Gaussian diffusion sphere model to predict deposition velocity onto wafers in laminar parallel airflow considering thermophoresis

Abstract

The Gaussian Diffusion Sphere Model (GDSM) was developed and improved to predict the particle deposition velocity onto a flat plate exposed to parallel airflow by considering thermophoresis in addition to the Brownian diffusion and the gravitational settling of particles. The plate surface temperature was varied and considered to be either hotter or colder than the temperature of the parallel airflow. The GDSM was able to estimate the particle deposition velocity under the influence of thermophoresis not only correctly but also very quickly, compared to the numerical approach to calculate the deposition velocity by simulating thermo-flow and particle transport. As the next step, the particle deposition velocities onto both face-up and face-down surfaces of the 450 mm wafer exposed to the parallel airflow were predicted with the GDSM by varying the wafer temperature. It was anticipated that the schemes of heating the wafer and placing the critical surface inverted during the horizontal transport of the wafer could greatly reduce the particulate contamination of the wafer critical surface.