Dynamic boundary conditions for a coupled convection-diffusion model with heat effects: applications in cross-contamination control

Abstract

This work investigates the mass transfer of the Airborne Molecular cross Contamination (AMCs) between the Front Opening Unified Pod (FOUP) and wafer (silicon substrates) during the microelectronics devices manufacturing using dynamic boundary conditions. Such cross-contamination phenomena lead to detrimental impact on production yield in microelectronic industry and a predictive approach using modelling and computational methods is a very strong way to understand and qualify the AMCs cross contamination processes. The FOUP is made of polymeric materials and it is considered as a heterogeneous porous media, it can asorb and desorb the contaminant, thus the modelled processes are the contamination of two-component in transient flow. Coupled diffusion and convection-diffusion model with heat effects are used to define the phenomena. The present methodology is, first using the optimization methods with the numerical solution in order to define the physical constants of various materials which have been studied experimentally and separately, and the second using the finite element methods including these physical constants and relevant interface condition in order to take into account the adsorption kinetics law. Numerical methods to solve the problem are proposed. The dynamics behavior of the AMCs analysis was determined thanks to the switch of Dirichlet to Neumann condition. The mathematical model preserves the classical forms of the diffusion and convection diffusion equations and yields to consistent form of the Fick's law. The computed results are in correlation with the experimental measurements. Some numerical results are presented in this work.