가열 또는 냉각되는 수평웨이퍼 표면으로의 입자침착에 관한 해석

Analysis of Particle Deposition onto a Heated or Cooled, Horizontal Free-Standing Wafer Surface

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.