A general prerequisite for computer simulations is the existence of an appropriate mathematical model describing the physical behavior. Therefore, an overview of common models used for topography simulations is provided in Chapter 2. After justifying the usage of a continuum model, models for particle transport as well as for surface kinetics are discussed. Generalized equations are presented, which are able to cover a large variety of different process models.

From the numerical point of view, two techniques are necessary to perform topography simulations. First, a method is needed which is able to describe the evolving geometry over time. This is the topic of Chapter 3, where an overview of different approaches including their basic ideas are given at the beginning. The main part of this chapter deals with the LS method which is used throughout this work. Chapter 4 continues thematically with the LS method and gives a detailed description of a fast LS framework which was developed and implemented using modern LS algorithms and data structures, enhanced by the capability of handling multiple material regions. The last part of this chapter describes the parallelization on shared memory computers.

The LS method requires the knowledge of the surface velocities in order to calculate the deformation of the geometry over time. Hence, a second method is required which efficiently calculates the required surface rates by solving the corresponding particle transport and surface reaction equations of the implemented model. The solution of the generalized model equations, as introduced in Chapter 2, is the topic of Chapter 5. There, Monte Carlo (MC) simulations are proposed to solve the transport equations and to overcome some limitations of the conventional direct integration technique. For this MC approach a well behaved scaling law can be obtained, if modern ray tracing techniques are used, which are discussed in more detail and which are optimized for the needs of topography simulation.

All the numerical techniques are finally demonstrated in Chapter 6 for a selection of different processes. Among the examples are simulations of CVD, plasma etching, anisotropic wet etching, the Bosch process, and focused ion beam (FIB) processing. Finally, Chapter 7 concludes with a brief summary and gives some ideas for future work.

Otmar Ertl: Numerical Methods for Topography Simulation