6英寸砷化镓单晶VGF法生长中坩埚-埚托间隙对晶体生长过程影响

在VGF法生长6英寸GaAs单晶的实际生长过程中,坩埚与坩埚托之间难以实现完全的理想贴合.坩埚与埚托之间的空隙对晶体生长过程中的温场和固液界面形状影响较大.通过模拟计算5种不同的空隙形状时的温场与热应力分布,发现随着空隙面积的增大,固液界面在轴向上的位置逐渐下降.在锥形空隙情况下,得到一个平坦的固液界面.设计了两种不同的空隙填充方案,模拟计算的结果表明,液态Ga完全填充时,在晶体轴向上热应力的分布较为平缓,有利于生长低位错、高质量的GaAs单晶.     

VGF法生长6英寸GaAs单晶生长速率的优化

晶体的生长速率关系着晶体质量和生产效率,保证晶体质量的同时,实现较高的生产效率是晶体生长速率优化的主要目标.VGF技术生长晶体时,晶体的生长速率主要取决于控温点的温度及降温速率.在保持加热器控温点不变的情况下,利用数值模拟方法研究了0.9,1.8,3.6mm·h-13个速率下6英寸VGF GaAs单晶的生长,通过对比不同生长速率下温度梯度(均为界面附近晶体中的温度梯度)和固-液界面形状的变化及热应力的分布,得出以下结果:随着晶体生长速率的增加,轴向温度梯度增大的同时,沿径向增加也较快;但由于受氮化硼坩埚轴向较大热导率的影响,晶体边缘轴向温度梯度迅速减小;径向温度梯度在晶体半径70 mm处受埚壁的影响均变为负值,晶体中大量的热沿埚壁流失,导致生长边角上翘;生长速率的增加使得界面形状由凸变平转凹,"边界效应"逐渐增强,坩埚与固-液界面的夹角逐渐减小,孪晶和多晶产生的几率增加;通过对比,1.8 mm·h-1生长时晶体界面平坦、中心及边缘处热应力均较小、生长速率较大,确定为此时刻优化的生长速率.     

VGF法生长6英寸Ge单晶中热应力的数值模拟优化

VGF技术生长单晶时温度梯度较低,生长速率较小,目前已成为生长大直径、低位错密度晶体的主流技术之一。采用数值模拟研究了VGF法6英寸低位错Ge单晶的生长,结果表明在采用自主研发的VGF炉生长6英寸Ge单晶时,晶体生长过程中晶体与熔体中均具有较低的温度梯度(这里的温度梯度是指的界面附近的温度梯度),尤其当晶体生长进入等径生长阶段后,晶体中的轴向温度梯度在2～3 K.cm-1之间,熔体中的轴向温度梯度0.8～1.0 K.cm-1之间;晶体中的热应力除边缘外均在(2～9)×104 Pa之间,低于Ge单晶的临剪切应力,且晶体生长界面较平整;坩埚与坩埚托之间的间隙对于晶体生长中的边界效应影响显著,将8 mm间隙减小至2 mm后,埚壁外侧的径向热流增加,使得晶体边缘的最大热应力减小至0.21 MPa和Ge单晶的临剪切应力相当,实现了热场的优化。     

VGF法GaAs单晶生长中热通量对固液界面形状的影响

采用专业的晶体生长模拟软件CGSim模拟了垂直梯度凝固法(VGF)GaAs单晶生长过程中固液界面形状及其变化;分析了生长过程中界面上不同位置的热通量及其变化,并利用能量守恒关系,分析了热通量对固液界面形状的影响,改进了前人在忽略凝固或熔化相变潜热的基础上推导出的固液界面形状和温度梯度之间的数学关系。结果表明:固液界面上各点热通量的不同导致各点生长速度的不同,从而形成偏离程度各异的固液界面形状。采用霍尔效应测量法检测了GaAs单晶中的载流子浓度分布,分析了固液界面形状对晶片电学均匀性的影响。结果表明:对于分凝系数k_01的溶质,平坦的固液界面,晶片中载流子浓度分布更为均匀;凸形界面,载流子浓度随晶片径向距离的增加而增加;凹形界面,载流子浓度随晶片径向距离的增加而降低;载流子浓度分布的不均匀性随固液界面非平坦性的增加而增加。     

4英寸VGFGaAs单晶生长的数值模拟与实验研究

利用数值模拟和实验相结合的方法,研究了4英寸VGF GaAs单晶的生长.首先基于炉体结构和所采用材料,建立一个和真实单晶生长系统接近的炉体模型.根据此模型,采用晶体生长模拟软件CrysMas计算得到整个炉体内的温度分布、晶体及熔体的温度梯度、界面位置等.通过对单晶生长不同时间点的模拟,制定了一套单晶的生长工艺.然后,严格遵循此工艺进行单晶生长实验.通过对实验和模拟结果的对比分析,建立了实验和数值模拟之间的联系,为进一步利用数值模拟指导晶体的实际生长提供了依据.最后,利用数值模拟研究了单晶生长中"边界效应",探讨了晶体生长过程中产生多晶的原因.     

数字模拟法研究坩埚锥角对VGF法GaAs单晶生长的影响

坩埚锥角是诱发VGF法GaAs单晶出现孪晶与多晶的重要因素之一,应用数值模拟的方法对其进行了研究与探讨,研究发现,在晶体生长的放肩阶段,坩埚锥角为60°,90°,120° 3种情况下,晶体生长的固液界面均凹向熔体,随坩埚锥角α的增大,接触角θ变小,非均匀形核几率增加,易诱发孪晶和多晶.根据热量传输分析,在晶体生长的转肩阶段,随坩埚锥角α的增大,沿轴向传走的热量减小,径向传走的热量增加,增大了径向的温度梯度,造成凹的生长界面,导致三相点处过冷度的增加,也增大了孪晶及多晶产生的几率.而在等径生长部分由于远离了坩埚直径增加的区域,坩埚锥角对成晶率的影响较小.考虑到晶体生长的效率,为获得较长的等径部分,需要设计合适的坩埚锥角.选取了90°的坩埚锥角,模拟及实验均证实这一角度即能有效提高单晶成晶率,又能保证一定的晶体生长效率,并生长出直径4英寸的VGF GaAs单晶.     

<100>P型4英寸低位错锗晶体电阻率径向均匀性的研究

P型锗单晶作为空间太阳电池外延层的衬底片,其电阻率均匀一致性极为重要。在直拉法锗晶体生长中,固液界面即为结晶前沿的等电阻面、等杂质浓度面。固液界面的形状和晶体中径向电阻率均匀性直接相关,对晶体质量有重大影响。因此,要提高外延层衬底片质量就是要控制晶体生长过程中的固液界面形状。晶体生长系统的热场分布和晶体生长工艺参数影响着固液界面的形状。结合数值模拟对影响固液界面形状的因素进行了研究,在TDR-Z80炉中进行的晶体界面实验、高电阻率均匀性单晶生长实验和数值模拟结果基本一致。同时对低位错锗单晶电阻率均匀性进行了表征与研究。优化工艺前的电阻率均匀性大于15%。优化工艺后获得的相对平坦固液界面极大地提高了径向电阻率均匀性,并且可控制在5%以内。     

水平磁场下18英寸直拉硅单晶生长工艺的三维数值模拟

利用计算机模拟仿真技术对适用于生长18英寸直拉单晶硅的40英寸热场在水平磁场下的生长工艺进行三维模拟仿真计算,重点分析了不同强度水平磁场作用下熔体和晶体中的温度场分布、熔体中流场的变化及其对晶体生长固/液界面形状的影响及其变化规律,并进一步研究了不同水平磁场强度对熔体和晶体中氧杂质含量分布影响。数值模拟计算结果表明:由于外加水平磁场的引入,熔体的流动呈现完全的三维、非对称特点,从而导致熔体内的温度场、氧杂质的分布呈现明显的三维非对称特性;水平磁场强烈影响固/液生长界面下熔体的流动特性,从而显著影响熔体的固/液生长界面形状及氧杂质传输过程。     

VGF法GaAs单晶位错分布的数值模拟和Raman光谱研究

采用数值模拟技术和Raman光谱法对4inch垂直梯度凝固(VGF)法GaAs单晶位错进行了研究。运用数值模拟软件计算了GaAs晶体生长过程中的位错分布,模拟计算与实验结果一致。通过Raman光谱测量,定量计算了晶片表面的残余应力分布。Raman测量结果表明,残余应力与位错密度分布基本一致。在VGF法生长的GaAs单晶中观察到了不完整的位错胞状结构,并利用Raman光谱法对其进行了微区分析。     

CUSP磁场对直拉硅单晶氧浓度分布影响的数值模拟

利用有限元分析软件对φ300mm直拉硅单晶生长过程进行模拟,分析了保持CUSP磁场对称面与熔体坩埚界面交点处的径向分量不变的情况下,硅单晶中氧浓度分别随CUSP磁场通电线圈距离、通电线圈半径的变化规律.随着通电线圈距离和半径的增大,晶体熔体固液界面氧浓度均逐渐降低.随着通电线圈距离和半径的增大,硅熔体径向磁场强度逐渐增大,对坩埚底部熔体向晶体熔体固液界面处对流的抑制作用加强,固液界面下方熔体轴向流速减小,使得从坩埚底部运输上来的富氧熔体减少,继而固液界面处的氧浓度降低.随着线圈距离和半径的增大,为保持所需磁场强度,施加电流也逐渐增大,从而能耗增大,与增大通电线圈距离相比,增大通电线圈半径所需的电流较大.通过实验,将CUSP磁场对单晶中氧浓度分布影响的数值模拟结果与实际晶体生长进行了对比,实验结果验证了数值模拟的结果.     

粉末注射成形充模过程凝固层形成规律研究

根据连续性、动量和能量守恒方程,以及固／液界面上能量平衡原理,建立了考虑凝固层后的一维流动模型,计算了模腔内壁上喂料凝固层厚度与工艺参数的关系,研究结果表明：模具入口附近凝固层厚度开始急剧增加,然后增加速率逐渐减缓;适当提高模具温度,可以减少凝固层厚度,有利于充模过程。     

An integrated model for dendritic and planar interface growth and morphological transition in rapid solidification

Rapid solidification can be achieved by quenching a thin layer of molten metal on a cold substrate, such as in melt spinning and thermal spray deposition. An integrated model is developed to predict microstructure formation in rapidly solidified materials through melt substrate quenching. The model solves heat and mass diffusion equations together with a moving interface that may either be a real solid/liquid interface or an artificial dendrite tip/melt interface. For the latter case, a dendrite growth theory is introduced at the interface. The model can also predict the transition of solidification morphology, e.g., from dendritic to planar growth. Microstructure development of Al-Cu alloy splats quenched on a copper substrate is investigated using the model. Oscillatory planar solidification is predicted under a critical range of interfacial heat-transfer coefficient between the splat and the substrate. Such oscillatory planar solidification leads to a banded solute structure, which agrees with the linear stability analysis. Finally, a microstructure selection map is proposed for the melt quenching process based on the melt undercooling and thermal contact conditions between the splat and the substrate.     

A monte carlo simulation study of dissolution of graphite in iron-carbon melts

A Monte Carlo (MC) simulation study has been carried out on the dissolution of graphite in Fe-C melts in the temperature range 1300 °C to 1600 °C. Atoms in graphite and iron melt were arranged on a rigid graphitic hexagonal lattice and interactions were assumed to be pairwise and short ranged. This hexagonal model of iron melts has been validated using saturation solubility of C in iron melts. The aim of this study was to investigate the effect of the atomic nature of the interfacial region on graphite dissolution. Using canonical ensemble, simulations were carried out as a function of carbon content of the melt, temperature, interface orientation, and surface roughness. A contact between graphite and melt resulted in the formation of a broad interfacial region containing high concentrations of C and Fe atoms. During the initial stages of contact, strong C-C bonds in the basal plane hinder the dissociation of C atoms and affect the overall dissolution rate. As dissolution proceeds, interfacial effects become less important and dissolution is controlled by mass transfer in the melt. Interfacial effects do not play an important role across prismatic planes. The simulation results also show an excellent agreement with the basic trends in experimental results on graphite dissolution.     

Computational modelling of heat⧹mass transfer near the LIQUID–SOLID interface during rapid solidification of binary metal alloys under laser treatment

This paper presents the results of an investigation into the problem of planar solid–liquid interface stability during rapid solidification of binary metal alloys under laser treatment. A new quantitative model is proposed. This model describes the self-organized development of stable spatially-periodic vortices in the melt near the solid–liquid interface due to concentration- (or thermal) capillary effectsfn2 together with effects due to the influence of normal concentration or temperature gradients directed from the interface towards the melt. These vortices give rise to a cellular structure at the solid–liquid interface of rapidly frozen melts.A computer code was developed to solve the set of second-order linear differential equations which describe heat and mass transfer at the liquid–solid interface. This model allows calculation of the liquid phase velocity field, the second component concentration field in the melt, as well as the temperature field in the liquid and solid phases near the solid–liquid interface at a given solidification rate.     

A Model for Predicting the Melt Temperature in the Ladle and in the Tundish as a Function of Operating Parameters during Continuous Casting

A mathematical model for predicting the melt temperatures in the ladle and in the tundish during continuous casting has been developed. First of all, a chain of models was created for the following stages of the ladle cycle; the preheating of the empty ladle, filling of the ladle, period in the ladle furnace, waiting period prior to casting, the casting period, and, finally, the free cooling period of the empty ladle. Models, written in CFD code, were used in sequence so that each simulation continued from the results of the simulation of the previous stage. An intermediate model was constructed to estimate the outlet temperature of melt drained from the ladle. Then the work was continued by performing simulations in the tundish, using as input the temperature of the simulated melt feed from the ladle and, as an initial condition, the temperature field of the remaining melt in the tundish. The final model “TEMPARV3” was created and tested by means of measured tundish data received from a steel plant. By means of statistical analysis the coefficients of correlation between the test data and model data at the start, in the middle period, and at the end of casting were calculated to be 0.9, 0.92 and 0.87, respectively. So, the most effective predictive power of the model in the tundish by means of a sequential casting schedule is realized during the middle period of the casting process. The model is applied interactively by a user interface, which expresses the predicted melt temperatures numerically and with graphical curves. The predictive model can be used off‐line as a tool for scheduling the stage operations in advance. The program may be utilized on‐line to estimate the superheat needed and to control periods of the operation. In extreme cases, when the model alerts the operator about the danger of superheat loss having a critical effect on casting, the operator has a chance to take adjustment measures. In addition to production work, the model could be of benefit for studying changes in operating parameters, for training operators, and for use as a “low‐cost computational pilot plant” in process development in general.     

Modeling of laser keyhole welding: Part I. mathematical modeling,numerical methodology,role of recoil pressure,multiple reflections,and free surface evolution

A three-dimensional laser-keyhole welding model is developed, featuring the self-consistent evolution of the liquid/vapor (L/V) interface together with full simulation of fluid flow and heat transfer. Important interfacial phenomena, such as free surface evolution, evaporation, kinetic Knudsen layer, homogeneous boiling, and multiple reflections, are considered and applied to the model. The level set approach is adopted to incorporate the L/V interface boundary conditions in the Navier-Stokes equation and energy equation. Both thermocapillary force and recoil pressure, which are the major driving forces for the melt flow, are incorporated in the formulation. For melting and solidification processes at the solid/liquid (S/L) interface, the mixture continuum model has been employed. The article consists of two parts. This article (Part I) presents the model formulation and discusses the effects of evaporation, free surface evolution, and multiple reflections on a steady molten pool to demonstrate the relevance of these interfacial phenomena. The results of the full keyhole simulation and the experimental verification will be provided in the companion article (Part II).     

Behavior of Boron in Molten Aluminum and its Grain Refinement Mechanism

The mechanism of heterogeneous grain refining of aluminum by ultrafine elemental boron particles was investigated. In order to facilitate the observation of the boron-aluminum interface, a boron filament was introduced in a melt at 1013 K (740 °C) containing different levels of Ti. The Al/B interface was studied using transmission electron microscopy and different phases were identified using the electron diffraction method. The experimental results showed that boron is dissolved in pure aluminum while its dissolution is inhibited in presence of titanium solute. A thin layer of TiB₂ formed at the surface of boron thickens with residence time in the melt. The mechanisms by which aluminum is crystallized on boron are discussed.     

Numerical Simulation of Turbulent Flows,Heat and Mass Transfer in Metallurgical Induction Processes

Comprehensive knowledge of the turbulent flows, heat and mass transfer processes in the melt of induction applications is required to realize efficient metallurgical processes. Experimental and numerical studies of the melt flow in induction furnaces show that the flow pattern, which comprises several vortices of the mean flow, and the temperature distribution in the melt are significantly influenced by low‐frequency large‐scale flow oscillations. Two‐ and three‐dimensional hydrodynamic calculations of the melt flow, using two‐equation turbulence models based on Reynolds Averaged Navier‐Stokes approach, do not predict the large‐scale periodic flow instabilities obtained from the experimental data. That is why the Large Eddy Simulation (LES) numerical technique was approved to be an alternative for the various k‐? model modifications. The results of the transient 3D LES simulation of the turbulent melt flow revealed the large‐scale periodic flow instabilities and the temperature distribution in the melt, which both are in good agreement with the expectations based on the data from the experiments. The studies, presented in this paper, demonstrate the possibility of using the three‐dimensional transient LES approach for successful simulation of heat and mass transfer processes in metallurgical applications.