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1.3 Outline of this Thesis

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.


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Next: 2. Mesh Refinement in Up: 1. Introduction Previous: 1.2 Mesh Adaptation

Wilfried Wessner: Mesh Refinement Techniques for TCAD Tools