Abstract The development of grain structures during directional solidification of multi-crystalline silicon (mc-Si) plays a crucial role in the materials quality for silicon solar cells. Three dimensional (3D) modelling of the grain boundary (GB) interaction and evolution based on phase fields by considering anisotropic GB energy and mobility for mc-Si is carried out for the first time to elucidate the process. The energy and mobility of GBs are allowed to depend on misorientation and the GB plane. To examine the correctness of our method, the known the coincident site lattice (CSL) combinations such as ( ∑ a + ∑ b → ∑ a × b ) or ( ∑ a + ∑ b → ∑ a / b ) are verified. We frther discuss how to use the GB normal to characterize a ∑ 3 twin GB into a tilt or a twist one, and show the interaction between tilt and twist ∑ 3 twin GBs. Two experimental scenarios are considered for comparison and the results are in good agreement with the experiments as well as the theoretical predictions.

中文翻译：

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多晶硅定向凝固过程中晶界相互作用和演化的三维建模

摘要 多晶硅（mc-Si）定向凝固过程中晶粒结构的发展对硅太阳能电池的材料质量起着至关重要的作用。首次通过考虑 mc-Si 的各向异性 GB 能量和迁移率，基于相场对晶界 (GB) 相互作用和演化进行三维 (3D) 建模以阐明该过程。GB 的能量和移动性可以取决于定向错误和 GB 平面。为了检验我们方法的正确性，我们验证了已知的重合点格 (CSL) 组合，例如 (∑ a + ∑ b → ∑ a × b ) 或 (∑ a + ∑ b → ∑ a / b )。我们进一步讨论了如何使用 GB 法线将 ∑ 3 twin GB 表征为倾斜或扭曲 GB，并展示倾斜和扭曲 ∑ 3 twin GB 之间的相互作用。