The simulation of topography changing processes in semiconductor manufacturing requires the implementation of two separate methods. First, a method to describe a surface and its evolution over time, and second, a method to determine the surface velocity. A well-established method of keeping track of the surface evolution is the level set method, which describes the surface implicitly as the zero level set of the level set function. For given surface velocities the movement of the surface can be obtained through the time integration of the level set equation. In our simulations we use new techniques to solve this equation efficiently. We apply the sparse field level set method, which is a further development of the narrow band level set method intended to speed up computation. Furthermore, we use the hierarchical run-length-encoded level set data structure in order to reduce the memory requirements to a minimum. Topography simulations, especially simulations of etching processes, require an incorporation of regions of different materials. We developed a multi-level-set method, which is also able to describe layers which are thinner than the grid constant.
For the calculation of the surface velocity, we use the Monte Carlo method. The trajectories of a huge number of particles are simulated in order to calculate the fluxes at the surface. If ballistic transport is assumed at feature-scale, all particle trajectories are straight lines. Therefore, modern ray tracing techniques can be applied to reduce the computational effort. The Monte Carlo method is well suited to describe more complex processes. For example, specular reflections of particles can be easily incorporated. A further advantage of the Monte Carlo method is that it can be easily parallelized on shared memory systems. Through the implementation of all these techniques, we are able to simulate various deposition and etching processes. A good example is our successful simulation of a Bosch process (as depicted in the figure).