Simulation of Microelectronic Structures using A Posteriori Error Estimation and Mesh Optimization

We present an error estimation driven three-dimensional unstructured mesh optimization technique based on a posteriori error estimation techniques. We briefly summarize error estimation techniques as well as mesh quality estimations and apply them to problems of semiconductor device and process simulation. We then optimize the tessellation of the simulation domain with different strategies. In contrast to other work [1, 2] our approach also covers three-dimensional domains with unstructured tetrahedral meshes. The major advantages of this approach is that tetrahedral meshes are locally adaptable and surfaces can be modeled with arbitrary precision. Maximum error criteria trigger the refinement procedure and increase the accuracy of the solution. The simulation domain is refined in regions of high error without any user interaction or hand crafted mesh generation which makes it applicable for real world problems.