A Homogenization Technique for the Development of Mesoscopic Scale Models for Chemical Vapor Deposition

Abstract

This dissertation presents a problem arising from the simulation of gas flow over microstructured surfaces. For the industrial application under consideration, the problem is appropriately given as a time-dependent nonlinear reaction-diffusion equation on a domain, which includes a flux condition on a boundary surface consisting of a microscopic fine structure. An equivalent problem for the bulk solution is derived, which incorporates all physical quantities of interest and which is accessible to efficient numerical simulation at the same time. This is achieved by applying a homogenization technique to the boundary condition, which eliminates the microscopic scale while retaining its effect on the bulk solution. The derivation presented in this dissertation is valid for a three-dimensional domain and a general boundary surface given in parameterized form. The underlying application area in semiconductor manufacturing is the modeling of chemical vapor deposition in single wafer reactors..