Mesoscopic Scale Modeling for Chemical Vapor Deposition in Semiconductor Manufacturing

Abstract

Low pressure chemical vapor deposition is a process, by which a thin layer of solid material is deposited onto the microstructured surface of a silicon wafer. Reactor scale models are used to model the flow of reacting chemicals on the scale of the chemical reactor. Feature scale models are designed to predict the evolution of the deposited film inside an individual feature. For a length scale intermediate to both classical models, the concept of a mesoscopic scale model is introduced. Depending on the typical length scale of the mesoscopic domain, either a continuum model or a kinetic model is appropriate to describe the flow mathematically. In both regimes, a homogenization technique is applied to the boundary condition at the microstructured surface to derive an equivalent boundary condition that is amenable to effective numerical simulations. In the near-continuum regime, this equivalent mesoscopic scale model is used in stand-alone to analyze cluster-to-cluster effects as well as to interface with both classical models to obtain an integrated process simulator. In the transition regime, a numerical example is given that validates the analysis.