Analysis of Fluid Flow and Heat Transfer in a Gas Phase Crystal Growth Furnace

Steady-state simulations of fluid flow and temperature field are presented for an equipment that is used to grow Zinc Selenide single crystals from the gaseous phases via physical (PVT) or chemical vapour transport (CVT). Due to the horizontal arrangement of the air-filled furnace pipe calculating the natural convection in the air requires a 3D (three-dimensional) treatment of the problem. The simulations have been done by applying the commercial finite-element package FIDAP. The Navier-Stokes equation is solved with the Boussinesq approximation. The heat transfer analysis comprises also internal radiation wall-to-wall exchange. Due to the presence of the ampoule in the pipe, the development of vortices with higher velocities is restrained, so that the maximum velocity is roughly 1/4 of that in the case without an ampoule.     

Using a Phase‐field‐like Approach for the Calculation of Melt Flow and Interface Shape during Czochralski Growth

A phase‐field‐like approach is introduced into the commercial general‐purpose program FIDAP^TM to calculate the melt‐crystal interface for a quasi‐stationary approach of the Czochralski growth. Temperature and flow field are solved using the segregated solver of the FIDAP^TM software.     

Numerical Simulation of Temperature and Flow Field in the Melt for the Vapour‐pressure‐ controlled Czochralski Growth of GaAs

The influence of the melt flow on the temperature field and interface during the vapour‐pressure‐controlled growth of GaAs was studied numerically with the commercial general‐purpose program FIDAP^TM. The thermal boundary conditions for the domain of seed, crystal, boron oxide and crucible were taken from a global calculation for an equipment used at the IKZ to grow 6″ crystals. Due to the large melt volume the buoyancy forces become rather strong and have to be counteracted by reasonable rotation rates. Preliminary results have been obtained for iso‐ and counter‐rotation showing that the flow field exhibits structures on small scales. High rotation rates are needed to counteract the buoyancy flow efficiently and to achieve a smooth flat interface. Even if the the flow structure is not resolved in detail, the interface shape can be deduced form the calculations.     

The Effect of Free Convection on Solid/Liquid Interface in the Czochralski Crystal Growth Method

This paper regards the interaction of free and forced convection in the Czochralski configuration. A relationship between the crystal rotation rate and growth parameters at which the crystallization front remains flat, at which the crystallization front remains almost flat, has been studied. This relationship is compared with experimental data.     

勾形磁场下提拉法生产单晶硅的数值模拟

本文给出了提拉单晶硅时,勾形磁场强度的计算公式,并对单晶硅在有无勾形磁场情况下熔体内流场和氧的浓度分布进行了数值模拟,计算出磁场作用下磁场强度和洛伦兹力及有无磁场时流函数、垂直截面处的速度场和氧的浓度分布.通过分析表明,勾形磁场能使流动更为平稳,能有效地降低熔体内及生长界面氧的浓度,并对产生这一现象的机理作了理论分析.     

轴向磁场作用下Czochralski浅液池内热对流特性研究

为了有效抑制熔体热对流并提高晶体的生长质量,采用三维数值模拟方法研究了轴向磁场对双向温差作用下Czochralski浅液池内Marangoni-热毛细对流的影响.在一个给定的底部热流密度条件下,探讨了轴向磁场对稳态流动和非稳态流动的影响,确定了不同磁场强度下流动由三维稳态流动向三维非稳态流动转变的临界Macri.结果表明:随着磁场强度的增大,临界Macri不断增大.轴向磁场对液池内稳态和非稳态Marangoni-热毛细对流均具有较好的抑制效果.对于稳态流动,磁场的引入会使自由表面温度波动幅值受到削弱,波数减少;对于非稳态流动,监测点P处的温度振荡随着磁场强度的增加不断逐渐减弱直至消失,流动由三维非稳态过渡为三维稳态,相应地,温度波动结构也会发生转变.     

富锂熔体中提拉法生长近化学计量比铌酸锂(LiNbO3)晶体

利用提拉法,在富锂(Li2O∶NbO3=58.5/41.5)熔体中生长了质量良好的近化学计量比铌酸锂单晶,其紫外吸收边位置为308nm,居里温度超过了1200℃.测量了其Z向晶片的压电系数d33,并且观察了Z向晶片的180°畴,结果证明除少数区域外,所生长晶体为单畴.     

三坩埚提拉法生长铽镓石榴石单晶研究

采用三坩埚提拉法生长出高质量铽镓石榴石(Tb3Ga5O12,TGG)单晶,晶体尺寸为φ25 mm×40 mm.通过X射线衍射、双晶衍射分析讨论TGG单晶的晶体结构和单晶性,并采用He-Ne激光费尔德常数测试装置测定TGG单晶的费尔德常数.结果表明:采用三坩埚提拉法生长的TGG单晶具有＜111＞取向、强度高,双晶摇摆曲线半峰宽为17 s;晶体在632.8 nm处的费尔德常数为0.553 min/cm·Oe.     

提拉法制备铜单晶研究

采用提拉法生长出大尺寸(111)铜单晶,晶体尺寸为ф(12～19)mm×85 mm.通过XRD、金相显微分析讨论了铜单晶的晶体结构与生长缺陷,并采用双臂电桥测定(111)铜单晶的电阻率.结果表明:晶体具有(111)取向、强度高,表明晶体取向良好;蚀坑呈典型三角锥形,位错密度在105～106 cm-2之间;在室温下,(111)铜单晶电阻率为1.289×10-8Ω·m.     

Bridgman法晶体生长的热物性各向同性坩埚的选择

本文对不同坩埚热物性组合时计算得到的结果进行了比较.对各向同性坩埚而言,应该优先选择具有与晶体和熔体的导热系数相当导热系数的材料,也可选择导热系数较大的材料.在强度允许的情况下,减小坩埚壁厚对晶体生长有利.     

Time-dependent simulation of Czochralski silicon crystal growth

We have developed a detailed mathematical model and numerical simulation tools based on the streamline upwind/Petrov-Galerkin (SUPG) finite element formulation for the Czochralski silicon crystal growth. In this paper we consider the mathematical modeling and numerical simulation of the time-dependent melt flow and temperature field in a rotationally symmetric crystal growth environment. Heat inside the Czochralski furnace is transferred by conduction, convection and radiation, Radiating surfaces are assumed to be opaque, diffuse and gray. Hence the radiative heat exchange can be modeled with a non-local boundary condition on the radiating part of the surface. The position of the crystal-melt interface is solved by the enthalpy method. The melt flow is assumed to be laminar and governed by the cylindrically symmetric and incompressible Navier-Stokes equations coupled with the calculation of temperature.     

Heat and Mass Transport Computation at the Sublimation Growth of SiC

Steady‐state heat and mass transport at the SiC growth process are computed by the general‐purpose finite‐element package FIDAP^TM. Specific features are the radiation exchange in several cavities at temperatures up to 2700 K and concentration dependent Stefan velocities resulting from sublimation/condensation at the vapour‐solid interfaces. The article describes the computational procedure in order to achieve convergence of the temperature and velocity field. The transport rate of the SiC building species meets the range of experimental results.     

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)     

钼酸铅单晶生长及其缺陷研究

本文通过CZ法生长钼酸铅单晶,讨论了温度梯度、拉速、转速等生长参数对晶体质量的影响,分析了晶体开裂、包裹物等宏观缺陷以及位错等微观缺陷的形成机理,并从晶体形态、包裹体和位错密度变化方面探讨了晶体生长参数与晶体缺陷之间的内在关系,从而优化温度梯度等生长参数.温度梯度为20～25℃/cm,晶体转速为28r/min,拉速为1.6mm/h时,生长出的晶体形态完整,无开裂现象,晶体中无气泡包裹体,位错密度明显减小,晶体尺寸达φ40mm×70mm,无散射颗粒,在波长0.42～5.5μm范围内,平均透光率为72.6;.     

采用延时修正法实施QUICK格式模拟提拉单晶体的生长

为了数值模拟提拉(又名Czochralski)法获得单晶体的生长过程,本文采用有限容积法离散控制方程,采用非均匀的交错网格避免不合理的振荡压力场,采用三阶精度QUICK (Quadratic Upwind Interpolation of Convective Kinematics)格式离散对流项,采用延时修正来实施QUICK格式获得满足主对角占优的代数方程组,采用SIMPLE(Semi-implicit Method for Pressure Linked Equations)算法耦合压力和速度场,给出了基于上述方法的方程、算法,并发展了程序,计算了Wheeler标准问题,计算结果与文献相当一致,同时本算法能模拟计算高葛拉晓夫数时的流动,显示出非均匀网格QUICK格式模拟晶体生长的优越性;另外本文将这一算法运用到单晶硅的数值模拟中,计算结果令人满意.     

Behavior of phosphorus impurities during Czochralski growth of high‐purity germanium single crystals

The effect of evaporation of phosphorus impurities from the melt is investigated as well as the contaminating effect of quartz glass crucibles on residual content and distribution of this impurities by length of high‐purity germanium single crystals. The residual content of phosphorus impurities is mainly influenced by the contaminating effect of crucible material and its distribution by length of crystals is described by the model accounting for the impurities income from crucible material. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

熔体法生长大尺寸有机晶体

大尺寸有机晶体在太赫兹波产生、中子探测、微波激射等多个关系国计民生、涉及国家安全的领域具有重要应用前景.但大尺寸有机单晶生长一直是国际公认的难题,无论是在生长理论、生长方法还是生长设备方面都远远落后,在整个人工晶体领域相对小众;而且有机晶体硬度低、脆性高、易解理等本征特性为加工和后期应用带来了很多困难,制约了相关领域的...     

Czochralski法生长Lu2SiO5：Ce晶体的发光特性

本文使用铱坩埚感应加热Czochralski法成功地生长出了无色透明且尺寸达5 0mm× 6 0mm的Lu2 SiO5:Ce晶体。XRD结构分析表明 ,该晶体为单斜结构。在室温下分别以X射线和紫外光为激发源测量了该晶体的发射光谱 ,获得的发射波长分别为 4 0 3nm和 4 2 0nm ,光衰减时间为 4 1ns,光产额达 32 0 0 0p/MeV。发射光谱的双峰结构以及晶体的发光特性证明其发光源于Ce3 离子的 5d1→5F5/ 2 和 5d1→5F7/ 2 跃迁。     

Czochralski法生长Lu2SiO5:e晶体的发光特性

本文使用铱坩埚感应加热Czochralski法成功地生长出了无色透明且尺寸达φ50mm×60mm 的Lu2SiO5:e晶体.XRD结构分析表明, 该晶体为单斜结构.在室温下分别以X射线和紫外光为激发源测量了该晶体的发射光谱,获得的发射波长分别为403nm和420nm,光衰减时间为41ns,光产额达32000p/MeV.发射光谱的双峰结构以及晶体的发光特性证明其发光源于Ce3+离子的5d1→5F5/2 和 5d1→5F7/2跃迁.