Particle deposition in parallel-plate reactors: Simultaneous diffusion and external forces

Particle deposition resulting from uniform external forces and Brownian motion is modeled in a parallel-plate reactor geometry characteristic of a wide range of semiconductor process tools: uniform, isothermal, downward flow exiting a perforated-plate showerhead separated by a small gap from a parallel, circular wafer. Particle transport is modeled using a Eulerian approach neglecting particle inertia and interception. Particles are assumed to originate in a planar trap located between the plates, such as would result for particles released from a plasma-induced particle trap after plasma extinction. Flow between infinite parallel plates is described by an analytic quasi-one-dimensional creeping flow approximation, where the showerhead is treated as a porous plate. An analytic, integral expression for particle collection efficiency (fraction of particles that end up on the wafer) is derived as a function of four dimensionless parameters: the flow Reynolds number, a dimensionless trap height, a dimensionless particle drift velocity, and the particle Peclet number. Numerical quadrature is used to calculate particle collection efficiency in terms of the controlling dimensionless parameters for external forces, which either enhance or inhibit particle deposition. Example calculations of collection efficiency are also presented in dimensional terms for a representative set of process conditions. Strategies to reduce particle deposition include the use of a protective external force and manipulation of the trap to keep it as far from the wafer as possible.