric fields around the disk was calculated from the Laplace equation. The Coulomb, the image, the dielectrophoretic and the dipole-dipole forces acting on a charged particle near the conducting rotating disk were included in the analysis. The averaged particle deposition vetocities and their radial distributions on the upper surface of the disk were calculated from the particle concentration equation in a Eulerian frame of reference, along with a rotation speed of 0∼1,000rpm, a temperature difference of 0∼5K and a charged disk voltage of 0∼1000V.Finally, an approximate deposition velocity model for the rotating disk was suggested. The present numerical results showed relatively good agreement with the results of the present approximate model and the available experimental data.

A Quasi Two-Dimensional Model for Gas Discharge Simulation Using FE-FCT Method (기체 방전의 시뮬레이션을 위한 FE-FCT를 이용한 준 2차원적 수치 모델)

  • Koh, Wook-Hee;Park, In-Ho
    • Journal of the Korean Vacuum Society
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    • v.17 no.6
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    • pp.511-517
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    • 2008
  • A quasi two-dimensional model for numerical simulation of gas discharge is presented, based on the finite-element flux-corrected transport method. A one-dimensional continuity convection-diffusion equation coupled Poisson's equation is solved to calculate the charge density variation and the electric field is evaluated by the classical disk method. Results calculated for various benchmark problems verify the accuracy of the proposed model and illustrate its performance. This model has been applied to a streamer simulation, and the results are shown to agree well with previously published results.

Numerical Simulation of Nitrogen Discharge at Medium Pressure between Point-Plane Electrodes (침-평판 전극 사이에서 중간 압력 질소 방전의 시뮬레이션)

  • Koh, Wook-Hee;Park, In-Ho
    • Journal of the Korean Vacuum Society
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    • v.17 no.6
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    • pp.487-494
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    • 2008
  • The numerical simulation of point-to-plane discharge of nitrogen at medium pressure has been achieved by a quasi-2d numerical model. In the model, we calculate the distributions of electric charges which are varying as temporal and space and determine the electric field depending on space charge distribution by solving Poisson's equation. The continuity equations are treated numerically by using FCT (Flux-Corrected Transport) Algorithm and FEM (Finite Element Method). The numerical simulation results make us to understand the physical characteristics of nitrogen discharge at 50 torr. The comparison with experimental results[1] shows a good qualitative agreement.