The simulation of semiconductor manufacturing steps allows for a better understanding of the underlying physics as well as for process optimizations, without the need for costly experiments. Many steps in the process chain for building integrated circuits alter the topography of the wafer surface by etching or deposition of new material layers. In this work, new numerical techniques for an efficient and more accurate simulation of such processes are presented.
A major concern of topography simulations is an accurate description of the geometric changes over time, especially in three dimensions. For this purpose, a fast framework based on the level set method was developed. Using the latest algorithms and data structures, such as the sparse field method and hierarchical run-length encoding, the computation time and the memory consumption was minimized, which enabled the handling of the time evolution of large three-dimensional geometries. An accurate description of different material regions and material-dependent surface rates, which is especially important for the simulation of etching processes, was achieved using a novel multi-level-set technique. Moreover, algorithms for geometrical operations and testing of directional visibility and connectivity have been realized. In order to capitalize on modern multi-core processors, a new approach for the parallelization of the hierarchical run-length encoding is presented.
Another concern of realistic topography simulation is the determination of surface rates. Advanced surface kinetics models require the calculation of the particle flux distributions on the surface. Although the particle transport can be approximated to be ballistic for many processes, their calculation is still computationally very intensive, since reemissions or specular-like reflexions need to be considered. Three-dimensional simulations are, therefore, often limited to simplified models or small structures. A promising approach to overcome these limitations is a Monte Carlo technique, which simulates many particle trajectories in order to derive the corresponding flux distributions. In this work, a new technique to apply the Monte Carlo calculation directly to the implicit level set surface representation is presented. Furthermore, in order to minimize the computational costs of this approach, advanced ray tracing algorithms and data structures were applied. These methods have been adapted and optimized for the requirements of topography simulations.
Finally, the presented numerical methods were tested on various process models which have been reported in literature in order to demonstrate their wide applicability, especially for large three-dimensional structures.