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.

Czochralski（CZ）过程产生的单晶的质量在很大程度上取决于发生结晶的相变界面的形状。这种形状受到许多效果的影响，例如构造，浮力，表面张力，湍流等。最关键的问题是三相交界处的位置，在该位置，融化，晶体和周围气氛相遇，因为它控制着界面的运动，因此直径以及因此，在这三个数字模拟中，这种三重连接从未计算出来，但始终计算出来。这个准状态的假设不符合现实。在这个项目中，开发了一种方法，用于对三重连接线运动的数值描述。基于迭代确定的接触角和Stefan条件的Laplace-Young方程，将使用自由表面/半月板形状与界面形状之间的数学关系。相位界面以及熔体的自由表面，因此允许三连接点自由移动，因此可以对整个CZ过程进行完全瞬态计算。移动网格方法用于跟踪接口。它将通过椭圆网平滑方法改进和扩展，以确保稳健性并加快收敛性。它允许对具有各种材料属性和边界条件的许多不同CZ配置执行时间相关的模拟。计划进行参数研究以确定与控制晶体质量相关的影响：弗里德里希 - 阿尔克斯 - 大学 - 大学 - 弗兰根·纽伯格（FAU-lstm）的流体力学研究所与富有nürnbergnberg（FHN-unürnberg）的工程工程系进行合作进行该项目。通过FAU-LSTM与FHN-VT的众多工业合作伙伴的基础研究结合，将在项目期间考虑小公司的关注。也就是说，伯格豪斯/弗里贝格公司的Siltronic AG公司对本项目表现出深刻的兴趣。