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## 3.1.2 Cell-Based Methods

Cell-based methods use a grid of cubic cells to represent the geometry. Numerical values assigned to cells describe their contents. One can distinguish between methods using discrete and continuous values.

In the first case integral values are used to mark vacuum cells or cells with same properties of matter [26,42,93,118,122,123]. To calculate the time evolution of the surface the state of the cells near the surface must be successively modified in consideration of the given surface rates. The cell removal technique, which was used to simulate photo resist development, determines the time required to completely remove each surface material cell [26,42]. Iteratively, the state of the cell with the smallest removal time is changed, and the removal times are recalculated for all surface cells. Another technique is the building block model which was applied to deposition simulation [118]. This stochastic technique successively adds material cells with a probability proportional to the local deposition rate.

A further method, developed at the Institute for Microelectronics at the Vienna University of Technology, is based on the so-called structuring element algorithm [93,122,123], which is based on the Huygens-Fresnel principle and can be applied to deposition as well as etching processes. Appropriate structuring elements are used to construct the surface front after a certain time step. In the case of isotropic deposition, these structuring elements are spheres with a radius equal to the time step multiplied by the deposition rate. The states of all cells covered by these structuring elements are changed to obtain the profile after each time step. By nature the discrete cell representation of the geometry leads to an unrealistic stepped contour. As a consequence, the determination of the surface orientation requires a costly averaging procedure [123].

Continuous cell values are able to describe the surface position more accurately. Values between 0 and describe the filled [29] or removed [54,106,139] fraction of the cell volume. The given surface rates and the conservation of mass result in cellular automata-like update rules for the values of the surface cells. The surface can be extracted using the equi-volume rate model (EVRM) [29], which also allows a more accurate computation of surface normals than the discrete approaches.

Contrary to segment-based methods the cell-based techniques are very robust and insusceptible to topographic changes. Due to the quite simple update rules the implementation is very easy for two- and three-dimensional cases.

Next: 3.1.3 The Level Set Up: 3.1 Boundary Evolution Techniques Previous: 3.1.1 Segment-Based Methods

Otmar Ertl: Numerical Methods for Topography Simulation