Influence of furnace design on the thermal stress during directional solidification of multicrystalline silicon

Directional solidification is one of the most popular techniques for massive production of multicrystalline silicon (mc-Si). Dislocation is one of the major defects that significantly affect the photovoltaic performance. For the analysis and optimization of stress-induced dislocation, a computational tool has been developed to investigate thermal stress distribution during directional solidification process of multicrystalline silicon. Temperature distribution in the furnace, S/L interface shape and melt flow are simulated. Parametric studies are further conducted to evaluate the effect of furnace design on the interface shape and on the maximum von Mises stress in the growing ingot. To consider the effects of the crucible geometry qualitatively, three-dimensional modeling of the thermal stress is performed with or without the constraint of the crucible. The regions of dislocation multiplication are evaluated by comparing von Mises stress to critical resolved shear stress (CRSS). The results imply that the dislocation in the growing ingot can be reduced by optimizing the design of the directional solidification furnace.     

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。     

Finite element analysis of dislocation density during bulk single crystal growth (effect of doping atoms in InP single crystal)

A computer code for simulation of dislocation density in a bulk single crystal during liquid encapsulated Czochralski (LEC) or Czochralski (CZ) growth process. In this computer code, the shape of crystal–melt interface and the temperature in a crystal at an arbitrary time were determined by linear interpolation of the results that were discretely obtained by heat conduction analysis of a CZ single crystal growth system. A dislocation kinetics model called Haasen–Sumino model was used as a constitutive equation. In this model, creep strain rate is related to dislocation density, and this model extended to multiaxial stress state was incorporated into a finite element elastic creep analysis program for axisymmetric bodies. Dislocation density simulations were performed using this computer code for InP bulk single crystals with about 8″ in diameter. In the analysis, the effect of dopant atoms on the dislocation density was examined. In the case of a low doped InP single crystal, dislocations are distributed in the whole of the crystal. On the other hand, in the case of a highly doped InP single crystal, dislocations are localized at both the central and peripheral regions of the crystal.     

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。     

Nucleation of GaN on sapphire substrates at intermediate temperatures by Hydride Vapor Phase Epitaxy

A novel approach to deposit GaN layers directly on a sapphire substrate by Hydride Vapor Phase Epitaxy is presented. The two‐step deposition process includes the growth of GaN nucleation layers at intermediate temperatures in the range of 750 – 900 °C and subsequent high‐temperature overgrowth at about 1040 °C. Closed and non‐closed nucleation layers with a thickness of up to 2 μm were produced and characterized by scanning and transmission electron microscopy, micro‐Raman spectroscopy and X‐ray diffraction. A growth temperature of 780 °C is found to be optimal with respect to density and size distribution of nucleation islands. Raman measurements performed on the nucleation layers reveal nearly zero residual stress indicating effective stress relaxation on cooling down from growth temperature. The results of first overgrowth experiments demonstrate the possibility to grow 10 μm thick, crack‐free GaN layers of high crystalline quality on the nucleation layers. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal cracking analysis and three‐dimensional effects during Kyropoulos sapphire growth

Kyropoulos (Ky) method is the most suitable technique for the growth of high‐quality sapphire single crystal for substrate applications. Cracks are often observed in the grown ingot that significantly reduces industrial productivity. In the paper, cracking causes are analyzed by examining crystal shape, thermal stress and three‐dimensional effects during the stable growth of sapphire crystal. It is found that locally induced thermal stress around the shoulder of the crystal is the largest. However, thermal stress is not fully responsible for the cracks, since the predicted stress level is lower than a critical value regarding crystal cracking. Polycrystalline growth or/and other crystal defects must be another factor that degrades the critical value and makes the crystal more fragile. Simulation results further show that crystal shape has less effect on the thermal stress level, although experiments have shown that crack‐free crystals usually have smooth surfaces. The initial cracking position in the ingot predicted in simulation agrees well with experimental observation after considering crystal defects in a qualitative discussion. From the view of three‐dimensional simulation, the variation of heating condition during growth may result in high thermal stress locally that leads to the cracks at one side of the crystal. Additionally, three‐dimensionally unexpected temperature drop of the heater may be responsible for the sticking‐to‐crucible phenomenon at the shoulder region of the grown crystal.     

Characterization of a Czochralski grown silicon crystal doped with 1020 cm‐3 germanium

A dislocation‐free silicon single crystal doped with 10²⁰ cm^‐3 germanium (Ge) has been grown using the Czochralski (CZ) growth technique. The Ge concentration in the seed‐end and tang‐end of the crystal was 8×10¹⁹cm^‐3and 1.6×10²⁰ cm^‐3, respectively. The effective segregation coefficient of Ge, the distribution of flow pattern defects (FPDs) and the wafer warpage have been characterized. Both the effective segregation coefficient and the equilibrium segregation coefficient of Ge in silicon were evaluated. Then, the density of FPDs was traced from seed‐end to tang‐end of the ingot, a suppression of FPDs by Ge doping was shown. That is probably because the Ge atoms consume free vacancies and thus a higher density of smaller voids is formed. Furthermore, the mechanical strength of wafers has also been characterized by batch warpage analysis. The warpage in the seed‐end was larger than that in the tang‐end of the ingot, showing that the mechanical strength of wafers is enhanced by Ge doping. Such improvement is interpreted by an enhanced dislocation pinning effect associated with the enhanced nucleation of grown‐in oxygen precipitates in the Ge‐doped silicon wafers. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth of benzophenone single crystals from solution: A novel approach with 100% solute ‐ crystal conversion efficiency

An unidirectional 60mm diameter benzophenone single crystal was successfully grown by utilizing a novel crystal growth method at room temperature. <110> oriented single crystal ingots were grown out of xylene as solvent and by fixing a seed at the bottom of the ampoule. The obtained benzophenone ingots with the sizes of 10mm, 25mm and 60mm diameter evident that ease in increasing the diameter of the ingot. The orientation of the ingot and the crystalline quality were justified by X‐ray studies. TG and DTA evaluated the thermal properties of the grown crystal. The optical transmission study and the powder SHG measurement show the suitability of the ingot for nonlinear optical applications. The achieved solute‐crystal conversion efficiency of hundred percent shows vital advantage of this technique for cost effectiveness. The microbial growth as in the case of amino acid based growth solutions can be more effectively controlled in the present method since the freshly prepared growth solution can be constantly made available to the growing crystal. © 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

热屏优化对大直径单晶硅生长影响的数值模拟

通过对28英寸热场生长300 mm硅单晶过程中结晶速率、固液界面形状、晶体中热应力及晶体中氧含量的数值计算提出了在该热场条件下热屏的优化方案。数值计算结果表明:对热屏底端与晶体表面和熔体自由液面的距离以及热屏材料(优化前热屏使用单一石墨材料,优化后采用辐射率较高的内壁材料结合反射率较高的外壁材料组成复合式热屏)的优化可以减少主加热器对晶体的热辐射使得固液界面更加平坦,藉此增加结晶速率,减小晶体内热应力和熔体中氧含量。     

Stress relaxation behavior of soda-lime glass between the transformation and softening temperatures

The compressive stress relaxation modulus of a container glass composition was investigated over a wide range of strain, time, modulus, and temperature. It is shown that the glass behaves in a linear viscoelastic manner up to a 2% strain level, and that the relaxation modulus is a smooth function of time, with no pseudo-rubbery plateau apparent down to a modulus of 10⁸ dyn/cm². The data cover roughly five decades of modulus, five decades of time, and a temperature range of 150° C above the glass transition, T_g = 536°C. Within experimental error, the effect of temperature on the stress relaxation behavior is to simply shift the modulus-time curves along the time axis with no change in shape. Temperature dependent shift factor data are expressed in terms of the WLF relation, and are shown to be in good agreement with data found in the literature for other silicate compositions. Viscosity data derived from the generated stress relaxation data agree well with data obtained by more direct methods.     

Birefringence simulation of annealed ingot of calcium fluoride single crystal

We developed a method for simulating birefringence of an annealed ingot of calcium fluoride single crystal caused by the residual stress after annealing process. The method comprises the heat conduction analysis that provides the temperature distribution during the ingot annealing, the elastic thermal stress analysis using the assumption of the stress-free temperature that provides the residual stress after annealing, and the birefringence analysis of an annealed ingot induced by the residual stress. The finite element method was applied to the heat conduction analysis and the elastic thermal stress analysis. In these analyses, the temperature dependence of material properties and the crystal anisotropy were taken into account. In the birefringence analysis, the photoelastic effect gives the change of refractive indices, from which the optical path difference in the annealed ingot is calculated by the Jones calculus. The relation between the Jones calculus and the approximate method using the stress components averaged along the optical path is discussed theoretically. It is found that the result of the approximate method agrees very well with that of the Jones calculus in birefringence analysis. The distribution pattern of the optical path difference in the annealed ingot obtained from the present birefringence calculation methods agrees reasonably well with that of the experiment. The calculated values also agree reasonably well with those of the experiment, when a stress-free temperature is adequately selected.     

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.     

Influence of the crucible bottom shape on the heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth

For the seeding process of oxide Czochralski crystal growth, influence of the crucible bottom shape on the heat generation, temperature and flow field of the system and the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and seed crystal. At first, the volumetric distribution of heat inside the metal crucible and afterheater inducted by the RF‐coil was calculated. Using this heat generation in the crucible wall as a source the fluid flow and temperature field of the entire system as well as the seed‐melt interface shape were determined. We have considered two cases, flat and rounded crucible bottom shape. It was observed that using a crucible with a rounded bottom has several advantages such as: (i) The position of the heat generation maximum at the crucible side wall moves upwards, compared to the flat bottom shape. (ii) The location of the temperature maximum at the crucible side wall rises and as a result the temperature gradient along the melt surface increases. (iii) The streamlines of the melt flow are parallel to the crucible bottom and have a curved shape which is similar to the rounded bottom shape. These important features lead to increasing thermal convection in the system and influence the velocity field in the melt and gas domain which help preventing some serious growth problems such as spiral growth. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

降温速率对升级冶金硅定向凝固生长多晶硅少子寿命的影响

对经过前期提纯的冶金级硅料进行一次性定向凝固生长多晶硅铸锭,研究了长晶阶段降温速率对多晶硅少子寿命的影响。结果显示降温速率越低,获得多晶硅少子寿命越高,但降温速率低到一定程度时,少子寿命反而会降低。通过测试生长多晶硅硅锭曲率半径、晶体结构等数据,分析了该现象的产生原因。这将有助于升级冶金硅一次性定向凝固生长多晶硅铸锭的生产应用。     

Characteristics of the binary faceted eutectic: benzoic acid – salicylic acid system

The consistent symmetry relations computed from the heterogeneous nucleation data of the non‐ideal benzoic acid – salicylic acid eutectic system verifies the validity of nucleation theory. The kinetics of crystal growth from the molten state of the system follows the dislocation mechanism. Anomalous behaviour of both viscosity and activation energy for the eutectic melt confirms the essence of specific interactions animating molecular clusters rich in predominating eutectic phase. Micromorphology of the system obeys the Hunt‐Jackson model. The plot between a mechanical property and variable anisotropic growth velocity for the eutectic composite evidentially complies with the Weibull probability distribution curve. The curve is perused with two cut‐off points corresponding to a lower strength limit in the slow and fast growth regions and an upper strength limit in the moderate growth region. The latter aspect reveals the theoretical strength of the eutectic crystallites. The strength‐growth relationship explicated thereby is linear, optimum and linear respectively in the slow, moderate and fast growth regions of solidification. The moderate anisotropic growth (∼2.96 X 10^‐7m³s^‐1) is of greater interest by virtue of its attribute to unifying and organizing the crystallites parallel to each other in the growth direction. The eutectic composite material obtained by this process attains remarkable superiority in the mechanical properties over its isotropic growth in an ice bath (∼273 K), and its constituent phases. The co‐relation between excess thermodynamic functions indeed predicting the liquidus character and the microstructural parameters inevitably structuring the morphology is presented. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Reconstruction of Dislocation Potential Relief by Means of Self-Blocking Effect

The effect of dislocation self-blocking in intermetallic compounds with an anomalous temperature dependence of yield stress has been theoretically and experimentally analyzed. In essence, this effect is a dislocation self-immersion in a deep potential relief valley (without external stress). The possibility of reconstructing the relief shape (from one-valley to two-valley) is shown and the relief parameters are reported. The allowed and forbidden regions for self-blocking are revealed. The method for determining the ratio of the valley depths by measuring the self-blocking limiting angles between the dislocation segments is proposed. Transmission electron microscopy images of the dislocation structure can be used to this end. As an example, this ratio is estimated for a superpartial dislocation sliding in the cube plane in Ni₃Ge.     

4 inch低位错密度InP单晶的VGF生长及性质研究

采用高压垂直温度梯度凝固法(VGF)生长了非掺、掺硫和掺铁的4 inch直径(100)InP单晶,获得的单晶的平均位错密度均小于5000 cm-2.对4 inch InP晶片上进行多点X-射线双晶衍射测试, 其(004)X-射线双晶衍射峰的半峰宽约为30弧秒且分布均匀.与液封直拉法(LEC)相比, VGF-InP单晶生长过程的温度梯度很低,导致其孪晶出现的几率显著增加.然而大量晶体生长结果表明VGF-InP晶锭上出现孪晶后,通常晶体的生长方向仍为(100)方向,这确保从生长的4 inchVGF-InP(100)晶锭上仍能获得相当数量的2~4 inch(100)晶片.由于铁在InP中的分凝系数很小,掺Fe-InP单晶VGF生长过程中容易出现组份过冷,导致多晶生长.通过控制生长温度梯度及掺铁量,可获得较高的掺铁InP单晶成晶率.对VGF-InP单晶的电学性质、位错密度及位错的分布特点、晶体完整性等进行了研究.     

Macro-segregation, dynamics of interface and stresses in high pressure LEC grown crystals

High dislocation density and strong dopant inhomogeneities have been found in high pressure liquid-encapsulated Czochralski (HPLEC) grown crystals. The origin and underlying mechanisms of these defects are attributed to the complex nature of transport phenomena in the HPLEC system. Our integrated computer model (MASTRAPP) can simulate this process by calculating the flow and heat transfer in both the melt and the gas, and thermal-elastic stress in the crystal. In this work, this model has been further extended to investigate the development of thermal stress in the growing crystal and the redistribution of dopant in the melt. The results for InP growth show complex gas flow and heat transfer pattern in the system. Two large stress spots are predicted by the model, one at the edge of the crystal just above the encapsulant layer and the other in the top corner of the crystal. Although the stress always remains largest at the first location, its value decreases as the crystal grows, due to the enhanced cooling of the crystal. A curved crystal/melt interface is also found to introduce high thermal stresses in its vicinity, which may be dangerous because of a high temperature at the interface and thus a low strength of the crystal. The model also predicts both radial and longitudinal dopant segregation in the growing crystal, and shows that the dopant redistribution in the melt is caused by the complex flow pattern in the melt. This is the first time, that a strong radial dopant segregation has been predicted based on a comprehensive flow model for a HPLEC growth.     

Transformations in liquid state and microstructure development in immiscible Fe60Cu20P10Si5B5 alloy

A five-component Fe₆₀Cu₂₀P₁₀Si₅B₅ immiscible alloy was arc-melt and melt-spun from various temperatures. The microstructure and chemical composition of the ingot and melt-spun ribbons were analyzed using scanning electron microscope SEM/EDS. The melt-spun ribbon was investigated by transmission electron microscope (TEM). The melting range of the alloy was investigated by means of differential thermal analysis (DTA) and for reference, the temperature change during free cooling of the alloy was controlled by pyrometer in the melt spinning device. Processing with the slow cooling rate produced the fractal surface structures formed by the Fe-rich regions and Cu-rich regions. The arrangement of the regions was characteristic for the liquid immiscible alloys. It was found that the microstructures of the melt-spun ribbons depended on the ejection temperature. The lower ejection temperatures resulted in the formation of the lamellar structures separated into Fe-rich and Cu-rich regions. This was due to rapid cooling within the miscibility gap. Ejection at higher temperatures, above the miscibility gap led to the formation of a uniform amorphous/crystalline composite.     

Dynamic interaction of dislocations with impurity subsystem in crystalline materials

The entrainment of impurities by moving dislocations results in the accumulation of impurities in dislocation cores, which eventually significantly modifies the dynamic properties of dislocations. In the framework of the kink mechanism, the possible modes of motion are found self-consistently and the conditions for dislocation immobilization are determined. The dependence of the immobilization stress (the parameter that is most important for ??defect engineering?? in semiconductors) on the material parameters and experimental conditions is calculated.