Coupled system of PDEs to predict the sensitivity of some materials constituents of FOUP with the AMCs cross-contamination
This paper deals a predictive model using modeling and computational methods to investigate the sensitivity of some materials constituents of the FOUP with the AMCs cross contamination. Required numerical tools which are employed in order to study the AMCs cross-contamination transfer phenomena between wafers and FOUPs were developed. Numerical optimization and finite elements formulation in transient analysis were established. Analytical solution of one dimensional problem was developed and the calibration process of physical constants was performed. This mode was used to study the sensitivity of some material with the cross contamination. The behavior of the AMCs in transient analysis was determined. The model framework preserves the classical forms of the diffusion and convection-diffusion equations and yields to consistent form of the Fick's law. The adsorption kinetics of the contaminant on the surface (interface contaminant/polymer) was assumed. The adsorption process and the surface roughness effect were also traduced as a boundary condition using the switch condition Dirichlet to Neumann and the interface condition. Many tests of contamination processes were assumed in order to study the sensitivity of the materials. Optimization methods with analytical solution were used to define physical constants for each material versus contaminant. Finite element methods including adsorption kinetic were also used and by using Henry law on the interface and the switch of Dirichlet to Neumann conditions.
Keywords: Cross-contamination, FOUP, mathematical modeling, finite element method, sensitivity study.
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