不同磁场对大直径单晶硅生长中的动量与热量输运影响的数值分析

本文采用紊流模型对大直径单晶硅在垂直磁场及勾形磁场作用时熔体内动量及热量输运作了数值模拟.采用有限体积法离散控制方程,采用SIMPLE((Semi-implicit Method for Pressure Linked Equations)算法耦合压力和速度场.对无磁场、垂直磁场及勾形磁场作用下熔体内的传输特性进行了比较.数值计算结果表明,垂直磁场对动量及热量的分布具有双重效应.垂直磁场强度过大,不利于晶体生长.随着勾形磁场强度的增加,熔体内子午面上的流动减弱,并且紊流强度也相应降低.     

径向三重流MOCVD反应器生长GaN的数值模拟

采用计算流体力学方法对生长半导体材料GaN的重要设备三重进口行星式MOCVD (金属有机物化学气相沉积) 反应室中的输运过程进行了二维数值模拟.从浓度场的角度分析反应器内衬底上方NH3和TMGa的浓度影响因素.根据对模拟结果的分析,发现较均匀的流场对应衬底上方的反应物浓度较高,降低反应器内压强,也可获得衬底上方较高的反应物浓度,由于MOCVD反应器内有较大的温差,因此热扩散效应不能忽视.     

基于显微组织图片的涂层热导率有限元计算研究

综合数字图像处理技术与有限元网格模型生成原理,提出了基于涂层显微组织图片的有限元网格模型生成方法。利用有限元程序,通过热障涂层特定区域的热导率计算,研究分析了涂层的隔热性能。以等离子喷涂ZrO2涂层为例,先将得到的ZrO2涂层物理图像由图形格式转换成数字格式;然后,通过阈值分割处理和有限元网格生成方法,生成包含涂层材料组元属性的有限元网格模型;在生成的有限元网格模型基础上,再进行ZrO2涂层热作用下的温度场模拟;最后,利用傅立叶热传导方程,计算了ZrO2涂层显微组织图片所代表区域的有效热导率。进一步分析了横向热导率和纵向热导率之间的差异。分析表明:等离子喷涂ZrO2涂层的横向热导率比纵向热导率要高,涂层有效热导率受孔隙率和孔隙形状共同影响。     

半绝缘SiC单晶生长和表征

使用升华法生长碳化硅(SiC)单晶,借助数值模拟方法优化温场,在不同条件下分别获得单一晶型的4H-SiC和6H-SiC单晶,利用拉曼光谱进行表征。采用V掺杂的方法,制备半绝缘SiC单晶,使用非接触式电阻率测试仪进行了测试,并对4H-SiC和6H-SiC电阻率进行了比较和分析。     

丁二醇对TiO2纳米晶体水热生长动力学的影响

采用水热法,以丁二醇和水作为混合溶剂,研究了二氧化钛纳米晶体的生长机理.X射线衍射(XRD)结果显示产物为锐钛矿纳米TiO2.用透射电镜(TEM)、高分辨透射电镜(HRTEM)等对不同时间的晶体结构进行表征,发现晶体生长具有明显的奥斯特瓦尔德熟化(OR)特征.颗粒粒径均处于纳米级,其粒径数值随温度增加而变大.丁二醇作为溶剂兼表面活性剂对于纳米晶体的生长起到重要调节作用.采用OR方程,分别对220 ℃、180℃、140℃三个温度下纳米TiO2的生长进行模拟,模拟曲线和实验结果吻合很好,并获得其生长活化能为15.0 kJ/mol.     

一种利用实验测量和数值计算确定3m点群晶体弹性系数的方法

将实验测量与数值计算相结合确定低对称性晶体弹性系数的方法可以弥补常规方法测量时造成的弹性系数非对角元误差大的不足.本文将该方法由正交系晶体推广到了三方系3m点群晶体,在数值计算中选取了目前公认的无约束最优化方法中最稳定的两种算法-单纯形法和BFGS法,并增加了弹性系数的约束条件,提高了方法的适应性和正确性.在此基础上,本文利用3m点群晶体LiNbO3和LiTaO3的弹性劲度系数[cij]和顺服系数[sij]的实验数据对该方法进行了讨论及验证.结果表明这种方法对3m点群晶体弹性系数非对角元的计算是可行的.另外,本文还对数值计算时,初值的选取和检验结果合理性等关键性问题进行了详细的讨论.     

一种计算层状声子晶体弹性波带结构的无网格弱形式RBF方法

本文提出了一种基于紧致径向基函数(RBF)的无网格局部弱形式方法来计算层状声子晶体的能带结构.位移函数由一组径向基函数表示,利用变分原理,考虑周期边界条件,导出了单位单元RBF方法的一般形式.通过求解矩阵特征值问题可以得到能带结构.用有限元法对新的弱形式RBF方法进行了验证.对于不同的声阻抗比和长度比,通过数值算例进行讨论,显示所提出的弱形式RBF方法与有限元和强格式RBF方法相比计算层状声子晶体的能带结构的效率.     

数值模拟顶部籽晶溶液生长法制备单晶碳化硅的研究进展

宽禁带半导体材料碳化硅(SiC)凭借着其高击穿场强、高热导率、耐高温、高化学稳定性和抗辐射等优异性能，在电力电子器件领域尤其是高温、高频、高功率等应用场景下有着巨大潜力。大尺寸、高质量、低成本的单晶SiC的制备是SiC相关半导体产品规模化应用的前提。顶部籽晶溶液生长(TSSG)法生长的单晶SiC有着晶体质量高、易扩径、易p型掺杂等优势，有望成为制备单晶SiC的主流方法。但目前由于该方法涉及的生长机理复杂，研究者对其内部机理的理解还不够充分，难以对TSSG生长设备和方法进行有效的改进与优化。利用计算机对TSSG法生长单晶SiC生长过程进行数值模拟被认为是对其内部机理探究的有效途径之一。本文首先回顾了TSSG法生长单晶SiC和相关数值模拟分析的发展历程，介绍了TSSG法生长单晶SiC和数值模拟的基本原理，然后介绍了数值模拟方法计算分析TSSG法生长单晶SiC模型涉及的主要模块、影响单晶生长的主要因素(如马兰戈尼力、浮力、电磁力等),以及对数值模型的优化方法。最后，指出了数值模拟方法计算分析TSSG法生长单晶SiC在未来的重点研究方向。     

陶瓷墙地砖干法制粉造粒过程湿含量数值分析

针对陶瓷墙地砖干法制粉过程粉体颗粒湿含量分布不均匀性问题.采用有限体积法建立干法制粉造粒过程欧拉-欧拉多相流模型,模拟干法造粒过程雾化液滴的分布情况,分析干法造粒过程中粉体颗粒的湿含量均匀性;同时搭建试验平台测试干法造粒粉体颗粒湿含量.数值仿真结果表明:当干法造粒时间为10 s、20 s、30 s时,粉体颗粒分布区域雾化液滴的质量比分布分别在0.08 ～0.09、0.09～0.1、0.11-0.12区域,且20 s时造粒室内雾化液滴分布均匀性均最佳.同时实验与仿真对比表明:当干法造粒时间为10 s、20s、30 s时,造粒室内雾化液滴最大质量比实验测得值为0.086、0.112、0.123,数值模拟值为0.09、0.1、0.12;造粒室内雾化液滴平均质量比实验测得值为0.081、0.102、0.109,数值模拟结果为0.082、0.096、0.118.从局部与整体角度表明数值模拟与实验结果基于吻合,说明数值模拟结果的真实性,为陶瓷墙地砖干法制粉粉体颗粒湿含量均匀性分析提供了可靠的理论依据.     

Ce∶KNSBN晶体两波耦合动态过程研究

本文在非同时读出条件下,采用实时数据采集系统,实验研究了e偏振光写入Ce∶KNSBN晶体两波耦合动态过程,发现不同的写入光强比和写入总光强对晶体中两波耦合过程产生明显的影响;当He-Ne 632.8nm激光通过Ce∶KNSBN晶体时,光扇效应存在明显的写入光强阈值特性,其阈值约为20mW/cm2.依据实验结果对考虑光扇影响的耦合波方程进行了修正,其数值计算与实验结果基本符合.     

The effects of argon gas flow rate and furnace pressure on oxygen concentration in Czochralski silicon single crystals grown in a transverse magnetic field

The effects of the argon gas flow rate and furnace pressure on the oxygen concentration in a transverse magnetic field applied Czochralski (TMCZ) silicon single crystals were examined through experimental crystal growth. A gas controller which had been proposed by Zulehner was used for this series of experiments. In the TMCZ gas-controlled crystals, a decrease in the oxygen concentration with a decrease in furnace pressure was found. A clear relationship between the oxygen concentration and the argon gas flow rate was not obtained due to the limited experimental conditions. The relationships between the oxygen concentration and the furnace pressure and the argon gas flow rate previously observed for Czochralski (CZ) crystals by a similar gas controller were confirmed by the present gas controller. The oxygen concentration changes in the TMCZ and the CZ crystals were analyzed in terms of the calculated flow velocity of the argon gas between the gas controller and the silicon melt surface. In contrast with the CZ gas-controlled crystals, the oxygen concentration was decreased with an increase in the flow velocity of argon gas in the TMCZ gas-controlled crystals. The surface temperature model and the melt flow pattern model which had been proposed in the previous report are discussed again in light of the present experimental results.     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1: non‐rotating seed

For the seeding process of oxide Czochralski crystal growth, the flow and temperature field of the system as well as the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and non‐rotating seed crystal. At first the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF coil was calculated. Using this heat source the fluid flow and temperature field were determined in the whole system. We have considered two cases with respect to the seed position: (1) before and (2) after seed touch with the melt. It was observed that in the case of no seed rotation (ω_seed = 0), the flow pattern in the bulk melt consists of a single circulation of a slow moving fluid. In the gas domain, there are different types of flow motion related to different positions of the seed crystal. In the case of touched seed, the seed‐melt interface has a deep conic shape towards the melt. It was shown that an active afterheater and its location with respect to the crucible, influences markedly the temperature and flow field of the gas phase in the system and partly in the melt. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional numerical investigation of the effects of an open window on the convective heat transfer of an oxide Czochralski system

A three‐dimensional numerical analysis was carried out for a real Czochralski crystal growth furnace containing only gas and without any melt and crystal in order to investigate the effects of a small observation window on the temperature and flow field of the system. For this approach, the induction heating equations, the Navier‐Stokes equation with Boussinesq approximation, the continuity and energy equations have been solved in cylindrical coordinates using the finite element method. It has been found that the flow and thermal fields in the system are obviously three‐dimensional and non‐axisymmetric. The gas enters the system through the window is directed towards the opposite side wall where it is divided into two parts of vertical direction as well as expands in horizontal direction. Consequently, there is a spiral gas flow in the crucible and afterheater which rotates upwards in azimuthal direction along the walls. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth

For the seeding process of oxide Czochralski crystal growth, influence of the crucible bottom shape on the heat generation, temperature and flow field of the system and the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and seed crystal. At first, the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF‐coil was calculated. Using this heat generation in the crucible wall as a source the fluid flow and temperature field of the entire system as well as the seed‐melt interface shape were determined. We have considered two cases, flat and rounded crucible bottom shape. It was observed that using a crucible with a rounded bottom has several advantages such as: (i) The position of the heat generation maximum at the crucible side wall moves upwards, compared to the flat bottom shape. (ii) The location of the temperature maximum at the crucible side wall rises and as a result the temperature gradient along the melt surface increases. (iii) The streamlines of the melt flow are parallel to the crucible bottom and have a curved shape which is similar to the rounded bottom shape. These important features lead to increasing thermal convection in the system and influence the velocity field in the melt and gas domain which help preventing some serious growth problems such as spiral growth. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle‐bottom of the crucible. The finite‐volume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 10¹² not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 10¹⁰. Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt‐crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.     

The role of inner and internal radiation on the melt growth of sapphire crystal

In this paper, for an inductively heated Czochralski furnace used to grow sapphire single crystal, influence of the inner (wall‐to‐wall) and crystal internal (bulk) radiation on the characteristics of the growth process such as temperature and flow fields, structure of heat transfer and crystal‐melt interface has been studied numerically using the 2D quasi‐steady state finite element method. The obtained results of global analysis demonstrate a strong dependence of thermal field, heat transport structure and crystal‐melt interface on both types of radiative heat transfer within the growth furnace.     

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.     

Macro-segregation, dynamics of interface and stresses in high pressure LEC grown crystals

High dislocation density and strong dopant inhomogeneities have been found in high pressure liquid-encapsulated Czochralski (HPLEC) grown crystals. The origin and underlying mechanisms of these defects are attributed to the complex nature of transport phenomena in the HPLEC system. Our integrated computer model (MASTRAPP) can simulate this process by calculating the flow and heat transfer in both the melt and the gas, and thermal-elastic stress in the crystal. In this work, this model has been further extended to investigate the development of thermal stress in the growing crystal and the redistribution of dopant in the melt. The results for InP growth show complex gas flow and heat transfer pattern in the system. Two large stress spots are predicted by the model, one at the edge of the crystal just above the encapsulant layer and the other in the top corner of the crystal. Although the stress always remains largest at the first location, its value decreases as the crystal grows, due to the enhanced cooling of the crystal. A curved crystal/melt interface is also found to introduce high thermal stresses in its vicinity, which may be dangerous because of a high temperature at the interface and thus a low strength of the crystal. The model also predicts both radial and longitudinal dopant segregation in the growing crystal, and shows that the dopant redistribution in the melt is caused by the complex flow pattern in the melt. This is the first time, that a strong radial dopant segregation has been predicted based on a comprehensive flow model for a HPLEC growth.     

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.