Abstract In FZ growth processes, the stability of the free surface is important in the production of single crystal silicon with high quality. To investigate the shape of the free surface in the FZ silicon crystal growth, a 3D numerical model that included gas and liquid phases was developed. In this present study, 3D Young-Laplacian equations have been solved using the Volume of Fluid (VOF) Model. Using this new model, we predicted the 3D shape of the free surface in FZ silicon crystal growth. The effect of magnetic pressure on shape of free surface has been considered. In particular, the free surface of the eccentric growth model, which could not be previously solved using the 2D Young-Laplacian equations, was solved using the VOF model. The calculation results are validated by the experimental results.

中文翻译：

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浮区 (FZ) 硅晶体生长过程中自由表面形状的 3D 数值模拟

摘要 在FZ生长过程中，自由表面的稳定性对于生产高质量的单晶硅很重要。为了研究 FZ 硅晶体生长中自由表面的形状，开发了一个包含气相和液相的 3D 数值模型。在本研究中，3D Young-Laplacian 方程已使用流体体积 (VOF) 模型求解。使用这个新模型，我们预测了 FZ 硅晶体生长中自由表面的 3D 形状。考虑了磁压力对自由表面形状的影响。特别是，以前无法使用 2D Young-Laplacian 方程求解的偏心生长模型的自由表面使用 VOF 模型求解。计算结果得到了实验结果的验证。