基于数据驱动的晶体直径模型辨识方法研究

直拉法硅单晶生长是一个多场多相耦合、物理变化复杂,且具有大滞后和非线性现象的过程,基于单晶硅生长系统内部机理所构建的机理模型由于存在诸多假设而无法应用于工程实际。因此,本文以现有CL120-97单晶炉拉晶车间的长期、海量晶体生长数据为基础,忽略炉内复杂的晶体生长环境,对影响晶体直径的拉晶参数进行关联性分析及特征量化,探寻拉晶数据中所蕴藏的规律信息,进而建立基于数据驱动的BP神经网络晶体直径预测模型,并针对现有BP神经网络易陷入局部极小值的问题,采用遗传算法对BP神经网络的阈值和权值进行优化,以提高晶体直径预测的准确性。通过实际拉晶数据对模型预测结果进行验证,结果表明,对任意选取的8组拉晶数据进行直径预测,预测的平均相对百分比误差为0.095 71%,证明该模型对于等径阶段晶体直径的预测是可行的。     

Analysis of the profile curves of the menisci for the sapphire tubes growth by EFG (Stepanov) technique

This paper deals with investigation of the behavior of the profile curves of the melt menisci for the case of the sapphire crystal growth by EFG (Stepanov) technique. The cases of external and internal circular menisci of the crystal tube are considered. The cases of the positive and negative angles of the contact of the profile curve with the working surface of the shaper are considered. Features of the profile curves are used in the automated control systems of the crystal growth using of the weight sensor. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mathematical simulation and X-ray diffraction investigation of the crystal structure of 1-phenyl-1-<Emphasis Type="Italic">tert</Emphasis>-butyl-3-methyl-1,3-dihydroisobenzofuran

An algorithm for using a priori generation of crystal structures by the discrete modeling method for the interpretation of data obtained from single-crystal X-ray diffraction experiments is considered. The crystal structure of 1-phenyl-1-tert-butyl-3-methyl-1,3-dihydroisobenzofuran is mathematically simulated using the discrete modeling of molecular packings and studied by X-ray diffraction. The simulation is performed for two isomers of the initial chemical compound that are possible from the viewpoint of the mechanism of the chemical reaction used in the synthesis of this compound. Appropriate models that can serve as starting models for solving and refining the crystal structure with the use of X-ray diffraction data are chosen from a complete set of calculated structural models in accordance with specific criteria. The structure is solved using a starting model calculated using the discrete modeling method and refined by the full-matrix least-squares procedure.     

Estimating the real crystal radius from the weight signal in a course of growth process by the Stepanov (EFG) technique

The method of estimating the real radius from the weight signal in a course of growth by the Stepanov (EFG) technique is developed. The transitional portion of the cylindrical crystal was grown during which calculation of changing real radius was carried out. Comparison of the real profile with calculated one was made.     

基于NARX动态神经网络直拉硅单晶直径预测模型

直拉法在制备硅单晶的过程中存在机理假设多、多场耦合下边界条件不明确和化学变化交错且相互影响等问题,导致无法建立准确的机理模型用于硅单晶生长过程控制。针对此问题,本文以单晶炉拉晶车间的大量晶体生长数据为基础,基于互信息理论提出的最大信息系数(MIC)算法,对与晶体直径相关的特征参数进行分析,然后基于带外源输入的非线性自回归(NARX)动态神经网络,建立多输入单输出的等径阶段晶体直径预测模型,并对三台单晶炉拉晶数据进行直径预测,预测的平均均方误差值为0.000 774。最后将NARX动态神经网络同反向传播(BP)神经网络进行对比分析,验证了该模型的优越性。结果表明,NARX动态神经网络为晶体直径的控制提供了一种更准确的辨识模型。     

Vertical optical floating zone furnace: Principles of irradiation profile formation

The light distribution within the vertical double-ellipsoid mirror furnace applied for floating zone crystal growth with optical heating is studied. During the last few years, this setup was intensively applied for crystal growth of intermetallic and oxide materials due to its advantages for radiation focussing, which is superior in some key features compared to other commercial horizontal and vertical optical floating zone facilities. A point source model was used as a light source to reveal basic principles of the irradiation profile formation, which can strongly affect the melt flows, as well as the curvature and stability of crystallization front. Effects of the lamp displacement along the vertical optical axis with respect to the focal point of the lower elliptical mirror and the effect of mirror apertures were studied as the prime factors, which determine the light profile on the crystal. The efficiency of the light focusing in the presented optical configuration is discussed.     

Modeling and X-ray diffraction investigation of the crystal structure of 1,1-diphenyl-3-methyl-6,7-dimethoxy-1,3-dihydroisobenzofuran

The results of a priori generation and X-ray diffraction investigation of the crystal structure of 1,1-diphenyl-3-methyl-6,7-dimethoxy-1,3-dihydroisobenzofuran are reported. The generation is performed by the discrete modeling of molecular packings in a crystal for two possible conformers of the compound under investigation. Appropriate models that can serve as starting models for refining the crystal structure by the fullmatrix least-squares method using the X-ray diffraction data are chosen from a complete set of calculated structural models of the studied compound in accordance with specific criteria. The structure is solved for a starting model calculated by the discrete modeling method and refined according to the full-matrix least-squares procedure.     

Influence of magnetic field on the director profile in nematic layer with curved surface

A nematic liquid crystal layer with a curved upper boundary exposed to a magnetic field directed along the layer plane has been studied. Strong nematic anchoring at the lower boundary surface is assumed. A phenomenological expression for the director profile is proposed to solve the problem on the director profile distribution in this system and its stability with respect to the rotational deformations in relation to the degree of the upper-surface roughness and the magnetic field value. The distribution parameters are found by optimizing the expression for the free energy of the liquid crystal system.     

激光晶体提拉生长模糊PID控制系统

本文设计了基于ARM Cortex-M3核、针对上称重法激光晶体的生长的控制方案硬件平台,运用模糊PID自适应控制算法对称重信号进行模糊处理确定晶体生长瞬间所需的温度场,根据生长模型在理论上进行了仿真,并实际运用到TDL-J50型激光单晶炉设备,实现了激光晶体的瞬时生长速率的精确而平稳的自动控制.     

基于ISOMAP-DE-SVM的Cz单晶硅等径阶段掉苞预测

针对目测法无法及时发现直拉单晶硅在等径生长阶段发生的掉苞问题,本文提出一种基于ISOMAP-DE-SVM的掉苞预测模型,可以在掉苞现象发生之前发出警告。首先剔除方差较小的参数,采用斯皮尔曼相关系数法剔除冗余参数,采用最大互信息法检验剩余参数的非线性相关性;然后将关键参数的均值和标准差作为等度量映射和多维放缩的输入,得到两份样本数据;最后将这两份样本数据分别输入到经过差分算法、遗传算法优化的支持向量机预测模型,得到4份预测结果。预测结果表明：基于ISOMAP-DE-SVM的预测模型具有收敛速度快、准确度高的特点,平均预测准确率可以达到96%;同时,所使用的方法揭示了单晶硅等径阶段的数据具有非线性特点。通过实际应用验证表明模型具有一定的工程实用价值。     

Generation of the structures of molecular crystals with two molecules related by the center of inversion in a primitive unit cell

An algorithm for the generation of possible crystal structures with two inversion-related molecules of known shape in a primitive unit cell is proposed within the method of discrete packing modeling in molecular crystals. The algorithm is based on the replacement of molecules by polycubes (geometric figures composed of identical cubes) and looking through a finite number of all the possible periodic packings of these polycubes with a given coefficient of packing. A program package for personal computers is developed on the basis of the proposed algorithm and is approved by the example of several crystal structures that were determined earlier by X-ray diffraction.     

Mathematical simulation and X-ray diffraction investigation of the crystal structure of (R)-[(R)-o-(1-N,N-dimethylaminoethyl)phenyl]-2,5-dimethoxyphenyl(phenyl)methanol

The crystal structure of (R)-[(R)-o-(1-N,N-dimethylaminoethyl)phenyl]-2,5-dimethoxyphenyl(phenyl)methanol is mathematically simulated by the discrete modeling of molecular packings. A complete set of possible model variants is analyzed using the proposed algorithm with the aim of choosing the appropriate models that can serve as starting models for solving and refining the crystal structure from X-ray diffraction data. The crystals of the compound under investigation are monoclinic, a = 9.268(2) Å, b = 8.802(2) Å, c = 13.176(3) Å, β = 94.01(3)°, space group P2₁, and Z = 2. The structure is solved for a starting model calculated using the discrete modeling method and refined by the full-matrix least-squares procedure to R(F) = 0.037 and ωR(F ²) = 0.097.     

Oxygen and carbon transfer during solidification of semiconductor grade silicon in different processes

A model is established for comparing the solute distribution resulting from four solidification processes currently applied to semiconductor grade silicon: Czochralski pulling (CZ), floating zone (FZ), 1D solidification and electromagnetic continuous pulling (EMCP). This model takes into account solid–liquid interface exchange, evaporation to or contamination by the gas phase, container dissolution, during steady-state solidification, and in the preliminary preparation of the melt. For simplicity, the transfers are treated in the crude approximation of perfectly mixed liquid and boundary layers. As a consequence, only the axial (z) distribution can be represented. Published data on oxygen and carbon transfer give a set of acceptable values for the thickness of the boundary layers. In the FZ and EMCP processes, oxygen evaporation can change the asymptotic behaviour of the reference Pfann law. In CZ and in 1D-solidification, a large variety of solute profile curves can be obtained, because they are very sensitive to the balance between crucible dissolution and evaporation. The CZ process clearly brings supplementary degrees of freedom via the geometry of the crucible, important for the dissolution phenomena, and via the rotation rate of the crystal and of the crucible, important for acting on transfer kinetics.     

Sensitivity Analysis on Indium Phosphide Liquid Encapsulated Czochralski Growth

The optimization of the InP liquid encapsulated Czochralski systems is usually difficult, time consuming and very expensive. Here, the relative importance of the different growth parameters (e.g., pull rate, system temperatures and geometry) on the growth interface deflection, the temperature gradients within the melt and the crystal and the dislocation density has been investigated through a sensitivity analysis. The sensitivity coefficients have been calculated by means of a mathematical model, previously validated, based on the thermoelastic theory for the dislocation formation and on the thermal capillary theory for the temperature field within the system. The crucible temperature profile has been selected as the more important parameter to control the crystal quality during the growth.     

Influence of a high vertical magnetic field on Te dopant segregation in InSb grown by the vertical gradient freeze method

A vertical gradient freeze apparatus was set up to investigate the influence of a vertical magnetc field on Te dopant segregation in InSb. Te-doped InSb crystals were grown in the presence and absence of an 80.0 kG magnetic field. The axial profile of the Te concentration in the crystal grown in the magnetic field was observed to be more uniform than that grown without magnetic field, which was attributed to the influence of the high magnetic field on Te dopant segregation by reducing convection in the melt.     

基于神经网络和遗传算法的铸锭晶体硅质量控制及工艺优化

铸锭晶体硅是太阳能级晶硅材料的重要来源之一,为了进一步降低硅片成本,需要在保证晶体质量的同时发展大尺寸铸锭晶硅。影响铸造晶体硅质量的热场控制核心参数包括晶体生长速度与生长界面温度梯度之比V/G、壁面热流q、生长界面高度差Δh和硅熔体内部温差ΔT等。针对铸锭晶体硅生长过程中的质量控制问题,本研究基于人工神经网络(ANN)模型对晶体生长过程建立了工艺控制优化方法,利用实验测量数据和数值仿真模拟结果构建铸锭晶体硅生长过程的工艺控制数据集,以底部隔热笼开口和侧、顶加热器功率比作为主要工艺控制参数,V/G、|q|、|Δh|和ΔT为优化目标,建立用于研究晶体生长工艺控制参数和热场参数之间映射关系的神经网络模型。使用训练完成的模型分析底部隔热笼开口及侧、顶加热器功率比对晶体生长过程热场的影响规律,并采用遗传算法(GA)对铸锭晶体硅生长过程的工艺控制参数以提高晶体质量为目标进行优化,最后结合实际生产中的检测图像讨论了V/G对晶体质量的影响。研究表明晶体生长中期的V/G沿横向变化较平缓,对应缺陷较少且分布均匀,因此增大V/G在横向上的均匀度也是提高晶体质量的一个重要因素。     

基于贝叶斯参数优化的无模型自适应硅单晶直径控制

直拉硅单晶的生长过程涉及多场多相耦合与复杂的物理化学变化,其中工艺参数的波动是导致晶体直径不均匀的重要原因,如何实现工艺参数的控制以获得理想的、均匀的晶体直径具有重要的研究意义。本文分析现有控制方法存在不稳定以及控制效果不佳的问题后,提出基于贝叶斯参数优化的无模型自适应控制模型来控制硅单晶生长过程中的晶体直径。首先以坩埚上升速度与加热器的功率作为控制输入参数,晶体直径作为输出,搭建无模型自适应控制模型,并分析算法的稳定性。其次将控制模型进行仿真实验,发现硅单晶直径控制模型中不同的超参数设定会影响控制过程的迭代次数以及控制效果。最后,利用贝叶斯优化超参数的取值范围,并进行最终的仿真实验,结果表明,经贝叶斯参数优化后的控制模型计算快、迭代次数少,输出的晶体直径稳定,同时将生长工艺参数控制在实际生产要求范围内。因此,基于贝叶斯参数优化的无模型自适应控制实现了硅单晶直径均匀稳定的有效控制,具有结合工程背景的实际应用前景。     

Short-range order in RE4Al3 metallic glasses (RE = Pr, Gd, Tb, Dy)

A suitable model structure of RE₄Al₃ metallic glasses (RE = Pr, Gd, Tb, Dy) has been selected by comparing experimental pair correlation functions with model pair correlation functions for disordered crystal structures. A non-linear least-squares profile analysis of the experimental pair correlation functions has been performed with the use of the characteristic structural parameters of the model structure as variable parameters. The partial atomic distances and the partial coordination numbers have been estimated on the basis of the best fitting parameters. It is established that the local atomic arrangement in RE₄Al₃ metallic glasses resembles that in tetrahedrally close-packed Zr₄Al₃-type crystalline compounds.     

RbCdF3:Ni2+晶体结构相变、光谱精细结构和EPR谱的研究

本文采用半自洽场(semi-SCF)3d轨道模型和μ-κ-α模型,利用完全对角化方法,建立了Oh、D4h对称晶体场局部结构参数与光谱精细结构、EPR谱之间的定量关系,统一解释了RbCdF3∶Ni2+晶体的光谱精细结构和EPR谱。所得理论结果与实验值符合很好。     

基于迁移学习的大尺寸铸锭晶体硅热场设计

不同尺寸的铸锭晶体硅生长过程具有相似性,小尺寸晶体的生长规律可以迁移至大尺寸。本文采用迁移学习(TL)对G8型铸锭炉进行热场设计,设计对象为侧、顶加热器位置及体积、侧隔热笼分区块高度,主要设计目标为减少晶体内部的位错缺陷、抑制硅锭边缘多晶且使晶体生长界面微凸。首先使用神经网络对已有的G7铸锭炉建立热场几何参数与热场评价参数间的映射模型,然后将该模型迁移至G8铸锭炉,对比不同模型结构对迁移过程的影响,采用Dropout分析模型是否存在过拟合,并使用遗传算法(GA)结合聚类算法(CA)对热场几何参数进行优化,以上为G8热场设计过程。最后对优化结果采用数值模拟方法研究其在晶体生长过程中的温度分布、固液界面形状等,最终选定的优化方案能够实现较高质量的长晶。将该方案同时应用于G7和G8热场并进行对比,结果表明G8在硅熔体和硅晶体中的轴向温度梯度均小于G7,在晶体生长界面沿径向的温度梯度也小于G7,这有利于减小晶体内部的热应力。