A multiscale domain decomposition approach for chemical vapor deposition

We consider the chemical vapor deposition process on a trenched Si-substrate. To understand the process (e.g. the layer conformality) at the trench scale (microscale), we need solutions at both the trench and reactor scales (macroscale). Due to huge difference in the sizes of these scales, straightforward numerical computations are very challenging. To overcome this difficulty, we consider a multiscale approach by introducing an intermediate scale (mesoscale). We start with time-continuous model describing the transport processes and then perform time discretization. At each time step, using the ideas of domain decomposition inspired from [4], we provide an iterative coupling conditions for these three different scales. Using weak formulation for the time-discrete equations, we prove the convergence of this iterative scheme at each time-step. The approach also provides an alternative proof for the existence of the solutions for the time-discrete formulation.