LEC法熔体内输运特性数值模拟及凝胶法晶体生长机理研究
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摘要
学科间的交叉、融合以及向微观世界不断深入是当今科学研究的两大重要特征。热科学与材料科学的交叉已成为近年来极具活力的新学科生长点;而一些全新的测试仪器,如原子力显微镜等的出现,为人们探索过去欲探索却无法探索的微观世界创造了条件。本课题利用热科学的基本理论,用数值计算方法,研究晶体生长中熔体内的热、质输运特性,并利用原子力显微镜对晶体生长界面的微观形貌进行观察,研究晶体生长的微观机理。分别选择了适合熔体生长的重要的化合物半导体材料砷化镓和适合凝胶法晶体生长的具有优良电、光特性的高氯酸钾作为研究对象。主要内容为:
(1)对LEC法砷化镓单晶生长中熔体内热量、动量及质量输运建立了三维时相关的紊流数学模型,在模型中考虑了熔体/晶体界面的溶质分凝效应,采用基于交错网格的有限容积法(FVM)进行数值求解。通过计算结果比较,认为低Re的k-ε紊流模型能较好地定量描述温度梯度及旋转驱动下的熔体流动特性;对已有文献中的CZ熔体流动特性进行数值模拟,并与其实验结果进行比较,验证了数学模型和计算方法的正确性。
(2)对浮力和热毛细力驱动的熔体内自然对流,通过改变加热温差分析了浮力和热毛细力对熔体流动状态的影响。研究结果表明,加热温差增大到某一临界值时,熔体流动将由轴对称的稳态流动转换为非轴对称的振荡流动;流动状态转换的机制归结为热毛细力引起的不稳定性,熔体高度的变化对流动状态转换的临界温差几乎没影响;熔体流动为非轴对称的振荡流动时,熔体内出现热流体波波型,该波波型没有沿周向旋转,仅是形状随加热温差增大由规则变为不规则。
(3)对浮力、热毛细力和晶体旋转共同作用驱动的混合对流,通过改变晶体转速,分析了各力及其相互作用对熔体流动状态的影响。研究结果表明,熔体中温度梯度驱动的浮力和热毛细力的联合作用与晶体旋转产生的离心力和科里奥利力的联合作用相匹配时,熔体流动表现为与热毛细不稳定流动不同的非轴对称振荡流动。通过对熔体内温度场分布特征的分析,揭示了引起该非轴对称的振荡流动的机制为斜压不稳定性。在斜压不稳定流动中,熔体内出现沿晶体旋转方向旋转且具有垂直方向的完全正关联特性的斜压热流体波。分析了LEC法砷化镓熔体内斜压热流体波波型的形成机理。数值预测到了发生斜压不稳定流动的熔体内的诸多流动特征。一定范围内的熔体高度变化对流动状态转换的临界晶体转速没有明显影响。得出了不同加热温差下的临界
The intersections and syntheses between different disciplines and the penetrating into the microcosm are the two important characteristics of the science research at present. The cross between thermal science and material science has become the vigorous growth point of the new subject in the recent years. At the same time, the coming forth of some neoteric measuring instruments such as the Atom Force Microscope make it possible for people to explore the unknown microcosm. With the aid of basic theory of the thermal science, the numerical simulation is performed to study the characteristics of heat and mass transport in the melt during crystal growth, and the Atom Force Microscope is used to observe the microtopography on the growth interface in order to study the crystal growth mechanism in the present dissertation. Gallium arsenide(GaAs) and potassium perchlorate(KClO4) are selected as research objects, respectively. The former is important compound semiconductor material and usually grown from melt, and the latter shows excellent electronic and optical properties and is suitable for gel crystal growth. The main contents are:
(1) A three-dimensional and time-dependent turbulent mathematical model is established for the heat、momentum and mass transport in the Liquid Encapsulated Czochralski (LEC) GaAs melt, in which the dopant segregation effect at the melt/crystal interface is considered. The numerical method is based on a finite volume discretization on staggered grids. A low-Reynolds number k-εturbulent model is proved to be suitable for capturing accurately the essentials of flow driven by temperature gradient and rotation in the melt. The turbulent mathematical model is used to simulate the CZ silicon melt convection in the previously published experiment, and its validity is evaluated by comparing the results with the experimental data.
(2) For the natural convection driven by the buoyancy and Marangoni force in the melt, the effects of the change of the buoyancy and Marangoni force on the flow state are analyzed by changing the temperature difference between the crystal and the crucible walls. The results show that the flow will transform from axisymmetric steady flow to non-axisymmetric oscillatory flow when the temperature difference exceeds the critical value, and that the mechanism of the transform is attributed to the Marangoni instability, and that the critical temperature difference value is found to be almost independent of the melt depth in the crucible. The thermal wave patterns are found to
(1)对LEC法砷化镓单晶生长中熔体内热量、动量及质量输运建立了三维时相关的紊流数学模型,在模型中考虑了熔体/晶体界面的溶质分凝效应,采用基于交错网格的有限容积法(FVM)进行数值求解。通过计算结果比较,认为低Re的k-ε紊流模型能较好地定量描述温度梯度及旋转驱动下的熔体流动特性;对已有文献中的CZ熔体流动特性进行数值模拟,并与其实验结果进行比较,验证了数学模型和计算方法的正确性。
(2)对浮力和热毛细力驱动的熔体内自然对流,通过改变加热温差分析了浮力和热毛细力对熔体流动状态的影响。研究结果表明,加热温差增大到某一临界值时,熔体流动将由轴对称的稳态流动转换为非轴对称的振荡流动;流动状态转换的机制归结为热毛细力引起的不稳定性,熔体高度的变化对流动状态转换的临界温差几乎没影响;熔体流动为非轴对称的振荡流动时,熔体内出现热流体波波型,该波波型没有沿周向旋转,仅是形状随加热温差增大由规则变为不规则。
(3)对浮力、热毛细力和晶体旋转共同作用驱动的混合对流,通过改变晶体转速,分析了各力及其相互作用对熔体流动状态的影响。研究结果表明,熔体中温度梯度驱动的浮力和热毛细力的联合作用与晶体旋转产生的离心力和科里奥利力的联合作用相匹配时,熔体流动表现为与热毛细不稳定流动不同的非轴对称振荡流动。通过对熔体内温度场分布特征的分析,揭示了引起该非轴对称的振荡流动的机制为斜压不稳定性。在斜压不稳定流动中,熔体内出现沿晶体旋转方向旋转且具有垂直方向的完全正关联特性的斜压热流体波。分析了LEC法砷化镓熔体内斜压热流体波波型的形成机理。数值预测到了发生斜压不稳定流动的熔体内的诸多流动特征。一定范围内的熔体高度变化对流动状态转换的临界晶体转速没有明显影响。得出了不同加热温差下的临界
The intersections and syntheses between different disciplines and the penetrating into the microcosm are the two important characteristics of the science research at present. The cross between thermal science and material science has become the vigorous growth point of the new subject in the recent years. At the same time, the coming forth of some neoteric measuring instruments such as the Atom Force Microscope make it possible for people to explore the unknown microcosm. With the aid of basic theory of the thermal science, the numerical simulation is performed to study the characteristics of heat and mass transport in the melt during crystal growth, and the Atom Force Microscope is used to observe the microtopography on the growth interface in order to study the crystal growth mechanism in the present dissertation. Gallium arsenide(GaAs) and potassium perchlorate(KClO4) are selected as research objects, respectively. The former is important compound semiconductor material and usually grown from melt, and the latter shows excellent electronic and optical properties and is suitable for gel crystal growth. The main contents are:
(1) A three-dimensional and time-dependent turbulent mathematical model is established for the heat、momentum and mass transport in the Liquid Encapsulated Czochralski (LEC) GaAs melt, in which the dopant segregation effect at the melt/crystal interface is considered. The numerical method is based on a finite volume discretization on staggered grids. A low-Reynolds number k-εturbulent model is proved to be suitable for capturing accurately the essentials of flow driven by temperature gradient and rotation in the melt. The turbulent mathematical model is used to simulate the CZ silicon melt convection in the previously published experiment, and its validity is evaluated by comparing the results with the experimental data.
(2) For the natural convection driven by the buoyancy and Marangoni force in the melt, the effects of the change of the buoyancy and Marangoni force on the flow state are analyzed by changing the temperature difference between the crystal and the crucible walls. The results show that the flow will transform from axisymmetric steady flow to non-axisymmetric oscillatory flow when the temperature difference exceeds the critical value, and that the mechanism of the transform is attributed to the Marangoni instability, and that the critical temperature difference value is found to be almost independent of the melt depth in the crucible. The thermal wave patterns are found to
引文
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