Abstract: Nowadays, with the increasing of the wafer's size and
the decreasing of critical size of integrated circuit manufacturing in
modern high-tech, microelectronics industry needs a maximum
attention to challenge the contamination control. The move to 300
[mm] is accompanied by the use of Front Opening Unified Pods for
wafer and his storage. In these pods an airborne cross contamination
may occur between wafers and the pods. A predictive approach using
modeling and computational methods is very powerful method to
understand and qualify the AMCs cross contamination processes.
This work investigates the required numerical tools which are
employed in order to study the AMCs cross-contamination transfer
phenomena between wafers and FOUPs. Numerical optimization and
finite element formulation in transient analysis were established.
Analytical solution of one dimensional problem was developed and
the calibration process of physical constants was performed. The least
square distance between the model (analytical 1D solution) and the
experimental data are minimized. The behavior of the AMCs
intransient 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 process and the surface roughness effect were also
traduced as a boundary condition using the switch condition Dirichlet
to Neumann and the interface condition. The methodology is applied,
first using the optimization methods with analytical solution to define
physical constants, and second using finite element method including
adsorption kinetic and the switch of Dirichlet to Neumann condition.
Abstract: A generalized Dirichlet to Neumann map is
one of the main aspects characterizing a recently introduced
method for analyzing linear elliptic PDEs, through which it
became possible to couple known and unknown components
of the solution on the boundary of the domain without
solving on its interior. For its numerical solution, a well conditioned
quadratically convergent sine-Collocation method
was developed, which yielded a linear system of equations
with the diagonal blocks of its associated coefficient matrix
being point diagonal. This structural property, among others,
initiated interest for the employment of iterative methods for
its solution. In this work we present a conclusive numerical
study for the behavior of classical (Jacobi and Gauss-Seidel)
and Krylov subspace (GMRES and Bi-CGSTAB) iterative
methods when they are applied for the solution of the Dirichlet
to Neumann map associated with the Laplace-s equation
on regular polygons with the same boundary conditions on
all edges.