To simulate the process steps used for manufacturing of semiconductors or Micro-Electro-Mechanical Systems (MEMS), it is necessary to confront problems. First, a robust numerical technique that is able to capture geometrical evolution over time is required. A very popular technique is the level set method, which represents a moving boundary implicitly as the zero level set of a function. Then, the time evolution of this level set function can easily be calculated by solving the level set equation using standard finite difference schemes. The original formulation of the level set method leads to a numerical complexity that scales with the simulation domain size rather than with the surface area, which corresponds to the optimal scaling law. In previous years, various improvements have been developed in order to realize an optimal scaling algorithm. Among them are the sparse field level set method and the hierarchical run-length-encoding method, which minimizes the computational costs and reduces the memory costs for storing a level set, respectively. We have combined both techniques within a level set framework. Our implementation was fully parallelized, in order to make use of modern multi-core CPUs and to further increase the calculation speed. Due to this speed-up, we are able to handle very large geometries.
Realistic topography simulations also require the solution of the physical model equations, in order to obtain the surface speeds as required by the level set method. For many processes ballistic particle transport to the surface can be assumed. Due to the absence of particle-particle interactions, the propagation of particles is linear, similar to light rays. Therefore, to calculate the particle transport a well known technique in computer graphics called ray tracing, can be applied. Since ray tracing can easily be parallelized, our topography simulator is able to perform physical topography simulations on very large geometries, as shown in the two figures.