High Knudsen Number Physical Vapor Deporition: Predicting Deposition Rates and Uniformity

Although the analogy between thermal radiation and collisionless molecular flow has been known since the experiments of Knudsen in the early 20^th century, it has not been exploited for mainstream analysis of physical vapor deposition processes. With the availability of commercial finite element and computational fluid dynamics software having built-in cavity radiation solvers with features such as automatic surface definition, meshing and view factor calculation, the analysis of thermal radiation problems has become a straightforward procedure. A direct result of this is the ease with which high vacuum deposition processes can be analyzed via the radiation-molecular flow analogy. There are several advantages of using the analogy as opposed to analytical and Monte-Carlo methods which have been traditionally employed for analyzing PVD processes. These include the ease of handling complex geometries and reduced computing times due to the replacement of the probabilistic calculations in Monte Carlo simulations with a deterministic one. In this paper, we demonstrate the use of a commercial finite element software, ABAQUS, for predicting deposition profiles from planar as well as tube sources and compare them with those presented in thin-film literature. We also compare the prediction of flow rates through long tubes with those calculated analytically by Knudsen. The predictions are in good agreement with the analytical and experimental data thus establishing the validity of the method in analyzing real-life deposition and molecular flow problems. Finally, we employ ABAQUS for predicting the thickness variation in an actual thin-film deposition setup and compare the results with experimental measurements.