

BiographyAlexander Scharinger was born in 1982 in Grieskirchen, Austria. He received a Bachelor's degree in Software & Information Engineering and a Master's degree in Logic and Computation from TU Wien in 2015 and 2018, respectively. He joined the Institute for Microelectronics in April 2019, where he is currently working on his doctoral degree within the scope of the Christian Doppler Laboratory for High Performance TCAD. His research interests include efficient algorithms and data structures for surface rate calculations, in particular ray tracing and stochastic sampling methods, for Process TCAD. 
Towards Efficient and Robust Surface Flux Calculations
In levelset based topographical simulations of semiconductor fabrication processes, calculating the flux of particles on the surface is an essential step in simulations of widely used fabrication processes, such as plasma etching, chemical vapor deposition, silicon oxidation and electroplating transport. However, the surface flux calculation is usually a computationally very expensive step when considering the entire simulation, and depending on the semiconductor geometry and the physical model, it can easily become prohibitively slow. We have developed a flexible topdown Monte Carlo surface flux software library using sharedmemory algorithms, which serves as a development and evaluation platform for various flux calculation algorithms. To compute the trajectories of the particles, we use Intel's high performance ray tracing library Embree. Our library enables extensive evaluations by providing flexible callback functions for physical interactions while maintaining full compatibility with parallel execution. Our library can employ userspecified particlesurface interactions and virtually any surface reflection mechanism.
A major aspect of our flux simulation library is its representation of the surface. Our approach is built on explicit representations of the surface; surfaces composed of triangles, discs and spheres are supported and have been evaluated. Triangle surfaces exhibit the best performance for raw particlesurface collision calculations. Topography simulators internally often use an implicit representation of the semiconductor surface (being most efficient with respect to solving the fundamental levelset problem), and one needs to perform an extraction step in order to obtain a triangle mesh. A marching cubes extracted triangular surface typically results in unnecessarily high mesh resolutions, however, leading to a considerable decrease in execution performance for subsequent meshprocessing algorithms. Fig. 1 shows the impact of different triangle mesh coarsening methods on the execution time of flux calculations performed by our library. On the other hand, a discbased surface can usually be created with little effort from an implicit representation of the surface. A complication with discbased surfaces is that in order to create an approximately closed surface the discs need to overlap. A consequence of this is that the flux calculation needs to perform multihit intersection computations.
Fig. 1: Execution time of flux calculations for a geometry with deep trenches using 10^{8} randomly sampled particles. The abscissa quantifies the amount of coarsening performed by a triangle mesh coarsening algorithm developed at the Institute.