NUMERICAL-ANALYSIS OF PARTICLE DEPOSITION ONTO HORIZONTAL FREESTANDING WAFER SURFACES HEATED OR COOLED

Numerical analysis was performed to characterize the particle depositi on behavior on a horizontal freestanding wafer with thermophoretic eff ect under the turbulent how field, A low Reynolds number turbulent k-e psilon model was used to analyze the turbulent flow field around the w ater. The deposition mechanisms considered were convection, Brownian a nd turbulent diffusion, sedimentation, and thermophoresis, The average d particle deposition velocities and their radial distributions for bo th the upper and lower surfaces of the wafer were calculated from the particle concentration equation in an Eulerian frame of reference, Whe n the wafer is unheated, in the diffusion-controlled deposition regime with particle size d(p) < 0.1 mu m the averaged particle deposition v elocity under the turbulent flow was about 1.3 times higher than the l aminar flow case, and the local deposition velocity near the center of the wafer was high equivalent to that near the edge. The particle dep osition on the lower surface was comparable to that on the upper surfa ce, When heated, the deposition-free zone, where the deposition veloci ty is lower than 10(-5) cm/s, exists between 0.096 mu m and 1.6 mu m w ith Delta T of 10K, indicating shifting behavior to larger size range compared with the laminar flow case. As for the local deposition veloc ities, for d(p) < 0.05 mu m, the deposition velocity is higher near th e center of the wafer than near the wafer edge, whereas for d(p)=2.0 m u m the deposition takes place mainly on the inside area of the wafer. The comparison of Phe present numerical results with the experimental data by Ye et al. (1991) showed seasonably good agreement, Finally, a n approximate deposition velocity model was suggested. The comparison of the model calculations with the present numerical results and the e xperimental data of Opiolka et al. (1994) showed good agreement.