Fast Model for Deposition in Trenches using Geometric Advection

We have developed and implemented a model for deposition in a trench, applicable to highly reactive chemistries with high sticking probabilities $(\sim 1)$. The presented model calculates the final deposited thickness for all relevant points inside the trench by finding the view-factor dependent surface rates and integrating those over the entire simulation time. The model also takes into account the shrinking view-factor due to deposition at the top of the trench. Subsequently, the calculated thicknesses along the trench are used to generate the final physical structure by geometric advection in a Level Set framework. We show that our model, combined with the geometric advection framework, can accurately generate the expected physical shape of the deposited film at simulation times 100 times faster than alternatives with iterative schemes. The method was compared to models using top-down ray tracing with Engquist-Osher and Lax-Friedrichs iterative advection schemes.