SiC晶体生长中气相组分输运特性

针对物理气相传输(PVT)法生长碳化硅(SiC)晶体,建立了一个二维生长动力学模型研究SiC生长腔内气相组分输运特性,该模型考虑了氩气与气相组分之间的流动耦合,Stefan流和浮力影响.研究表明:在压力较低的情况下,自然对流对气相组分的输运过程影响很小,可以忽略,而当压力增高时,自然对流强度显著增大,不可忽略.其次,随着生长温度升高对流的作用增强,生长腔内输运过程由扩散向对流转变,最终对流主导组分的输运过程.随着压力升高对流作用减弱,扩散为气相组分主要输运方式.     

用升华法生长SiC晶体的一种新颖的坩埚设计

本文提出一个用PVT法生长SiC晶体的坩埚的新颖设计.分析了生长腔中有无锥形档板对腔内及籽晶温度场的影响;比较了档板取不同厚度时SiC粉源升华面和籽晶表面的温度分布.得出了在腔内增设档板后晶体生长面的温度更趋均匀的结论;获取了随着档板厚度的增加,腔内的轴向温度梯度随之增加,但同时晶体生长面的温度也会降低的设计原则.根据计算结果,选取档板厚度等于2mm为优化参数.     

蓝宝石晶体热性能的各向异性对SAPMAC法晶体生长的影响

采用有限元法对冷心放肩微量提拉法蓝宝石晶体生长过程中晶体内的温度、应力分布进行了模拟计算,结合实验结果讨论了蓝宝石晶体热性能的各向异性对晶体生长的影响.研究结果表明,对于冷心放肩微量提拉蓝宝石晶体生长系统,较大的轴向热导率有利于提高晶体的生长速率和界面稳定性,而稍大的径向热导率则有利于保持微凸的生长界面.晶体内的热应力受径向热膨胀系数的影响显著,随着径向热膨胀系数的增大而增大,最大热应力总是出现在籽晶与新生晶体的界面区域.在实验中选α轴为结晶取向,成功生长出了直径达230mm、高质量蓝宝石晶体.     

焰熔法生长金红石单晶体生长室内温度分布的数值模拟

以氢气和氧气的燃烧为基础,研究了焰熔法生长金红石单晶体过程中生长室内的温度分布特征,分析了H2和O2流量对温度分布的影响.结果表明:中心轴向温度随喷嘴距离的增加而升高,在距喷嘴92 mm处达到最高温度3290.3 K后开始下降;晶体熔帽径向温度随直径的增加逐渐减小,熔帽边缘温度则急剧升高;随着H2流量增加,生长室内中心轴向和径向温度逐渐增大,H2流量增加2L/min,中心最高温度平均升高130℃,最高温度的位置向下移3.1mm,晶体熔帽表面温度平均升高70℃;增加内O2和外O2流量均导致生长室内中心轴向和径向温度降低,而使晶体熔帽上的压力升高,外O2对温度的影响较大,而内O2对晶体熔帽压力的影响较大.     

晶体对热辐射的吸收对晶体生长的影响

本文综述了晶体对熔体热辐射吸收对晶体生长的影响,包括对热腔热耗散的影响;对晶体生长温度时间特性的影响;对液流形态和固液界面形状的影响;对晶体界面反转的影响;对晶体中温度分布和应力分布的影响.     

热交换法蓝宝石晶体生长的数值模拟研究

针对热交换法蓝宝石晶体各生长阶段的温场、流场和热应力进行数值模拟研究,并讨论了上部保温层结构、热交换器内管高度对晶体生长的影响.结果表明:长晶初期,固液界面呈椭球形;等径阶段,固液界面平坦,晶体与坩埚壁不接触;长晶后期,中心轴向晶体生长速率增加,晶体中心首先冒出熔体液面.随晶体高度增加,熔体对流由初期的两个涡胞变为等径阶段的一个涡胞,最大对流速度量级为10-3 m/s.晶体中最大热应力分布在晶体底部,热应力分布呈W型.增加炉体上部保温层,长晶后期固液界面变得平坦;降低热交换器内管高度,有利于降低晶体底部热应力.     

西门子反应器中硅棒的热传递模型

考虑西门子反应器中对流、辐射以及化学反应热三种热传递形式,建立了硅棒的二维轴对称热传递模型.相比于对流和化学反应热,辐射是最主要的传热方式.基于此模型分析了12对棒西门子反应器中硅棒辐射位置和反应器壁发射率对硅棒内部径向温度分布以及电流密度分布的影响.结果表明:直流电加热时,硅棒内部径向方向上形成了明显的温度梯度,且外环硅棒内部温度梯度要大于内环硅棒温度梯度;降低反应器壁发射率,外环硅棒温度梯度减小,电流密度分布更为均匀.     

泡生法生长蓝宝石单晶的热场改进与模拟优化

在泡生法蓝宝石单晶生长中,单晶炉内的热场对晶体质量至关重要.本文首先对单晶炉的顶部热屏、环形加热器和炉底保温进行了改进,然后结合计算机数值模拟,对热场改进前、后晶体的轴向和径向温度梯度、晶体表面温度分布、加热器功率等进行分析对比.结果表明:改进后的倾斜热屏增强了单晶炉内的辐射传热,对已生长出的晶体起到了后热作用,降低了晶体内的热应力;对加热器和底部钼保温层的改进,减小了加热器与坩埚间的热阻,增强了炉内的保温作用,使加热功率降低了约8%.     

旋转对Cz法硅晶生长过程中热输运和熔体流动影响的数值模拟

建立了一个120 kg单晶炉的二维轴对称全局模型,分别对无旋转、加入晶体旋转、加入坩埚旋转、同时加入晶体旋转和坩埚旋转的四种工况展开了数值模拟研究.得到了晶体旋转及坩埚旋转对晶体生长过程的拉晶功率、炉内温度分布和熔体流动的影响;得到了不同晶体长度下拉晶炉内的温度分布以及熔体流动的变化规律.结果显示,加入晶体旋转对晶体生长过程的拉晶功率、温度分布和熔体流动的影响小于坩埚旋转的影响;随着晶体长度的增加,晶体旋转及坩埚旋转对温度分布和熔体流动的影响不断减小.因此在单晶炉设计和优化过程中应考虑整个晶体生长过程.     

导模提拉法生长Tb3Sc2Al3O12(TSAG)晶体及性质表征

本文采用导模提拉法成功生长了Tb3Sc2Al3O12 (TSAG)晶体,并对所生长晶体进行了物相分析和单晶结构分析,探讨了多晶原料的烧结温度对晶体颜色的影响.Sc3+和Al3+的浓度分布测试表明,导模提拉法能较好地克服因分凝效应引起的Sc3+浓度分布不均,可以生长获得浓度分布均匀的TSAG晶体.磁光性能测试表明,Sc3+掺入对晶体在400～1100 nm波长范围内的磁光性能影响不大,所生长TSAG晶体的费尔德常数仅比Tb3Al5O12 (TAG)晶体低6; ～8;.     

Some features of two commercial softwares for the modeling of bulk crystal growth processes

Two commercial codes, FIDAP and MARC, have been used to model a number of crystal growth processes in collaboration with industrial and research teams. Examples of global and local simulations in the field of heat transfer, hydrodynamics, chemistry and mechanics are given and the results are compared to experimental measurements, with good agreement as a rule. This establishes that such codes can be used to help improve crystal growth processes, while full global transient models still belong to software specifically written in order to model crystal growth. Emphasis is put on the necessity to validate the numerical results by comparison with experiments and to have a clear understanding of the physical laws hidden behind the software.     

Global heat loss and thermal stress analysis in Czochralski crystal growth

Based on our invention of an energy‐efficient Czochalski crystal growth furnace, a 2D‐axisymmetric numerical simulation model of LiNbO₃ crystal growth is developed. The heat transfer, melt and gas flow, radiation and the interface deflection have been examined. Heat losses in the furnace and the insulator, as well as the heating power and thermal stress distribution at three stages of crystal growth are calculated in detail. It is found that a large proportion of heat dissipates through the water‐cooling system, and at the steel shell of the furnace, gas convection heat transfer is the major cooling mechanism. Less heat dissipation by radiation and more heat flux by gas convection to the crystal sidewall results in a larger concentrated thermal stress, which may induce large crystal cracks in the growth process. The simulation results of heating power are in coincidence with the actual power of our furnace, which verifies the feasibility of our model. The detailed information with respect to the device obtained from simulation can help to optimize the energy‐saving design and growth process.     

Numerical and experimental studies on crack formation in LiNbO3 single crystal

A global analysis of heat transfer was carried out in an inductively heated Czochralski (CZ) furnace which was actually used to grow LiNbO₃ single crystals, and then the temperature profiles obtained were used to calculate the three-dimensional thermal stress field in the crystal. By comparing the numerical results with the experimental ones, it was found that controlling the thermal environment in the CZ furnace so that the thermal stresses at the crystal surface might not exceed a certain value is important to realize the cracking free growth operation. In this study, this was accomplished through some modifications in the furnace design such as insertion of an after-heater into the furnace. These findings were verified by additional numerical simulations and crystal growth experiments for some growth conditions.     

Heat transfer and convection in Czochralski growth of large BGO Crystals

In the present work, numerical modeling has been performed to analyze heat transfer and melt convection during bismuth germanate Bi₄Ge₃O₁₂ (BGO) crystal growth by the Czochralski growth method. In addition to global heat-transfer modeling, the suggested model accounts for the radiative heat exchange in the crystal and melt convection together with the crystallization front formation. The model helped to analyze the modification of the growth setup made by including additional heater. The numerical predictions obtained with CGSim software agree well with available experimental data.     

Time-dependent simulation of the growth of large silicon crystals by the Czochralski technique using a turbulent model for melt convection

A numerical model is developed to perform the dynamic and global simulation of Czochralski growth. The effect of melt convection is taken into account by means of an eddy viscosity flow model, which can represent the mixing effect of flow oscillations on the heat transfer. Our method is used to investigate the dynamics of the growth of a 40 cm silicon crystal.     

Addition of an insulating element to the Modified Markov Method for CdTe single crystals growth

CdTe single crystal, were grown by the Modified Markov Method. We have introduced an insulating element between the furnace and the growth chamber, trying to minimize the radiation effects in the crystal. Numerical simulation of the heat transfer phenomena predict a reduction of the axial temperature gradient in the growth chamber, confirming by numerical experimental measurements, leading to a more uniform growth. An improvement in the surface morphology and in the crystal quality as well was achieved, evaluated by the combination of X‐ray rocking curves, etch pit density determination and low temperature photoluminescence. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vibrational control of crystal growth from liquid phase

Modeling and numerical simulations of the convective flows induced by the vibration of the monocrystal during crystal growth have been performed for two configurations simulating the Cz and FZ methods. This permitted to emphasize the role of different vibrational mechanisms in the formation of the average flows. It is shown that an appropriate combination of these mechanisms can be used to counteract the usual convective flows (buoyancy- and/or thermocapillary-driven) inherent to crystal growth processes from the liquid phase. While vibrational convection is rather complex due to these identified mechanisms, the new modeling used in the present paper opens up very promising perspectives to efficiently control heat and mass transfer during real industrial applications of crystal growth from the liquid phase.     

Simulation of temperature and flow fields in an inductively heated melt growth system

The goal of the research presented here is to apply a global analysis of an inductively heated Czochralski furnace for a real sapphire crystal growth system and predict the characteristics of the temperature and flow fields in the system. To do it, for the beginning stage of a sapphire growth process, influence of melt and gas convection combined with radiative heat transfer on the temperature field of the system and the crystal‐melt interface have been studied numerically using the steady state two‐dimensional finite element method. For radiative heat transfer, internal radiation through the grown crystal and surface to surface radiation for the exposed surfaces have been taken into account. The numerical results demonstrate that there are a powerful vortex which arises from the natural convection in the melt and a strong and large vortex that flows upwards along the afterheater side wall and downwards along the seed and crystal sides in the gas part. In addition, a wavy shape has been observed for the crystal‐melt interface with a deflection towards the melt. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional simulation of melt flow in Czochralski crystal growth with steady magnetic fields

Three-dimensional transient numerical simulations were carried out to investigate the melt convection and temperature fluctuations within an industrial Czochralski crucible. To study the magnetic damping effects on the growth process, a vertical magnetic field and a cusp magnetic field were considered. Due to our special interest in the melt convection, only local simulation was conducted. The melt flow was calculated by large-eddy simulation (LES) and the magnetic forces were implemented in the CFD code by solving a set of user-defined scalar (UDS) functions. In the absence of magnetic fields, the numerical results show that the buoyant plumes rise from the crucible to the free surface and the crystal–melt interface, which indicates that the heat and mass transfer phenomena in Si melt can be characterized by the turbulent flow patterns. In the presence of a vertical magnetic field, the temperature fluctuations in the melt are significantly damped, with the buoyant plumes forming regular cylindrical geometries. The cusp magnetic field could also markedly reduce the temperature fluctuations, but the buoyant plumes would break into smaller vortical structures, which gather around the crystal as well as in the center of the crucible bottom. With the present crucible configurations, it is found that the vertical magnetic field with an intensity of 128 mT can damp the temperature fluctuations more effectively than the 40 mT cusp magnetic field, especially in the region near the growing crystal.     

Numerical design of Metal‐Organic Vapour Phase Epitaxy process for gallium nitride epitaxial growth

The paper presents the results of numerical simulations and experimental measurements of the epitaxial growth of gallium nitride in Metal Organic Vapor Phase Epitaxy within a AIX‐200/4RF‐S reactor. The aim was to develop optimal process conditions for obtaining the most homogeneous crystal layer. Since there are many factors influencing the chemical reactions on the crystal growth area such as: temperature, pressure, gas composition or reactor geometry, it is difficult to design an optimal process. In this study various process pressures and hydrogen volumetric flow rates have been considered. Due to the fact that it is not economically viable to test every combination of possible process conditions experimentally, detailed 3D modeling has been used to get an overview of the influence of process parameters. Numerical simulations increased the understanding of the epitaxial process by calculating the heat and mass transfer distribution during the growth of gallium nitride. Appropriate chemical reactions were included in the numerical model which allowed for the calculation of the growth rate of the substrate. The results obtained have been applied to optimize homogeneity of GaN film thickness and its growth rate.