Comparison of three turbulence models for simulation of melt convection in Czochralski crystal growth of silicon

Abstract

Accurate simulation of heat transfer and oxygen segregation in large-scale Czochralski growth of silicon requires modeling of turbulent convection in the melt. We test three models for turbulent convection for the calculation of the flow, temperature field and oxygen transport in a prototypical model of the Czochralski melt. Each of the models is based on the k– ε turbulence model, but differs in the form of model and the description of the flow near solid boundaries. The three formulations are: (I) a traditional k– ε model using wall functions at solid boundaries, (II) a k– ε model with a one-equation model for the flow near solid boundaries, and (III) a low-Reynolds number k– ε model that does not require an independent description of the flow near the wall. Calculations using a finite-volume method with collocated grids shows large difference in the predictions of these models, especially for the highly separated flows driven by buoyancy. In the limit of week turbulence only the low-Reynolds number model gives solutions which are consistent with the laminar regime flow.