For process and device simulation, very high mesh densities are often required to obtain accurate simulation results. Unfortunately, the required mesh densities depend often on a direction. Conventional mesh-refinement strategies generate isotropic meshes with a high amount of mesh points, reaching the memory and time limits in particular for three-dimensional simulations. For a better resolution of the carrier concentrations, for instance, a boundary-conforming mesh-generation method with tunable mesh spacings in almost orthogonal directions was developed. Similar to elliptic mesh generation, the mesh points are placed inside the simulation regions based on the solution of partial differential equations. The method used can produce highly anisotropic mesh densities in the regions of particular interest. In contrast to elliptic grid generation, which produces structured grids, the method used generates triangular or tetrahedral (unstructured) Delaunay meshes in two or three dimensions, respectively, which are very well suitable for the process and device simulators.

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