Large eddy simulation of Marangoni convection in Czochralski crystal growth

Large eddy simulation model is used to simulate the fluid flow and heat transfer in an industrial Czochralski crystal growth system. The influence of Marangoni convection on the growth process is discussed. The simulation results agree well with experiment, which indicates that large eddy simulation is capable of capturing the temperature fluctuations in the melt. As the Marangoni number increases, the radial velocity along the free surface is strengthened, which makes the flow pattern shift from circumferential to spiral. At the same time, the surface tension reinforces the natural convection and forces the isotherms to curve downwards. It can also be seen from the simulation that a secondary vortex and the Ekman layer are generated. All these physical phenomena induced by Marangoni convection have great impacts on the shape of the growth interface and thus the quality of the crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the impact of stress on intrinsic defect formation during single crystal silicon growth

The incorporation of intrinsic point defects during silicon crystal growth from the melt is discussed using most recent data for intrinsic point defect thermal equilibrium concentration and diffusivity. It is shown that by taking into account the impact of stress on the thermal equilibrium concentration of vacancies and self-interstitials, the intrinsic point defect properties derived from self- and metal-diffusion experiments can be used to model point defect incorporation and clustering during silicon crystal growth from the melt. The solution is however not unique and a large uncertainty still remains on the real thermodynamic parameters of both intrinsic point defects. Only comparison with a wide range of experimental data from crystal pulling experiments—taking into account also the stress effects—will allow to further narrow down the uncertainty ranges on the intrinsic point defect properties in silicon.     

The color of langatate crystals and its relationship with composition and optical properties

Langatate crystals grown by the Czochralski method in 〈0001〉 and 〈01 1〉 directions both without subsequent annealing (from colorless to orange crystals) and with vacuum (colorless and pale‐green crystals) and air (orange crystal) annealing have been investigated by neutron diffraction, X‐ray diffraction and optical spectroscopy. The main types of point defects were compared with absorption bands: oxygen vacancies ‐ V_O^•• (0.35‐0.36 µm), the vacancies in the lanthanum position ‐ V_La‴ (0.29‐0.30 µm); the absorption band at 0.48‐0.49 µm is typical for the colored samples. The relationship between the X color coordinate (red component) and the oxygen contents has been obtained. The green color of the sample annealed in vacuum is due to the presence of Ta⁺³ ions in the La(Ta³⁺,Ga)O₃ phase that has the structural and geometric agreement with langatate structure. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

直拉单晶硅生长时空洞演化的相场模拟

为研究大直径直拉硅生长时空洞的演化规律,建立了与有限元模型所模拟的晶体生长温度场相结合的空洞演化相场模型,并应用该模型模拟研究了空洞形貌及其分布状态的变化过程以及不同初始点缺陷浓度对空洞演化的影响规律.结果表明:直拉硅单晶生长过程中,空洞的演化经历了孕育-形核-长大-稳定四个阶段,其形貌和分布状态亦由孤立的球形向偏聚的串珠形转变;与较低的点缺陷浓度相比,初始点缺陷浓度较高时,空洞的数目、平均尺寸、面积分数普遍较大,孕育阶段缩短、形核和长大阶段延长;空洞的偏聚及合并、长大的现象显著;当温度低于980 K时,大直径的空洞数目不再增加.     

氟化钙单晶炉温场的计算机模拟及改进

对氟化钙晶体生长炉的顶部保温、加热器和下保温装置进行了改进研究.结合数值模拟,对改进前后晶体的轴向温度梯度、径向温度梯度和固液界面附近温度分布进行了对比分析.模拟结果表明,改进了顶部保温后增加了晶体炉内的辐射传热,有效降低了温度梯度,减小了晶体内热应力从而避免了晶体开裂;对加热器和底部保温进行改进后,减少了坩埚底部的热损失,相同温度时降低了加热功率.     

Measurement of physical properties of DyScO3 melt

Rare earth scandate crystals ReScO₃ (Re=La, Ce, Pr, Nd, Sm, Eu, Gd, Tb and Dy) can be grown from the melt at temperatures of about 2100 °C. The needs of thermal insulation of the whole system are very high in order to reach the melting point and to control the thermal gradients which are required by the Czochralski (Cz) method. The consequence is that in‐vivo system observations are practically almost impossible or very hard to perform. Therefore numerical investigations using a mathematical model of the real system can be very helpful. However, numerical models need some physical properties of the considered real system (e.g. density, viscosity, thermal expansion coefficients, thermal conductivity). Most material properties of high melting oxides are not referenced in the literature or they are incomplete and inaccurate. Because the accuracy of qualitative and quantitative results of numerical simulations depend on the used physical properties, we performed corresponding measurements in an adapted Cz configuration at a temperature around the melting point of DyScO₃ (2060 °C). The results are presented and discussed in this work. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growth

In order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth, refined structural and spectroscopic characteristics of Tm-doped NaGd(WO4)2 single crystals

The details of Tm³⁺-doped NaGd(WO₄)₂ single-crystal growth are discussed, the results of precise investigations of its structural and spectroscopic characteristics, as well as the analysis of cross-relaxation process of Tm³⁺ ions (³H₄→³F₄, ³H₆→³F₄) in this crystal are presented. Based on the Judd–Ofelt theory, three intensity parameters, spontaneous emission probabilities, fluorescence branching ratios and fluorescence quantum efficiency from ³H₄ and ³F₄ levels were refined.     

提拉法生长高质量氟化镁单晶

设计了适合提拉法生长氟化镁单晶体的温场,采用提拉法成功生长出了直径100 mm的高质量氟化镁单晶.晶体内无气泡等宏观缺陷、无开裂;通过精密退火处理后,晶体透过率达到95;,平均应力双折射小于0.5 nm/cm.上述结果表明采用提拉法可以生长高质量的氟化镁单晶.     

Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals

The results of three‐dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three‐dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two‐dimensional steady and three‐dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three‐dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.