Abstract Horizontal ribbon growth (HRG), in which a thin sheet of solidified material is pulled horizontally from the surface of a molten pool, is proposed as an efficient technique for growth of single-crystal silicon sheets. Despite recent results, some details of the process are still not understood, in particular the solidification mechanism at the triple junction point (TJP) where the solid, the liquid, and the surrounding gas meet. The solidification mechanism in the HRG process is investigated in this paper both analytically and numerically, incorporating the solidification kinetics that lead to faceted growth. The conventional solid-liquid problem in the HRG process is formulated analytically in the vicinity of the triple junction point (TJP). The temperature distribution is obtained for the liquid and solid regions as a function of the underlying parameters of the HRG process, such as the material properties, the ribbon pull speed, and the cooling heat fluxes. Using the analytical results, the TJP temperature, the facet length, interfacial temperature gradients, and liquid supercooling can be predicted. The analytical formulation is validated against accurate numerical simulations of the same problem, showing a good agreement in predicting the temperature gradients and the facet growth. The findings of this study suggest that using the analytical model, the behavior of the solid ribbon and the existence of a supercooled region in the liquid in the HRG process can be predicted without the need for numerical simulations. The model also gives criteria for optimal performance of the HRG process.

中文翻译：

---

水平带状生长结晶过程中刻面凝固的分析

摘要 水平带状生长 (HRG) 是一种从熔池表面水平拉出凝固材料薄片的方法，是一种有效的单晶硅片生长技术。尽管最近取得了成果，但该过程的一些细节仍不清楚，特别是固体、液体和周围气体相遇的三重连接点 (TJP) 处的凝固机制。本文通过分析和数值研究了 HRG 过程中的凝固机制，并结合了导致刻面生长的凝固动力学。HRG 过程中的传统固液问题是在三重连接点 (TJP) 附近解析制定的。液体和固体区域的温度分布是根据 HRG 过程的基本参数（例如材料特性、带拉速度和冷却热通量）获得的。使用分析结果，可以预测 TJP 温度、小平面长度、界面温度梯度和液体过冷。解析公式针对同一问题的精确数值模拟进行了验证，显示出在预测温度梯度和小平面生长方面的良好一致性。这项研究的结果表明，使用分析模型，可以预测 HRG 过程中固体带的行为和液体中过冷区域的存在，而无需进行数值模拟。