Abstract This paper quantifies the effects of different operating conditions on the stability of the crystallization interface in the horizontal ribbon growth (HRG) process. Specifically, we perform a linear stability analysis of the base state, and we derive the profiles for thermal, solutal and flow fields with regard to small-amplitude normal mode perturbations of the base state. Within the velocity boundary layer induced by the removal of solid ribbon, a linear Couette flow is assumed; at the outer edge of the boundary layer, all perturbations are assumed to dissipate. Critical operating conditions and the unstable modes have been identified. To that end, we demonstrate that fast pulling velocity (greater than 100 mm/min), low wedge factors (the ratio of the length to the thickness of the wafer is less than 500), and insufficient heat removal (temperature gradient G l is less than 200 K/cm) lead to instabilities. A finite bandwidth of wavenumber for instability occurs for all the unstable modes.

中文翻译：

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杂质对横向带状生长稳定性的影响

摘要 本文量化了不同操作条件对水平带状生长（HRG）过程中结晶界面稳定性的影响。具体来说，我们对基态进行线性稳定性分析，并推导出与基态的小振幅正常模式扰动有关的热场、溶质场和流场的分布。在去除固体带引起的速度边界层内，假设线性库埃特流；在边界层的外边缘，假设所有扰动都会消散。已经确定了临界操作条件和不稳定模式。为此，我们证明了快速的拉拔速度（大于 100 毫米/分钟）、低楔形因子（晶片的长度与厚度之比小于 500）、散热不足（温度梯度 G l 小于 200 K/cm）导致不稳定。对于所有不稳定模式，出现不稳定波数的有限带宽。