Particle deposition on wafers: a comparison between two modeling approaches

Abstract

The rate of particle deposition on wafers and the particle concentration profile above a wafer surface are calculated and compared using two different model approaches. Both methods deal with the steady-state, two-dimensional flow, temperature and concentration profiles above a flat surface. In the first approach, these governing equations are solved numerically by finite difference techniques. In the second approach, boundary layer theory is utilized to approximate the flow and temperature profiles, a perturbation technique is used to approximate the inertial effects, and the concentration profile is solved numerically via finite difference methods. Comparisons are made for calculations representing both one- and two-dimensional geometries for stagnation flow to a wafer. Mechanisms that were considered to effect particle deposition included convection, diffusion, sedimentation, electrical forces and thermophoresis. In all cases, comparisons between model approaches were quite good. Of particular interest was the prediction of particle deposition for the situation in which both electrical forces and thermophoretic forces influenced the particle. It was seen that the ‘beneficial’ effects of thermophoresis (i.e. the formation of a particle-free zone for certain ranges of particle size) were completely negated by quite modest attractive electrical forces.