In general, semiconductor topography simulations are a vital part of the set of process technology computer-aided design (TCAD) simulation toolset. However, the here presented algorithm and findings are applicable to other fields in a similar manner. In this work we focus in particular on topography simulations for modeling semiconductor device fabrication processes, since the merging of fronts often occurs there. This implicit representation allows the level-set method to robustly handle the merging of fronts without self-intersections. If the grid resolution is equivalent in all coordinate directions then it is called a regular grid with resolution \(\Delta x\). Which is discretized on a grid with resolutions \((\Delta x_1 \dots \Delta x_n)\). Our algorithm and findings are applicable to other fields of applications such as surface simplification. We show, however, that the latter is still a viable option, and that our algorithm is able to reliably detect features on geometries stemming from complicated, practically relevant geometries. For performance reasons, our algorithm can be in principal linked to different curvature calculation methods, however, as will be discussed, two particularly attractive options are available: (i) A novel extension of the standard curvature calculation method for level-set functions, and (ii) an often disregarded method for calculating the curvature due to its purported low numerical accuracy. Our approach is based on two different, complementary curvature calculation methods of the zero level-set and an optimized feature detection parameter to detect features. To that end, we present a fast parallel geometric feature detection algorithm for three-dimensional level-set functions. Feature detection has to be computationally efficient and sufficiently accurate to reliably detect the critical points. To efficiently increase the accuracy in regions neighboring these critical points, automatic hierarchical domain refinement is required, guided by robust feature detection. These models tend to produce surfaces with critical points where accuracy is paramount. In the latter, the level-set method is employed for topography simulations of semiconductor device fabrication processes, being driven by complicated physical and chemical models. The level-set method is widely used in expanding front simulations in numerous fields of computational research, such as computer graphics, physics, or microelectronics.
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