The generation of locally adapted conforming tetrahedral meshes is an important component of many modern algorithms in the finite element solution of partial differential equations. Typically, such meshes are produced by starting with a coarse initial tetrahedral mesh followed by mesh adaptation on demand over space and time. During the calculation of a time step a combination of error estimation and refinement mechanism is necessary to deliver higher accuracy, if needed, by increasing the spatial resolution. Features for refinement based on different kinds of error estimations and refinement methods applied to an initial mesh have been added to the three-dimensional Finite Element Diffusion and Oxidation Simulator FEDOS.
Using strict isotropic meshes for three-dimensional process simulation is not practicable. The need of calculation time and the limitation of memory tend to result in anisotropic adapted meshes which are more manageable. The idea is to create tetrahedral elements with special geometric qualities by manipulation of an initial coarse mesh. Different kinds of refinement methods have been implemented, investigated, and added to FEDOS.
It is well known that the simulation of time-to-failure for copper (Cu) metal lines requires modeling of vacancy electromigration as well as void nucleation, growth, and movement. Because of the complexity of this problem, different approximate approaches to its physical formulation and solution appear in the literature. Based on our work for two-dimensional electromigration-induced void migration and our experience with mesh adaptation techniques, a computational method for three-dimensional tetrahedral mesh refinement and hierarchical coarsement according to the demands of advanced electromigration simulation has been investigated.