The simulation of topography changing processes for semiconductors or Micro-Electro-Mechanical Systems (MEMS) manufacturing requires a method that is able to describe non-static geometries. A wide-spread technique is the level set method, which represents a moving boundary as the zero level set of an implicit function. The time evolution of this level set function can be calculated by solving the level set equation. The main advantage of this method is its robustness and the inherent incorporation of topographic changes.
Over recent years, several techniques have been developed to make this level set method more efficient: The sparse field level set method reduces the computational costs during time evolution. Hierarchical Run-Length-Encoding (HRLE) stores a level set function in a very memory efficient way. By combination of both methods, we have developed a fast level set framework for topography simulation. In addition, this framework is able to handle multiple material regions, which is necessary for the simulation of many processes, particularly with regard to etching processes. Different material regions are represented by several level sets for the surface and the interfaces. If the level set representation is appropriately chosen, then very thin layers with thicknesses smaller than the grid spacing can be accurately represented and incorporated over the time evolution. This is of importance for the simulation of etching processes with high selectivity. Our technique has been successfully applied to simulate alternating etching and deposition cycles of a Bosch process, where three material regions (the mask, the substrate and the passivation layer) are incorporated.
The framework also makes use of the HRLE data structure to realize efficient algorithms that are useful for topography simulation: Boolean operations of level sets, which can be used for geometrical structuring, can be realized with optimal complexity. Furthermore, the visibilities, which are necessary for uni-directional etching, can be efficiently determined. We have also developed an algorithm for the fast detection of voids that can emerge during deposition processes.