Numerical Analysis of Particle Deposition onto Horizontal Freestanding Wafer Surfaces Heated or Cooled

ABSTRACT

Numerical analysis was performed to characterize the particle deposition behavior on a horizontal freestanding wafer with thermophoretic effect under the turbulent flow field. A low Reynolds number turbulent κ-ε model was used to analyze the turbulent flow field around the water. The deposition mechanisms considered were convection, Brownian and turbulent diffusion, sedimentation, and thermophoresis. The averaged particle deposition velocities and their radial distributions for both the upper and lower surfaces of the wafer were calculated from the particle concentration equation in an Eulerian frame of reference. When the wafer is unheated, in the diffusion-controlled deposition regime with particle size d_p < 0.1 μm the averaged particle deposition velocity under the turbulent flow was about 1.3 times higher than the laminar flow case, and the local deposition velocity near the center of the wafer was high equivalent to that near the edge. The particle deposition on the lower surface was comparable to that on the upper surface. When heated, the deposition-free zone, where the deposition velocity is lower than 10⁻⁵ cm/s, exists between 0.096 μm and 1.6 μm with δT of 10K, indicating shifting behavior to larger size range compared with the laminar flow case. As for the local deposition velocities, for d_p < 0.05 μm, the deposition velocity is higher near the center of the wafer than near the wafer edge, whereas for d_p = 2.0 μm the deposition takes place mainly on the inside area of the wafer. The comparison of the present numerical results with the experimental data by Ye et al. (1991) showed reasonably good agreement. Finally, an approximate deposition velocity model was suggested. The comparison of the model calculations with the present numerical results and the experimental data of Opiolka et al. (1994) showed good agreement.