Theoretical analysis of the shape evolution of crystals grown by pulling

This paper proposes a geometric model for crystal growth by pulling. On the basis of the model, effects of the growth processes on the evolution of crystal shape were studied. Besides some effects already adopted in practice to control the crystal diameter, our results revealed several novel effects: a crystal grown under fixed process parameters could grow with a self‐stabilized diameter after shoulder‐expanding; decreasing the convex degree of solid liquid interface would enhance the increasing rate of crystal diameter or reduce the decreasing rate of crystal diameter. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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。     

Automated growing of large single crystals controlled by melt level sensor

The process of single crystal pulling is considered with simultaneous starting material make-up into the melt and heater temperature control in response to a signal generated by the electronic contact melt level sensor, viz.: (i) conditions ensuring the radial broadening steadiness; (ii) effect of melt level displacement, melt temperature changes, changes of solid/liquid interface shape, melt evaporation on the growing crystal diameter; (iii) conditions of crystal purification from impurities and uniform distribution of dopant.     

On the void distribution and size in shaped sapphire crystals

Ribbon and rod sapphire pulling has been performed in three different crystal growth equipments in order to study the effect of the installation, of the atmosphere, of the die shape, of the feed material and of the pulling rate on the distribution, number and diameter of the characteristic voids (micro‐bubbles) in the crystals. The location of the bubbles in the crystals depends on the die geometry; however, in most cases they are essentially located close to the crystal periphery and then can be efficiently removed by lapping. After statistical analysis of the results, it is demonstrated that the number of gas moles incorporated in the crystals, inside the voids, is totally independent of any growth parameter. It is also shown that the bubble diameter depends only on the pulling rate. Consequently, for a given pulling rate, the number of bubbles auto‐adjusts in order to satisfy the constant molar gas incorporation. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Iso‐Diameter Growth of β ‐BaB2O4 (BBO) Crystals by Flux Pulling Method

The iso‐diameter growth of β ‐BaB₂O₄ (BBO) crystals by the flux pulling method have been studied based on the phase equilibrium diagram in the BaB₂O₄‐Na₂O pseudo‐binary system and from the interface stability. The mathematical expressions for the cooling rate in the growth of the crystals with constant diameter under stable growth conditions are derived, the experimental phenomena such as diameter contraction and difficulty to grow a lengthy crystal by the flux pulling method are explained, the prerequisite for iso‐diameter BBO crystal growth from the flux is suggested; a new continuous charging flux pulling method is introduced to grow large‐sized high quality crystals with a relative high growth rate.     

晶体生长过程建模及解耦控制

晶体生长过程中其直径的控制是通过调节生长速度和热场温度而实现的.控制系统是一个双入双出系统,输入输出之间存在耦合关系.本文采用前馈补偿解耦的方法,实现了单晶炉生长控制中的解耦控制,并通过仿真及实验证明了方法的有效性.     

ø300 mm直拉硅单晶生长过程中的变晶现象及其影响因素

直拉法生长直径300 mm硅单晶过程中,直径均匀是获得高品质硅单晶的关键。在生产实践中发现,当硅晶体进入等径生长阶段,过高的提拉速度会引起晶体发生扭晶现象,导致晶线断裂随即变晶,对等径生长不利。本文采用数值模拟和理论相结合的方法分析了ø300 mm硅单晶生长过程中扭晶现象的成因,建立了不同提拉速度下晶体直径与熔体温度分布的关系,分析了晶体发生扭晶的影响因素。结果表明,随着提拉速度的增加,熔体自由表面产生过冷区且该过冷区随提拉速度的增加不断扩大,过冷区的产生是导致晶体发生扭晶的主要原因。提出了一种基于有限元热场数值模拟的最大稳定提拉速度的判别方法,并给出了通过改变晶体旋转速度来改善熔体自由表面温度分布的工艺措施建议,从而避免晶体扭晶现象的发生。研究结果对设计大尺寸硅单晶生长热场具有一定的指导作用。     

Analyses of Crystal Shape Monitoring of LEC-Grown InP Crystals by using a Disc Approximation Approach

This paper analyzes crystal shape monitoring for automatic diameter control (ADC) during the liquid encapsulated Czochralski (LEC) growth of InP crystals. The crystal diameter (shape) is monitored numerically (diagrammatically) by using a disc approximation approach based on precise weight and pulling length measurements. The error in the diameter calculation based on the approximation is estimated to be sufficiently small for practical use. The monitoring accuracy was investigated for crystal bodies with nearly flat growth interfaces, and for their shoulder portions with largely convex growth interfaces. For the straight body portions, the accuracy depended on diameter, d, and improved from ±15% for d=10 mm to ±3% for d=50mm. For the shoulder portions, the diameter was monitored with nearly the same accuracy. This method has therefore made it possible to monitor the growing crystal visually in real time, and was applied to the growth of <111> InP crystals with a cone angle of less than 39° and a smooth appearance to avoid twinning.     

Temperature field design,process analysis and control of SAPMAC method for the growth of large size sapphire crystals

In this paper, the relationship between quality of sapphire crystal and growing parameters of SAPMAC (Sapphire growth technique with micro‐pulling and shoulder‐expanding at cooled center) method was discussed. Optimized temperature distribution and technique control were proposed by theoretical analysis, numerical simulation computation and experimental validation to obtain large size sapphire crystals. For a‐axis crystallized direction, with 1.0‐5.0mm/h growth velocity and 10‐30K/h temperature decreasing speed, large sapphire single crystal (∅︁240mm×210mm, 27.5kg) having high optical quality was successfully grown. The absorption spectrum of standard samples was measured as well. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystallization rate control for alkali halide crystal growth by the VGF technique with a skull layer

This study describes the ability to use the melt‐level control for stabilization of the crystallization rate during NaI crystal growth by the VGF technique with a skull layer. It is shown that a conventional linear decrease of the heater temperature leads to a nonuniform crystallization rate and deterioration of crystal quality. A method and algorithm of temperature control for the stabilization of the crystallization rate during crystal growth is proposed. The series of growth experiments with NaI(Tl) crystals proved the efficiency of this approach and ability to obtain scintillators with high registration efficiency, about 6.3% energy resolution for a ¹³⁷Cs (662 keV) source.     

Ce∶LuAG闪烁晶体的生长研究

Ce∶LuAG晶体是一种性能优良的闪烁材料,但采用提拉法生长Ce∶LuAG时,经常出现开裂和包裹物缺陷。本文通过理论与实践相结合的方式分析了温度梯度、提拉速度、晶体旋转速度和热应变等因素对晶体产生缺陷的影响,并提出了解决办法,给出了适合生长优质Ce∶LuAG晶体的工艺参数:熔体上方温度梯度在5 ℃/mm左右,放肩角度在30°~60°,提拉速度1.0~1.5 mm/h,晶体旋转速度15~25 r/min。最后成功生长出直径30 mm、等径长50 mm质量较为完好的Ce∶LuAG单晶,晶体内核心面积小。     

Capillary shaping of crystals pulled downward from a melt by the crucibleless AHP method

A model is proposed for capillary shaping of a crystal in the crucibleless variant of the AHP (axial heat flux close to the phase interface) method when the melt in the form of a film flowing over the AHP heater is fed to a meniscus. The meniscus and the film of the melt are described by the same equation with a discontinuous right-hand side. The dependences of the crystal radius and the thickness of the melt film on the parameters of the process are numerically investigated, and the capillary stability of the pulling process is analyzed. It is demonstrated that, in this method, the thickness of the melt layer between the crystal and the heater can be considerably larger than the capillary constant.     

大尺寸电阻加热式碳化硅晶体生长热场设计与优化

大尺寸低缺陷碳化硅(SiC)单晶体是功率器件和射频(RF)器件的重要基础材料,物理气相传输(physical vapor transport, PVT)法是目前生长大尺寸SiC单晶体的主要方法。获得大尺寸高品质晶体的核心是通过调节组分、温度、压力实现气相组分在晶体生长界面均匀定向结晶,同时尽可能减小晶体的热应力。本文对电阻加热式8英寸(1英寸=2.54 cm)碳化硅大尺寸晶体生长系统展开热场设计研究。首先建立描述碳化硅原料受热分解热质输运及其多孔结构演变、系统热输运的物理和数学模型,进而使用数值模拟方法研究加热器位置、加热器功率和辐射孔径对温度分布的影响及其规律,并优化热场结构。数值模拟结果显示,通过优化散热孔形状、保温棉的结构等设计参数,电阻加热式大尺寸晶体生长系统在晶锭厚度变化、多孔介质原料消耗的情况下均能达到较低的晶体横向温度梯度和较高的纵向温度梯度。     

A novel method of temperature control for a crystal growth puller

A facile method to control the contracting rate of the thermal expansible bars for pulling crystal is first suggested. The thermal expansible bars, set in a modified Dewar flask whose vacuum degree is controlled, are heated to designed temperature and then switch off the power to let it cool down at a desired rate, which depends largely on the changeable vacuum degree. This new approach is expected to completely eliminate the effects, which possibly reduces the smooth extent of thermal expansion, caused by the minor temperature fluctuations during crystal growth process and to realize the utmost smooth and slow pulling rate. It is expected to install this apparatus in optical floating zone furnace, instead of traditional motor, to grow peritectic crystal, such as crystal Bi‐2223, since for the peritectic reaction, in principle, the extremely slow growing rate is considerably essential.     

提拉法晶体生长数值模拟研究进展

数值模拟方法是了解晶体生长过程中各种物理现象和问题的重要手段,可以为晶体生长工艺参数的设定、温场设计等提供参考.本文介绍了最近几十年来数值模拟技术对提拉法生长晶体过程中物理问题的研究进展,同时对晶体生长过程中界面形状、液流、速度场、温度场、各种输运过程以及工艺条件和参数对晶体生长的影响等的数值模拟进行了介绍.     

A modified heater system for RF-Czochralski equipments

The temperature gradients in a Czochralski-type crystal growth equipment with induction heating can be advantageously influenced by additionally heating the growing crystal and the crucible bottom during the pulling procedure. An experimental solution is presented for both afterheater and bottom heater coupled to the same induction coil as the crucible.     

Automated pulling of large-diameter alkali halide scintillation single crystals from the melt

Principles of a new high-productivity automated method for pulling large-diameter alkali halide crystals are described. On the stage of radial growth, the melt geometry is varied continuously by its level elevation in the conical crucible due to feeding by the melted raw material controlled by a lifting electrocontact probe. The melt level is stable when the crystal is grown in height. An automated system to control the crystal diameter has been developed using time intervals between feeding operations as the controlling parameter. This system allows control over the crystal diameter to an accuracy better than 1% over the range from 400 to 450 mm at the pulling rate from 6 to 6.5 mm/h. The method is used to produce scintillation alkali halide single crystals on an industrial scale.     

Analysis of the diametral response of a czochralski crystal (I) the diameter-melt temperature relation

The paper is the first in a series which presents results on the small-signal diametral response of a Czochralski crystal grown in a resistance furnace to variations in the heating temperature and pulling rate. It is shown that the small-signal diameter variation is related to the small-signal bulk melt temperature and pulling rate variation via a second order linear differential equation.     

直拉单晶炉加热系统的优化设计与分析

降低单晶硅电池的生产成本,是提高光伏产业效益的关键。在等径拉晶过程中,采用分段加热可以减少加热器的输出功率,降低加热系统的能耗。本文在分析单晶硅拉晶过程中加热区域及能耗的基础上,提出细分加热器结构改进加热电路对单晶炉加热系统进行优化。实验设计了两段加热和三段加热两种模型(即方案1和方案2),并分别将其导入有限元仿真软件进行模拟实验。结果表明,两段加热对拉晶过程的影响较大,三段加热对拉晶过程的影响较小,后者更能保证拉晶过程的稳定进行。能耗计算发现,前者能耗降低为6.98％,而后者能耗降低达到了9.49％。因此,采用三段加热的优化设计更有利于降低光伏企业的生产成本。     

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。