Particle deposition velocity onto a wafer or a photomask in a laminar parallel flow

Abstract

Particulate contamination is one of the critical problems that decrease product yield in semiconductor manufacturing. It is therefore important to quickly and correctly predict the particle deposition velocity for controlling the level of particulate contamination. Gaussian diffusion sphere model (GDSM) was employed to predict the mean mass transfer coefficient over a flat plate in a laminar parallel flow. The GDSM was validated for the one-dimensional flat plate by comparing with the laminar boundary layer theory in wide ranges of Schmidt number and fluid temperature. The GDSM was then used to predict the mean mass transfer coefficient over finite flat plates of common areal shapes, i.e., square, rectangle, circle, ellipse, and rhombus, with various aspect ratios. From the GDSM results, the mean Sherwood number correlation was suggested in the form of ShW =BR eW1/2S c1/3. The correlation constant was determined as B=0.691 for square/rectangular flat plates, B=0.769 for circular/elliptical flat plates, and B=0.921 for rhombic flat plates. The applicable Reynolds number range of the correlation was proposed by comparing with the simulation data. Finally, the equation to predict the particle deposition velocity onto a wafer or a photomask surface exposed to a parallel flow was suggested. © 2010 The Electrochemical Society.