3D modeling and simulation of the triple junction line movement in Czochralski crystal growth

直拉晶体生长中三重连接线运动的 3D 建模和模拟

• 批准号: 34506764
• 负责人: Professor Dr.-Ing. Tilmann Botsch
• 金额: --
• 依托单位: Lehrstuhl für Strömungsmechanik (LSTM)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2007
• 资助国家: 德国
• 起止时间: 2006-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/34506764?language=en
• 关键词: 3D; modeling; simulation; triple; junction

The quality of single crystals produced by the Czochralski (Cz) process strongly depends on the shape of the phase change interface, where the crystallization takes place. This shape is influenced by numerous effects such as convection, buoyancy, surface tension, turbulence etc. The most critical issue is the position of the triple phase junction, where the melt, the crystal and the surrounding atmosphere meet, because it controls the interface movement and thus the diameter and resulting shape of the crystal. However, in state-of-the-art 3D numerical simulations this triple junction is never computed explicitly but always locally fixed. This quasisteady-state assumption does not meet the reality.In this project, a method is developed for the numerical description of the movement of the triple junction line. A mathematical relation between the free surface/ meniscus shape and interface shape based on a Laplace-Young equation with an iteratively determined contact angle and a Stefan condition will be utilized. The phase interface as well as the free surface of the melt and thus the triple junction is allowed to move freely, so that fully transient computations of the entire Cz process can be conducted. The moving grid method is used to track the interfaces; it will be improved and extended by elliptic grid smoothing methods to ensure robustness and speed up convergence. Thus it allows to perform time-dependent simulations for many different Cz configurations with various material properties and boundary conditions. Parametric studies are planned conducted to identify the influences relevant for controlling the crystal quality.Remark:The project is conducted in cooperation between the Institute of Fluid Mechanics at the Friedrich-Alexander-University Erlangen-Nürnberg (FAU-LSTM) and the Department of Process Engineering at the University of Applied Sciences Nürnberg (FHN-VT). Through the coupling of fundamental research at the FAU-LSTM with the numerous industrial partners of the FHN-VT, the concerns of small companies will be taken into consideration during the project. Namely the company Siltronic AG, Burghausen/Freiberg, shows deep interest in the present project.

由直拉法（Cz）生产的单晶的质量在很大程度上取决于结晶发生的相变界面的形状。这种形状受到对流、浮力、表面张力、湍流等多种效应的影响。最关键的问题是三相结的位置，即熔体、晶体和周围大气相遇的位置，因为它控制着界面运动，从而控制着晶体的直径和形状。然而，在最先进的3D数值模拟中，这种三重连接从未明确计算，但总是局部固定的。本计画发展一种方法，以数值方式描述三相汇流线之运动。将利用基于Laplace-Young方程的自由表面/弯月面形状与界面形状之间的数学关系，该方程具有迭代确定的接触角和Stefan条件。相界面以及熔体的自由表面，从而三重连接点被允许自由移动，从而可以进行整个Cz过程的完全瞬态计算。采用移动网格方法跟踪界面，并通过椭圆网格光顺方法对其进行改进和扩展，以保证鲁棒性和加快收敛速度。因此，它允许执行与时间相关的模拟许多不同的Cz配置与各种材料属性和边界条件。计划进行参数研究，以确定控制晶体质量的相关影响。备注：该项目由埃尔朗根-纽伦堡弗里德里希-亚历山大大学流体力学研究所（FAU-LSTM）和纽伦堡应用科学大学工艺工程系（FHN-VT）合作进行。通过将FAU-LSTM的基础研究与FHN-VT的众多工业合作伙伴相结合，小公司的担忧将在项目期间得到考虑。即世创电子材料股份公司博格豪森/弗赖贝格对本项目表现出浓厚的兴趣。