Validation of a numerical model for Czochralski growth of cesium iodide and calcium fluoride

Numerical modeling of the Czochralski (CZ) growth process, which includes the multiphysical interactions of electromagnetism, heat transfer, phase change, and melt flow, is an essential tool for process development and optimization. However, validation of such models is mostly insufficient due to the lack of in-situ measurement data, and open-source models are hardly available. To address these issues, a new 2D and 3D CZ growth model has been developed using the open-source tools Elmer for global time-harmonic electromagnetism, steady-state heat transfer and phase change modeling, coupled with OpenFOAM for transient or steady-state melt flow modeling. The model is published under an open-source license. The model is validated with a focus on electromagnetism and heat transfer using a model experiment with cesium iodide (CsI, melting point: 627 °C), targeting oxide/fluoride materials. For the 2D model, a satisfying agreement between model experiment and simulation regarding crucible and crystal temperature is achieved in regions with constant crystal diameter. With the 3D model, 3D flow patterns caused by an asymmetric crucible temperature distribution due to an asymmetric magnetic field of the induction heater are observed and in reasonable agreement with the experiment. However, both models yield heater currents up to 38 % higher than those observed in the experiment. The transferability of the validation results to calcium fluoride (CaF₂) growth for laser cooling application is discussed. The CaF₂ growth process is modeled in 3D to investigate the cause of a rough crystal surface observed in the experiment. It might be caused by a rotating 3D flow structure, while the observation window in the insulation and after-heater is of low influence on the temperature distribution and, thus, the crystal surface structure.