Radiative Heat Transfer in a Resistance Heated Floating Zone Furnace: A Numerical Study with FIDAPTM

This paper presents a numerical study of radiative heat transfer in a floating zone (FZ) furnace which was performed by using the commercial finite element program FIDAP^TM. This resistance furnace should provide a temperature higher than the melting temperature of silicon (i.e. T_max ≈ 1500 °C) and a variable temperature gradient at the liquid/solid interface (≥ 25 K/cm). Due to the high working temperatures, heat radiation plays the dominant role for the heat transfer in the furnace. For this reason, the quality of view factors used in the wall‐to‐wall model was carefully inspected with energy‐balance checks. A numerical model with two control parameters is applied to study the influence of material and geometrical parameters on the temperature field. In addition, this model allows us to estimate the internal thermal conditions which were used as thermal boundary conditions for partial 3D simulations. The influences of an optical lens system on the radial symmetry of the temperature field were examined with these partial 3D simulations. Furthermore, we used the inverse modeling method to achieve maximum possible temperature gradients at the liquid/solid interface according to the limitation of maximum available power and the maximum stable height of a melt zone.     

Modeling analysis of liquid encapsulated Czochralski growth of GaAs and InP crystals

The results of three‐dimensional unsteady modeling of melt turbulent convection with prediction of the crystallization front geometry in liquid encapsulated Czochralski growth of InP bulk crystals and vapor pressure controlled Czochralski growth of GaAs bulk crystals are presented. The three‐dimensional model is combined with axisymmetric calculations of heat and mass transfer in the entire furnace. A comprehensive numerical analysis using various two‐dimensional steady and three‐dimensional unsteady models is also performed to explore their possibilities in predicting the melt/crystal interface geometry. The results obtained with different numerical approaches are analyzed and compared with available experimental data. It has been found that three‐dimensional unsteady consideration of heat and mass transfer in the crystallization zone provides a good reproduction of the solidification front geometry for both GaAs and InP crystal growth.     

移动加热器法生长碲锌镉晶体的组分输运与界面形貌研究

移动加热器法(THM)生长碲锌镉晶体时,界面稳定性对晶体生长的质量有很大影响。本文基于多物理场有限元仿真软件Comsol建立了THM生长碲锌镉晶体的数值模拟模型,讨论了Te边界层与组分过冷区之间的关系,对不同生长阶段的物理场、Te边界层与组分过冷区进行仿真研究,最后讨论了微重力对物理场分布的影响,并对比了微重力与正常重力下的生长界面形貌。模拟结果表明,Te边界层与组分过冷区的分布趋势是一致的,在不同生长阶段,流场中次生涡旋的位置会发生移动,从而导致生长界面的形貌随着生长的进行发生变化,同时微重力条件下形成的生长界面形貌最有利于单晶生长。因此,在晶体生长的中前期,对次生涡旋位置的控制和对组分过冷的削弱,是THM生长高质量晶体的有效方案。     

A novel way of modifying the thermal gradient in Vertical Bridgman‐Stockbarger Technique and studies on its effect on the growth of benzophenone single crystals

In order to grow benzophenone single crystal, an organic nonlinear optical material, a cost‐effective Vertical Bridgman‐Stockbarger system has been designed and fabricated by employing a two‐zone, transparent furnace made out of immiscible liquids. Transparent, optical quality benzophenone single crystals were successfully grown as a result of a suitable thermal gradient achieved by means of introducing an intermediate liquid in between the two immiscible liquids. The effect of change in the volume of the intermediate liquid thereby the thermal gradient on the growth parameters was analyzed. The quality of the grown single crystal was justified using X‐ray powder diffraction analysis, FTIR, TG‐DTA and optical transmission studies. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Movable partition designed for the seed‐assisted silicon ingot casting in directional solidification process

For the seed‐assisted casting process for silicon ingots, different partition blocks were designed in the directional solidification (DS) furnaces to preserve the seed crystals and optimize the thermal field in the hot‐zone. A transient global model was established to investigate the effects of different partition blocks during the solidification process. The simulation results showed that the partition blocks can significantly influence the temperature distributions and the melt flow fields. From the designed partition blocks, the movable partition block was more favorable for the seed‐assisted DS process. A suitable temperature gradient and a flat seed‐melt (s‐m) interface were obtained, which facilitated the preservation of seed crystals effectively, and an optimized crystal‐melt (c‐m) interface was achieved as well. One of the designs of the movable partition blocks was implemented in quasi‐mono crystalline silicon casting experiments and it has been confirmed that the designed movable partition block was helpful for the improvement of the single crystal area.     

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.     

On the Design of Double‐Ellipsoid Mirror Furnace and its Thermal Characteristics for Floating‐Zone Growth of SrxBa1‐xTiO3 Single Crystals

We have designed a double ellipsoid mirror furnace for floating‐zone crystal growth using lamps with rectangular filaments. Its thermal characteristics were studied using an alumina tube for several system configurations. A simple comparison with a commercial furnace that used cylinder lamps for the heating profile was also conducted. By adjusting lamp orientation and positions, one could modify heating profiles easily. In general, the thermal characteristics of the furnace were consistent with the model's prediction [J. Crystal Growth 173 (1997) 561]. The effects of growth chamber and heat pipe were further illustrated. Furthermore, a suitable system configuration leading to better heating uniformity and lower thermal gradients near the growth interface was found for the floating‐zone growth of Sr_xBa_1‐xTiO₃ single crystals.     

TEM analysis of the container effect of Au‐based catalyst droplets during vapour‐liquid‐solid growth of axial ZnTe/CdTe nanowires

Axial heterostructure nanowires (NWs) of ZnTe/CdTe were grown by vapour‐liquid‐solid growth realized in a molecular beam epitaxial chamber. By alternative supply of Zn or Cd and constant Te the heterostructure was generated. The liquid phase is provided by a Au‐based eutectic droplet which stays at the tip of the NW during the entire growth. For structural and chemical characterization by TEM the NWs were harvested from the substrate and transferred to a holey carbon film. The NWs exhibit an expansion of the diameter correlated with the interface region between ZnTe and CdTe. Idiomorphic growth of the CdTe is evident from electron diffraction experiments. The growth rate of CdTe appears to be smaller compared to that of ZnTe at the same temperature. Both, quantitative high‐resolution TEM and energy dispersive X‐ray spectroscopy line scans reveal a smeared ZnTe/CdTe interface along about 200 nm. The smearing is due to both, the liquid catalyst which buffers the supply of Cd instead of Zn at the liquid/solid interface and to the strain which is induced by the lattice mismatch. It forces the system to consume the remnant Zn for the NW growth in favour of Cd. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Melt growth and post‐grown annealing of semiinsulating (CdZn)Te by vertical gradient freeze method

We present results of development of CdZnTe semi‐insulating crystals prepared by Vertical Gradient Freeze method in a 4‐zone furnace. We applied the way of growth of the crystal from the top when the first crystallization seed is created on the surface of the melt. The typical height of the crystals is 5 cm. Resistivity and photoconductivity profiles measured along the growth axis by contactless method are compared and their mutual correlation is explained based on a model of relative shift of the Fermi level and the midgap level present in the material. The influence of the Fermi level on electron trapping and recombination is summarized. We present here results of a two‐step annealing method aimed at reduction of Te inclusions while keeping the resistivity high. We employed CdTe:Cl VGF grown samples to eliminate Te inclusions observed in as grown crystals by two‐step post grown annealing in Cd and Te atmosphere and present a model of the processes leading to high resistivity material after annealing.     

Optimisation of the VGF growth process by inverse modelling

Numerical and experimental results on the thermal optimisation of vertical gradient freeze crystal growth are presented. An inverse modelling approach is described aimed at solidification with a constant growth rate and planar solid–liquid interface. As a result of modelling an optimised growth process characterised by a modified ampoule configuration and thermal regime was established. For experimental confirmation Ga-doped germanium single crystals were grown with the optimised process. In good agreement with the numerical results, solidification with an almost constant growth rate was achieved with the interface deflection being significantly lower than in conventionally grown crystals.     

Solutal convection during growth of organic NLO crystals

Effect of solutal and thermal convection plays very important role when a large thermal gradient is applied during crystal growth. To address this problem, we have purified m.nitroaniline (m.NA) and m. dinitrobenzene (m.DNB) and studied crystal growth and effect of growth parameters on the optical quality. Crystals of pure and binary alloy of m.dinitrobenzene and m.nitroaniline were grown by vertical directional solidification method in a two zone transparent furnace. Effect of doping and temperature gradient on the solid-liquid interface morphology and quality of crystal was determined by studying the bulk transparency and nonlinearity.     

Analysis of the dopant segregation effects at the floating zone growth of large silicon crystals

A computer simulation is carried out to study the dopant concentration fields in the molten zone and in the growing crystal for the floating zone (FZ) growth of large (> 100 mm) Si crystals with the needle-eye technique and with feed/crystal rotation. The mathematical model developed in the previous work is used to calculate the shape of the molten zone and the velocity field in the melt. The influence of melt convection on the dopant concentration field is considered. The significance of the rotation scheme of the feed rod and crystal on the dopant distribution is investigated. The calculated dopant concentration directly at the growth interface is used to determine the normalized lateral resistivity distribution in the single crystal. The calculated resistivity distributions are compared with lateral spreading resistivity measurements in the single crystal.     

System of Mathematical Models for the Analysis of Industrial FZ-Si-Crystal Growth Processes

A system of coupled mathematical models and the corresponding program package is developed to study the interface shape, heat transfer, thermal stresses, fluid flow as well as the transient dopant segregation in the floating zone (FZ) growth of large silicon crystals (diameter more than 100mm) grown by the needle-eye technique. The floating zone method with needle-eye technique is used to produce high-purity silicon single crystals for semiconductor devices to overcome the problems resulting from the use of crucibles. The high frequency electric current induced by the pancake induction coil, the temperature gradients and the feed/crystal rotation determine the free surface shape of the molten zone and cause the fluid motion. The quality of the growing crystal depends on the shape of the growth interface, the temperature gradients and corresponding thermal stresses in the single crystal, the fluid flow, and especially on the dopant segregation near the growth interface. From the calculated transient dopant concentration fields in the molten zone the macroscopic and microscopic resistivity distribution in the single crystal is derived. The numerical results of the resistivity distributions are compared with the resistivity distributions measured in the grown crystal.     

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。     

Growth of cadmium zinc telluride by liquid phase electroepitaxy

This study was undertaken to examine the feasibility of growing CdZnTe by liquid phase electroepitaxy. Based on our successful LPEE system of GaInAs, a new crucible to grow CdZnTe was developed. The development presented numerous difficulties. The physical properties of CdZnTe make this material very difficult to grow. All components of the system were investigated. Electromigration of the solute across the solution carries species towards the growth interface. In liquid Cd‐Zn‐Te, the CdTe and ZnTe species remain associated, contrary to the GaInAs system. Experiments showed that LPEE growth of CdZnTe is possible and the electromigration mechanism functions well in the CdZnTe solution. Despite this, other problems remained with the new LPEE system. The preparation of the solution proved difficult without pressurizing the LPEE crucible. Control of the reaction required the use of pre‐compounded CdTe and ZnTe. Proper control of the solution saturation is imperative to ensure minimal dissolution of the seed prior to growth initiation and a reasonable growth rate during growth. The solution remained an issue during the duration of growth due to the high vapor pressures of the constituents. Tellurium evaporation during growth could lower solution volume until electrical contact across the solution is broken. Careful preparation of appropriate solution volume was imperative for successful growth. In LPEE, a uniform electric current passage across the growth interface is necessary for uniform and stable growth interface. This requires the design of a uniform contact zone between the bottom graphite electrode and the seed crystal. The contact zone issue was not adequately resolved in this study. However, a number of successful growth runs were achieved despite the electrical contact problems. Results show that the LPEE of growth CdZnTe is feasible. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A numerical study of convection during THM growth of CdTe with ACRT

The accelerated crucible rotation technique (ACRT) is an effective way to increase mixing in the solution zone in travelling heater method (THM) growth and to obtain higher growth rate limits. In this paper, detailed numerical calculations of the combined thermally driven and forced convection during THM growth of CdTe from a Te-rich solution are presented. The effects of various parameters of ACRT on the mixing are considered and a possible optimum cycle for high growth rate limits is given.     

Synthesis of TeO2 nanowires via a facile thermal oxidation method

TeO₂ is of considerable interest for piezoelectric, ther‐moelectric, acousto‐optic and nonlinear optical applica‐tions. In this work, we report a facile synthetic tech‐nique for obtaining high‐quality TeO₂ nanowires (NWs) via a thermal oxidation of Te NWs in a large quantity. The synthetic conditions were systematically optimized to transform from Te NWs to TeO₂ NWs using a furnace oven. The optimal conditions for the formation of high‐quality TeO₂ NWs were found to be 300 °C for 1 hr in an oven furnace. The NWs were characterized using X‐ray diffraction, field‐emission scanning electron mi‐croscopy, high resolution transmission electron micros‐copy and Raman scattering. Diffuse reflectance spec‐trum was also used to determine the band gap (3.78 eV) of synthesized TeO₂ NWs.     

Singular ring‐shaped distribution of Nd in NdxY1‐xVO4 crystals grown by floating zone method

A singular ring‐shaped distribution of high Nd concentration was observed in Nd‐doped YVO₄ single crystals grown by the floating zone (FZ) method. The ring‐shaped distribution appeared 500‐1000 μm inside from the rim of the crystals. Results of growth experiments by the anisotropic heating floating zone (AHFZ) method showed that the Nd concentration was high at the high‐temperature side of the grown crystals. We found a small concave projection at a part of the convex solid‐liquid interface by quenching the molten zone during growth. The cause of the singular ring‐shaped distribution of the Nd‐rich area was discussed in relation with the concave projection at the interface and the convection in the molten zone. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of a static magnetic field on silicon transport in liquid phase diffusion growth of SiGe

Liquid phase diffusion experiments have been performed without and with the application of a 0.4 T static magnetic field using a three‐zone DC furnace system. SiGe crystals were grown from the germanium side for a period of 72 h. Experiments have led to the growth of single crystal sections varying from 0 to 10 mm thicknesses. Examination of the processed samples (single and polycrystalline sections) has shown that the effect of the applied static magnetic field is significant. It alters the temperature distribution in the system, reduces mass transport in the melt, and leads to a much lower growth rate. The initial curved growth interface was slightly flattened under the effect of magnetic field. There were no growth striations in the single crystal sections of the samples. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)