Recursive M-tree method for 3-D adaptive tetrahedral mesh refinement and its application to Brillouin zone discretization

We present a high speed adaptive tetrahedral mesh refinement method based on the recursive multi-tree algorithm. To our knowledge, this is the first refinement algorithm that is able to improve the quality of the original mesh. In this paper, the method has been applied to discretize the Brillouin zone of silicon for full band Monte Carlo device simulation. Densities of states for seven electron and hole bands of silicon are computed based on the new refined tetrahedral meshes.