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.     

Three-dimensional simulation of floating-zone crystal growth of oxide crystals

The floating-zone (FZ) method is a popular technique for the growth of high-temperature oxide crystals. However, the growth usually requires skillful control of the zone stability, which is strongly coupled with heat flow, interfaces, and the grown crystal morphology. In this report, we present a three-dimensional self-consistent simulation of floating-zone oxide growth in a mirror furnace by taking these factors into account simultaneously. This model is based on an efficient finite volume method with multigrid acceleration and interface tracking. The steady growth of a YAG crystal in a double-ellipsoid mirror furnace is taken as an example to illustrate the intricate coupling of convection, interfaces, meniscus, and the grown crystal shape.     

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.     

Dislocations and dislocation reduction in space grown GaSb

The behaviour of dislocations in GaSb crystals grown in space both from a stoichiometric melt (floating zone method, FZ) and a Bi solution (floating solution zone, FSZ) respectively, is studied. Predominantly straight 60° dislocations with Burgers vectors of the type b = a/2 <110> in (111) glide planes are identified. In the 20 mm long FZ single crystal the linear growing out of the dislocations is observed which reduces the dislocation density in the centre of the crystal to values below 300 cm^–2. The Bi incorporation in the FSZ crystal results in a misfit between seed and grown crystal and in a network of misfit dislocations at the interface. Thermocapillary convection during growth as well as the surface tension may be the reasons for the presence of curved dislocations and the higher dislocation density within a 1 – 2 mm border region at the edges of both of the crystals. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth and magneto‐optical characteristics of cerium‐doped terbium gallium garnet by the floating zone method

Cerium‐doped terbium gallium garnet single crystal having a large Verdet constant was grown by floating zone (FZ) method, which was suitable for the use in optical devices. The lattice parameters and the X‐ray rocking curve measurement of the crystal was determined by X‐ray diffraction analysis. The Verdet constant of the crystal (B = 0.55 T) at the wavelength of 632.8 nm was −165.8 rad m⁻¹ T⁻¹ at room temperature, 23.7% larger than that of pure TGG (−134.0 rad m⁻¹ T⁻¹). The performance of the high optical quality and excellent magneto‐optical properties of the crystal shows the great potential of using this new method to meet the increasing demand of VI‐NIR Faraday rotators.     

Magnetic anisotropy of large floating‐zone‐grown single‐crystals of SrRuO3

SrRuO₃ is a highly interesting material due to its anomalous‐metal properties related with ferromagnetism and its relevance as conductive perovskite layer or substrate in heterostructure devices. We have used optical floating zone technique in an infrared image furnace to grow large single crystals of SrRuO₃ with volumes attaining several hundred mm³. Crystals obtained for optimized growth parameters exhibit a high ferromagnetic Curie temperature of 165 K and a low‐temperature magnetization of 1.6 μ_B at a magnetic field of 6 T. The high quality of the crystals is further documented by large residual resistance ratios of 75 and by crystal structure and chemical analyzes. With these crystals the magnetic anisotropy could be determined.     

Growth and dielectric properties of Ta2O5 single crystal by the floating zone method

Large Ta₂O₅ single crystal with high‐dielectric permittivity was successfully grown by floating zone (FZ) method under air atmosphere. The grown crystal that has been obtained was typically about 8 mm in diameter and 90 mm in length. The crystal growth parameters were optimized. The crystal symmetry, characterized by means of X‐ray diffraction (XRD), was found to be tetragonal. The relative permittivity and loss tangent along growth and [001] direction were measured in the temperature range between ‐200 °C and 200 °C, which showed a strong dielectric anisotropy. At a frequency of 1 MHz and 20 °C, the dielectric permittivity along the growth direction and [001] direction are 81.17 and 25.04 respectively. The stabilization of high‐temperature phase can explain the dielectric enhancement.     

Characterization of large‐sized Nd:YAG single crystals grown by horizontal directional solidification

Nd³⁺‐doped Y₃Al₅O₁₂ single crystals have been grown by the horizontal directional solidification (HDS) method in different thermal zone. The Grashof (G_r), Prandtl (P_r), Marangoni (M_a) and Rayleigh (R_a) numbers of melt in HDS system have been discussed for our experimental system to understand the mechanism of melt flow patterns and concentration gradient of dopant. The concentration gradient of Nd³⁺ ions was explained with melt flow processes during crystal growth in different thermal zone, and results indicated that high growth temperature will be helpful for uniformity of dopant in HDS‐grown single crystal. The main microscopic growth defects such as bubbles and irregular inclusions in HDS‐grown Nd:YAG crystals were observed, and the causes were discussed as well. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

红外LED用GaAs单晶的垂直梯度凝固制备研究

GaAs单晶是当前光电子器件的主要衬底材料之一,在红外LED中有着重要应用。但杂质浓度高、迁移率低等缺点会严重影响红外LED器件性能。为生产出低杂质浓度、高迁移率、载流子分布均匀、高利用率的红外LED用掺硅垂直梯度凝固(VGF)法GaAs单晶,本文研究了热场分布、合成舟和炉膛材质、工艺参数对单晶的成晶质量、杂质浓度、迁移率、载流子分布的影响。利用CGSim软件对单晶生长热场系统进行数值模拟研究,温区一至温区六长度比例为8∶12∶9∶5∶5∶7时,恒温区达到最长,位错密度达到1 000 cm^-2以下,成晶率达到85%。采用打毛石英合成舟进行GaAs合成,用莫来石炉膛替代石英炉膛,可以获得迁移率整体高于3 000 cm²/(V·s)的GaAs单晶,满足红外LED使用要求。对单晶生长工艺参数展开研究,采用提高头部生长速度、降低尾部生长速度的方式提高单晶轴向载流子浓度均匀性,头尾部载流子浓度差降低33%,尾部迁移率从2 900 cm²/(V·s)提高到3 560 cm²/(V·s)。单晶有效利用长度提高33...     

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)     

The Precipitation of Barium Chromate with Slow Development of Supersaturation. Kinetics of the Crystal Growth

Slow barium chromate precipitation was studied in well-stirred solutions — final concentration 0.002 mole 1⁻¹ — at 20°C at mixing rates varying from 0.2 to 2 · 10⁶ mole 1⁻¹ sec⁻¹; the kinetics of the crystal growth process were studied by chemical analysis and by optical microscopy. The crystal growth started after induction periods; regular growth then took place on the nuclei formed during these periods. For the main growth, up to about seventy percent precipitation time, growth rates at any time depended on the (residual excess solute concentrations in solution)². Immediately after the induction periods, crystal lengths varied with growth time according to the relation, for the main growth, crystal lengths varied with growth time according to a more complex relation, where k_l is the rate constant for surface growth, R_c is the rate of development of metal salt concentration and K is a constant that depends on the number of precipitate crystals. After some growth time τ = τ^*, when l_τ = l_τ*, all fresh solute added to the solution was utilised immediately and was deposited onto the growing crystals; then, for the final thirty percent precipitation, crystal lengths varied with growth time according to the relation, .     

Investigations for the improvement of the radial doping homogeneity of dislocation-free floating zone silicon crystals

In order to improve the doping inhomogeneities of dislocation free FZ Silicon crystals with diameters ≧ 75 mm investigations were carried out to influence the shape and curvature of the crystallization interface during the crucible-free floating zone crystal growth process. In this works shapes and geometries of the applied melting inductors and the relative positions of these inductors to the seed axis were examined concerning the values of radial macroscopic and microscopic doping inhomogeneities in dependence on other growth parameters, for instance crystal rotation rate. The application of eccentric inductor-seed positions effects a decreasing “bending value” of the crystallization interface, that means an improvement of the macroscopic radial doping inhomogeneity with crystal rotation rate in the range between 4 and 8 min⁻¹.     

Growth of ZnO single crystals by an induced nucleation from a high temperature solution of the ZnO‐PbF2 system

To grow ZnO single crystals from a high temperature solution of the ZnO‐PbF₂ system, a gas cooling system was assembled at the bottom of the crucible to induce nucleation in the initial growth stage. The growth experiments were carried out in a homemade vertical Bridgman furnace and Pt crucible of 28 mm in diameter was used. The furnace temperature was set to 1100°C and the flow rate of the oxygen gas was optimized as 3.0 l/min. ZnO crystal up to 5∼8mm in the thickness was obtained with the lowering rate of 0.3 mm/h. XRD patterns showed that the as‐grown crystal was pure ZnO Wurtzite phase. The impurity ions were analyzed by the glow discharge mass spectroscopy (GDMS) as 390.0 ppm and 40.0 ppm for Pb²⁺ and F^‐, respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

冷心放肩微量提拉法大尺寸蓝宝石单晶生长过程的模拟分析

利用数值模拟方法计算了冷心放肩微量提拉法(SAPMAC)蓝宝石晶体生长过程.结合晶体直径变化、裂纹出现位置与延续方向、晶体透明性等实验现象,通过与提拉法、温梯法、坩埚移动法等相对比,分析了冷心放肩微量提拉法晶体生长各阶段的工艺特点,并根据模拟计算结果对晶体生长系统和晶体生长控制工艺进行了改进.分别利用增大热交换器的散热参数、降低加热温度、改进降温曲线、调节外加轴向和径向温度梯度的方式来实现对晶体生长的引晶、放肩、等径和收尾控制.通过实验比较证明了改进后的晶体生长系统和晶体生长控制工艺能够生长出性能较好的大尺寸蓝宝石晶体.     

Optimierung von Kristallisationsparametern beim Zonenschmelzen aus Temperatur-Feld-Berechnungen

The distribution of temperature in the crystal during the growth process decides the crystal perfection and first of all depends on the external conditions: on the nature and geometry of heater arrangement and on the enviroment of the crystal („atmosphere”︁, crucible, pull-respectivly hold rods a.s.o.). – A mathematical model is presented by which it's possible to calculate the distribution of temperature in the crystal on the basis of these external conditions. The efficiency of the theoretical model is discussed and evaluated by means of the special arrangement of vertical zone levelling. Important crystallization parameters are determined by use of the mathematical model for the growth of monocrystals of the Bi_1−xSb_x mixed crystal system through zone levelling.     

Photoacoustic studies on the thermal properties of the NLO compound: L‐alaninium maleate

Studies on thermal and optical properties are very essential for a nonlinear optical material. Photoacoustics (PA) is a recently developed non‐destructive testing (NDT) tool for studying such properties. L‐Alaninium maleate (C₃H₈NO₂⁺·C₄H₃O₄^‐), an organic non‐linear optical (NLO) material was synthesized using submerged seed solution method and was characterized by single crystal X‐ray diffraction (XRD) and density. PA technique was used to determine the thermal parameters of LAM crystals. Moreover, possible phase transition analysis was conducted to ascertain the thermal stability. Scanning electron microscopic (SEM) studies were also carried out and crystal‐packing features discussed. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Crystallization of vitamin C in a continuous DT MSMPR crystallizer – Size independent growth kinetic model approach

The experimental results concerning continuous mass crystallization process in L(+)‐ascorbic acid – water system are presented and discussed. Influence of L(+)‐ascorbic acid concentration in a feeding solution and mean residence time of suspension in laboratory DT MSMPR crystallizer on product crystal size distribution as well as nucleation and growth kinetics were determined. Kinetic parameter values were evaluated on the basis of size–independent growth (SIG) kinetic model (McCabe's ΔL law). It was observed, that within the examined range of crystallizer productivity (120–1600 kg LAA crystals m^–3h^–1) crystal product population of mean size L_m from 0.2 to 0.3 mm and CV from 66.6 to 49% is withdrawn. Linear growth rate values present decreasing trend (from ca. 7 · 10^–8 to ca. 6 · 10^–8 m s^–1) with the productivity increase (assuming constant mean residence time of suspension τ = 900 s). Occurrence of secondary nucleation within the circulated and mixed suspension, resulting from crystal attrition and breakage, was observed. The parameter values in design equation connecting linear growth rate and suspension density with nucleation rate were determined. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)