Prediction of Flow and Heat Transfer in a Czochralski Crucible using LES with Interface Tracking

Abstract

The Czochralski (Cz) method is the preferred process for growing large silicon single crystals for wafers which are used in electronic and photonic devices. The liquid silicon (P r = 0.013) is contained in an open crucible which is rotating, while the counterrotating crystal is pulled from the melt. Due to this setup, centrifugal and Coriolis forces, buoyancy, and Marangoni convection occur in the fluid as well as thermal radiation from the surface and the phase change due to crystallization. The shape of the interface between melt and crystal is crucial for the quality of the resulting crystal. Therefore, the influences of all effects on the crystallization front need to be investigated. Unfortunately, the flow inside the melt is fully turbulent (Re ≈ 10^4, Ra ≈ 10^7), which makes numerical predictions difficult. It can be shown that the turbulent structures in this case are highly anisotropic and thus classical RANS models are not applicable. Highly accurate Direct Numerical Simulations (DNS) require high resolution and therefore use massive computational resources. Large Eddy Simulation (LES) combines the advantages of both: The large turbulent scales are computed directly, whereas the small scales are modeled. Thus a relatively high accuracy is achieved with moderate computational effort, so that parametric studies can be conducted easily.