Parallel Velocity Extension for Level-Set-Based Material Flow on Hierarchical Meshes in Process TCAD

The level-set method is widely used for high-accuracy 3-D topography simulations in process technology computer-aided design (TCAD) because of its robustness to topological changes introduced by the involved complicated physical phenomena. Particularly challenging are material flow processes, such as oxidation, reflow, and silicidation, as these require the solution of intricate physical models and the extension of the model-dependent velocity fields to the entire simulation domain at every time step to accurately compute the advection. This velocity extension, thus, introduces yet another computational burden at every time step, which is significant when considering that high-accuracy material flow simulations can easily require several hundred time steps and are applied multiple times in cutting-edge fabrication processes of integrated circuits. In this work, a shared-memory parallel scalar and vector velocity extension algorithm for level-set-based material flow simulations on hierarchical meshes is introduced, allowing to further reduce the turnaround time of TCAD workflows. The performance is evaluated by investigating a representative material flow simulation of 3-D thermal oxidation of silicon. A parallel speedup of 7.1 for the vector-valued extension and 6.6 for the scalar-valued extension is achieved for ten threads; the latter outperforms a previous approach by up to 60%.