Design of a 1500 Gs cusp superconducting magnet and its application simulation for 300 mm Czochralski crystal growth process

This study focuses on the design and numerical simulation of a 1500 Gs industrial-grade superconducting cusp magnet applied to a 300 mm Czochralski (CZ) crystal growth process. A two-dimensional (2D) global - three-dimensional (3D) local model is established, along with large eddy simulation (LES) with a standard Smagorinsky turbulence model in melt flow to analyze the influence of zero Gauss plane (ZGP) positions on melt flow, heat transfer, and oxygen concentration distribution. The results indicate that adjusting the ZGP position significantly alters the melt flow structure, temperature distribution, and impurity transport mechanisms. A small temperature gradient is found in cases that ZGP is 100–150 mm below the free surface due to the flow parallel to heat transfer direction, which enhances heat transfer from crucible to crystal. The velocity and temperature oscillations beneath the crystallization region are significantly reduced as ZGP shifts away from freesurface. Furthermore, oxygen concentration distribution does not follow a direct correlation with ZGP height but is instead influenced by the melt flow pathways. At ZGP = −100 and −150 mm, a portion of the melt bypasses the free surface, limiting oxygen evaporation and leading to increased impurity retention. Notably, the cusp magnetic field (CMF) model in this work integrates actual superconducting coil designs with industrial parameters (geometry, material properties, and currents), bridging idealized models and industrial practice. This approach enables precise evaluation of magnetic field effects on crystal growth, guiding defect suppression and oxygen control in production. The physics-informed design framework enhances manufacturing predictability by aligning simulations with operational realities.