Mixed element trees: a generalization of modified octrees for the generation of meshes for the simulation of complex 3-D semiconductor device structures

This paper addresses the problem of the allocation of spatial grids for complex nonplanar three-dimensional (3-D) semiconductor device structures. We have characterized the class of meshes suitable for the integration of the device equations with the usual numerical schemes as being a subclass of the class of Delaunay meshes. We propose an algorithm for the efficient generation of such admissible meshes based on the iterative refinement of coarse elements. The generated meshes permit an exact geometrical modeling of rather general domain boundaries of modern silicon devices avoiding the “obtuse angle problem” by construction