Flux profile modeling: Monte Carlo simulation and numerical computation

Abstract

Spatial variations in flux are a result of the shape of the Knudsen cell crucible (K-cell) and the geometry of the growth chamber. In this article, a process simulation tool based on a phenomenological model is proposed and elaborated. Two different models based on physical principles are investigated. Model I includes the primary flux from the liquid surface and a secondary flux re-emitted from the crucible walls for the total flux at the platen. No intermolecular collisions are considered in this model. Since the investigated 10000 g SUMO crucible has a tapered region leading to the crucible opening (the smallest radii opening), molecules undergo extensive interwall and intermolecular collisions in that region. The simulation of intermolecular collisions requires considerable time and limits the usage of the modeling tool in the industry. Thus, the effect of intermolecular collisions is captured through the assumption of a virtual flux source (VFS) at the neck in model II. For the two models, a Monte Carlo approach and a numerical approach are employed for theoretical analysis. The Monte Carlo and numerical approaches as implemented are equivalent and produce essentially the same results. The results of model II from both approaches using cos2 θ distribution from the VFS best describes the experimental data for the SUMO 10000 g crucible. Further comparison with experimental data is necessary to validate the cos2 θ model.