Improving the quality of meshes for the simulation of semiconductor devices using Lepp-based algorithms

摘要

This paper discusses a new post-process algorithm for generating valid Delaunay meshes for the Box-method (finite-volume method) as required in semiconductor device simulation. In such an application, the following requirements must be considered: (i) in critical zones of the device, edges aligned with the flow of the current (anisotropic meshes) are needed; (ii) boundary and interface triangles with obtuse angles opposite to the boundary/interfaces are forbidden; (iii) large obtuse angles in the interior of the device must be destroyed and (iv) interior vertices with high vertex-edge connectivity should be avoided. By starting from a fine Delaunay mesh that satisfies condition (i), the algorithm produces a Delaunay mesh that fully satisfies condition (ii) and satisfies conditions (iii) and (iv) according to input tolerance parameters γ and c, where γ is a maximum angle tolerance value and c is a maximum vertex-edge connectivity tolerance value. Both to destroy any target interior obtuse triangle t and any target high vertex-edge connectivity, a Lepp-Delaunay algorithm is used. The elimination of obtuse angles opposite to the boundary and/or interfaces is done either by longest edge bisection or by the generation of isosceles triangles. The Lepp-Delaunay algorithm allows a natural improvement of the input mesh by inserting a few points in some existing edges of the current triangulation. Examples of the use of the algorithm over Delaunay constrained meshes generated by a normal offsetting approach will be shown. A comparison with an orthogonal refinement method followed by Voronoi point insertion is also included.