An Effective Viscosity Equation for the CFD Analysis of the Micro Flows in the Confinement Ring

For plasma etching equipment, the confinement ring is installed between the outlet of the reactor chamber and the pumping channel. The fact that the micro flows in the confinement ring behave in far beyond the continuum regime makes it difficult for engineers to perform CFD analysis with sufficient accuracy. In order to solve this problem, a Bosanquet-type effective viscosity equation is used to compensate the errors for the rarefied gases. A fast approach is proposed to determine the feasible values of the two parameters in the effective viscosity equation based on the pumping experiment results. The effective viscosity equation for micro flows in the confinement ring is further derived. Good agreement is observed between the CFD simulations using the effective viscosity equation and the experiment results. This work will help engineers perform more precise CFD simulations and further improve product design, especially for the pumping system. Moreover, the fast approach to determine the parameters’ values in the effective viscosity equation is also helpful for engineers to tackle other similar problems.