Conclusion

Summarizing the main contributions in the first part, first generalized Bernstein polynomials were proposed as a standard means for approximating functions for TCAD purposes (cf. Chapter 7). In addition to their very favorable approximating properties, which were proven (cf. Chapter B), they can be implemented in a straightforward manner. Their usefulness was demonstrated in two real world examples and an algorithm for extracting Monte Carlo simulation results based on generalized Bernstein polynomials was devised and implemented (cf. Chapter 11). It is expected that the advantages of the generalized Bernstein polynomials will be recognized, although there is long history in RSM of using polynomials of degree $2$ for the same purposes.

Second global optimizers like genetic algorithms and simulated annealing are a useful supplement to local optimizers (cf. Chapter 8). Both optimization approaches are available in the SIESTA TCAD framework for optimization and inverse modeling, which was described in Chapter 9.

The second part focused on applications. First Chapter 11 underlines the usefulness of generalized Bernstein polynomials as mentioned above. The next two chapters are about topography simulation. In Chapter 13 contributions to the level set method met in the development of a topography simulator. In Chapter 12 several deposition processes were simulated and compared to measurements provided by industrial partners, where good agreement was found. Finally two interesting inverse modeling problems were solved in Chapter 14 and Chapter 15. Especially the problem in Chapter 15 posed high demands on the SIESTA framework.