Particle Transport in Parallel-Plate Reactors

Abstract

A major cause of semiconductor yield degradation is contaminant particles that deposit on wafers while they reside in processing tools during integrated circuit manufacturing. This report presents numerical models for assessing particle transport and deposition in a parallel-plate geometry characteristic of a wide range of single-wafer processing tools: uniform downward flow exiting a perforated-plate showerhead separated by a gap from a circular wafer resting on a parallel susceptor. Particles are assumed to originate either upstream of the showerhead or from a specified position between the plates. The physical mechanisms controlling particle deposition and transport (inertia, diffusion, fluid drag, and external forces) are reviewed, with an emphasis on conditions encountered in semiconductor process tools (i.e., sub-atmospheric pressures and submicron particles). Isothermal flow is assumed, although small temperature differences are allowed to drive particle thermophoresis. Numerical solutions of the flow field are presented which agree with an analytic, creeping-flow expression for Re < 4. Deposition is quantified by use of a particle collection efficiency, which is defined as the fraction of particles in the reactor that deposit on the wafer. Analytic expressions for collection efficiency are presented for the limiting case where external forces control deposition (i.e., neglecting particle diffusion and inertia). Deposition from simultaneous particle diffusion and external forces is analyzed by an Eulerian formulation; for creeping flow and particles released from a planar trap, the analysis yields an analytic, integral expression for particle deposition based on process and particle properties. Deposition from simultaneous particle inertia and external forces is analyzed by a Lagrangian formulation, which can describe inertia-enhanced deposition resulting from particle acceleration in the showerhead. An approximate analytic expression is derived for particle velocity at the showerhead exit as a function of showerhead geometry, flow rate, and gas and particle properties. The particle showerhead-exit velocity is next used as an initial condition for particle transport between the plates to determine whether the particle deposits on the wafer, as a function of shower-head-exit particle velocity, the plate separation, flow rate, and gas and particle properties. Based on the numerical analysis, recommendations of best practices are presented that should help tool operators and designers reduce particle deposition in real tools. These guidelines are not intended to replace detailed calculations, but to provide the user with a general feel for inherently-clean practices.