This thesis is separated into two major parts, where the first one presents
theoretical concepts of mesh adaptation techniques, in
two chapters. Based on the
tetrahedral bisection method different extensions are presented to incorporate
anisotropy. This allows to produce meshes with direction dependent mesh
densities. The advantage is the reduction of mesh nodes compared to strict
isotropic meshes and, therefore, a dramatic reduction of computational costs.
As the first section is related to pure geometric refinement methods, the
latter one is focused on data driven partitioning methods. The usage of pure
geometric driven refinement methods controlled by data stored on the mesh is the
driving point of this part. The idea is to use gradient fields and also the
Hessian matrix of simulation quantities to control the refinement process and
at least to produce finer meshes in particular regions of the domain which
require a higher accuracy.
The second part of this thesis is related to more application-oriented mesh
refinement techniques which reflect the demands of sophisticated TCAD
tools. Chapter 4 deals with the simulation of diffusion,
carried out with the numerical method of finite elements (FE). A heuristic
error estimator is developed which controls an anisotropic gradient driven
refinement method to increase the accuracy of the simulation.
Chapter 5 covers the issue of a dynamic refinement-coarsement scheme
used for tracking the movement of an electromigration induced void.
Modeling of the transition between the void and the metal interconnect line is
performed by a so-called diffuse interface. It is in the nature of this
approach that in the interface area a good spatial resolution is needed.
The last chapter of the application-oriented part covers a different group of
numerical calculations, the so-called full band Monte Carlo simulations. For this kind
of simulations a numerical representation of the band structure of silicon in
the unit cell of the reciprocal lattice, the so-called Brillouin zone, is
used to capture the dependence of the carrier energy on the wave
vector. However, the discretization of the Brillouin zone can be improved by
sophisticated refinement techniques which are presented in this chapter.
The thesis is concluded by Chapter 7 where a short summary and an outlook for further work is given.