Heating, venting and aerosol particles dynamics in a vacuum clean chamber: An analytical investigation

It is empirically observed and broadly used in the semiconductor manufacturing industry that the clean environment of in-vacuum processing can be enhanced through heating from outside the clean chamber. This paper reports an analytical investigation of this problem and presents the results that confirm the speeding effects of changing the temperature gradient at one end of the clean chamber on venting the aerosol particles from inside the clean chamber. First, a mathematical frame for the basic problem is formulated and then various analytical techniques are employed to reduce a set of coupled nonlinear partial differential equations to linear equations, and finally, numerical results are obtained from explicit, analytical formulas.