• 대한기계학회논문집
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• 제19권5호
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• pp.1319-1332
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• 1995

Numerical analysis was performed to characterize the particle deposition behavior on a horizontal free-standing wafer with thermophoretic effect under the turbulent flow field. A low Reynolds number k-.epsilon. turbulence model was used to analyze the turbulent flow field around the wafer, and the temperature field for the calculation of the thermophoretic effect was predicted from the energy equation introducing the eddy diffusivity concept. The deposition mechanisms considered were convection, diffusion, sedimentation, turbulence and thermophoresis. For both the upper and lower surfaces of the wafer, the averaged particle deposition velocities and their radial distributions were calculated and compared with the laminar flow results and available experimental data. It was shown by the calculated averaged particle deposition velocities on the upper surface of the wafer that the deposition-free zone, where the deposition velocite is lower than 10$^{-5}$ cm/s, exists between 0.096 .mu.m and 1.6 .mu.m through the influence of thermophoresis with positive temperature difference of 10 K between the wafer and the ambient air. As for the calsulated local deposition velocities, for small particle sizes d$_{p}$<0.05 .mu.m, the deposition velocity is higher at the center of the wafer than at the wafer edge, whereas for particle size of d$_{p}$ = 2.0 .mu.m the deposition takes place mainly on the inside area of the wafer. Finally, an approximate model for calculating the deposition velocities was recommended and the calculated deposition velocity results were compared with the present numerical solutions, those of Schmidt et al.'s model and the experimental data of Opiolka et al.. It is shown by the comparison that the results of the recommended model agree better with the numerical solutions and Opiolka et al.'s data than those of Schmidt's simple model.

• 대한기계학회논문집B
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• 제21권10호
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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.

• 대한기계학회논문집
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• 제17권9호
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• pp.2315-2328
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• 1993

The turbulence effect of particle deposition on a horizontal free-standing wafer in a vertical flow has been studied numerically by using the low-Reynolds-number k-.epsilon. turbulence model. For both the upper and lower surfaces of the wafer, predictions are made of the averaged particle deposition velocity and its radial distribution. Thus, it is now possible to obtain local information about the particle deposition on a free-standing wafer. The present result indicates that the particle deposition velocity on the lower surface of wafer is comparable to that on the upper one in the diffusion controlled deposition region in which the particle sizes are smaller than $0.1{\mu}m$. And it is found in this region that, compared to the laminar flow case, the averaged deposition velocity under the turbulent flow is about two times higher, and also that the local deposition velocity at the center of wafer is high equivalent to that the wafer edge.