Anisotropic mesh refinement for the simulation of three-dimensional semiconductor manufacturing processes

This paper presents an anisotropic adaptation strategy for three-dimensional unstructured tetrahedral meshes, which allows us to produce thin mostly anisotropic layers at the outside margin, i.e., the skin of an arbitrary meshed simulation domain. An essential task for any modern algorithm in the finite-element solution of partial differential equations, especially in the field of semiconductor process and device simulation, the major application is to provide appropriate resolution of the partial discretization mesh. The start-up conditions for semiconductor process and device simulations claim an initial mesh preparation that is performed by so-called Laplace refinement. The basic idea is to solve Laplace's equation on an initial coarse mesh with Dirichlet boundary conditions. Afterward, the gradient field is used to form an anisotropic metric that allows to refine the initial mesh based on tetrahedral bisection.