摘要
设计一种二维轴对称和三维混合的数值计算模型,对水平磁场作用下的直拉硅单晶生长进行了研究。结果表明,由于水平磁场的非轴对称性,只有在三维模型中才能获得确切的温度、速度分布。温度场、熔体中的流函数和固液界面形状在水平磁场的作用下也具有非轴对称性,这种非轴对称性随磁场强度的变化而改变。提高晶体旋转速度有利于减小固液界面形状的非轴对称性,并会改变界面形状的凹凸程度;提高坩埚旋转速度则有利于提高熔体中温度分布的均匀性,但会扩大熔体中的径向温度梯度。
A two-dimensional axisymmetric and three-dimensional mixed numerical models were designed for Czochralski silicon single crystal growth in horizontal magnetic field.The results show that the exact distribution of temperature and velocity can be calculated only through three-dimensional simulation due to non-axial symmetry of the horizontal magnetic field.The stream function of melt and the shape of solid-liquid interface also have non-axial symmetry,and such non-axial symmetry changes with magnetic field intensity.The increase of crystal rotation velocity is favorable for the decrease of the non-axial symmetry of the solid-liquid interface shape,changing the unevenness of the interface shape.The increasing crucible rotation enhances the uniformity of temperature distribution in the melt,however,the radial temperature gradient of the melt increases.
出处
《材料热处理学报》
EI
CAS
CSCD
北大核心
2013年第7期193-198,共6页
Transactions of Materials and Heat Treatment
基金
国家自然科学基金(61075044)
教育部科学技术研究重点项目(212169)
关键词
直拉硅单晶
水平磁场
数值模拟
非轴对称性
Czochralski silicon crystal
horizontal magnetic field
numerical simulation
non-axial symmetry
