String/segment-based algorithms represent the surface as a list of line segments in two dimensions and as list of polygonal/triangular segments in three dimensions. Two-dimensional implementations can be found in  and . Their advantages are a high level of accuracy in representing and moving the surface as well as an implicit polygonal data format which makes the resulting geometries easy to be meshed and to be used as input for consequent grid-based programs. Nevertheless, they need insertion and deletion of segments at corners and edges and require careful concepts in order to avoid formation of non-physical loops and self-intersections of the evolving surface. For these reasons only two three-dimensional implementations of this method can be found, namely, one by Edward Scheckler  and one by Eberhard Bär . Another string-based approach, EVOLVE, has been applied to many two-dimensional simulations with close relation to equipment scale considerations and in excellent agreement with experimental data . For its three-dimensional expansion  the physical modeling parts of EVOLVE were combined with the facet motion algorithm proposed by Scheckler .
Another group of topography programs can be summarized under the term Monte Carlo methods. The geometry representations of these programs bases primarily on orthogonal grids. Similar to Monte Carlo simulations in other fields their application focuses on the fundamental physical and chemical particle-particle and particle-surface interactions on atomistic level and therefore mainly addresses single process simulation. The method comprises works by Pelka  and very comprehensive works by Smy, Brett, and Dew . Their approach combines results from the three-dimensional reactor scale Monte Carlo particle transport simulator SIMSPUD with the feature scale simulator SIMBAD, thus resulting in interpolated three-dimensional deposition profiles . This approach is very closely related to the manufacturing process since it incorporates experimental data such as target erosion profiles and deals with the evolution of the grain structure in the deposited films. Monte Carlo models combining particle transport simulation and surface reaction kinetics for plasma etching processes are also well established  and similarly in  which gives a very complete comparison between two- and three-dimensional simulations.
Ever since its introduction to modeling of semiconductor processes , the level set technique has attracted much interest for tracking the motion of surfaces. A very complete compilation of different models for semiconductor topography simulation with the level set technique is given in . The importance of this new method is highlighted by the numerous similar implementations which are emerging, e.g.,  and . Interestingly enough the group at the Center of Integrated Systems at Stanford University has dropped its segment-based development for SPEEDIE  and now focuses on level set methods .
Additionally, several implementations for topography simulators can be found in the area of cellular methods, such as the early implementation of the cell-removal algorithm , and MASTER . From the point of view of the used geometry representation, the approach presented in this thesis also belongs to this group of cellular simulators. Its so called structuring element algorithm was first published in . A very similar pixel-based two-dimensional algorithm followed in . For the sake of completeness a shock-tracking algorithm  with broad applications in simulation of sputtering processes  has to be mentioned.
When talking about success of the different approaches, a look at commercial packages and the algorithms they use for topography simulation is helpful. Avant!1 most recently has released TAURUS, a multi-dimensional process and device simulation package completely based on level set techniques. Despite the enthusiasm about level set techniques at academic level, this is still the only important commercial implementation. Silvaco2 most recently published a new approach, where mesh generation and topography simulation is directly coupled . The main goal of the newly developed technique is to avoid the procedure to extract the zero level for the level set function, which is not a trivial task for three-dimensional structures. Furthermore the new technique is intended to circumvent the memory and CPU time restrictions due to the large number of grid points necessary for the level set methods.
ISE AG3 relies on PROSIT for its three-dimensional geometry generation. This is a solid modeling tool for emulating etching and deposition processes, which uses different models resembling to ``brushes'' used in image processing. Trough a research project of the European Community ISE closely worked together with Sigma-C4a German TCAD vendor who provides a complete topography simulation package with the deposition algorithms from  and the etching method from  as well as modules for lithography simulation.
This overview and the many kinds of different approaches it presents underlines that topography simulation can be tackled in many different ways. Each of the methods has specific advantages and drawbacks. People involved in topography simulation should always carefully check different approaches available for best suitability to their needs.
Among all these algorithms cellular methods are renowned for their extraordinary robustness. Further advantages, especially when talking about cellular algorithms for tracking surface movement, are that they implicitly avoid the formation of non-physical loops as observed in segment-based algorithms  and therefore save efforts of implementing complicated self-intersection detection and delooping methodologies. Thus their coding can be kept very clear, foreseeable, and self-explaining. Finally, when considering only the evolution of the surface, they require no special treatment for emerging voids or sections of material being separated from the bulk, since they are volume-based and need no adding or deleting of segments.
For these reasons a cellular algorithm was the preferred method for this thesis about modeling of etching and deposition processes. I do not state that our cellular algorithm is the only method of choice for any kind of topography simulation. Yet, it was selected for its robustness and, not to forget, for its availability for a quick start for feature scale modeling for etching and deposition processes in semiconductor manufacturing.