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.     

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.     

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)     

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。     

Modulating dopant segregation in floating-zone silicon growth in magnetic fields using rotation

The feasibility of modulating dopant segregation using rotation for floating-zone silicon growth in axisymmetric magnetic fields is investigated through computer simulation. In the model, heat and mass transfer, fluid flow, magnetic fields, melt/solid interfaces, and the free surface are solved globally by a robust finte-volume/Newton's method. Different rotation modes, single- and counter-rotations, are applied to the growth under both axial and cusp magnetic fields. Under the magnetic fields, it is observed that dopant mixing is poor in the quiescent core region of the molten zone, and the weak convection there is responsible for the segregation. Under an axial magnetic field, moderate counter-rotation or crystal rotation improves dopant uniformity. However, excess counter-rotation or feed rotation alone results in more complicated flow structures, and thus induces larger radial segregation. For the cusp fields, rotation can enhance more easily the dopant mixing in the core melt and thus improve dopant uniformity.     

Floating zone growth and characterization of ruby single crystals

Large, high optical quality single crystals of ruby have been grown successfully by the floating zone method under air atmosphere. The size of the grown crystal is typically 60‐70 mm in length and 7‐8 mm in diameter. The obtained crystals were red and did not have any macroscopic defects such as cracks and inclusions. Grown crystals were characterized by powder X‐ray diffraction (XRD) methods, polarized optical microscopy, scanning electron microscopy (SEM). The absorption and fluorescence spectra were measured at room temperature and the dielectric constant measurements of ruby crystals were also presented. Defects occurring in single crystals of ruby during crystal growth by floating zone method are described, and their correlation with the growth parameters is discussed. The origin and control of these defects in grown crystals were studied and the optimum method was proposed. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Floating zone growth of high-quality SrTiO3 single crystals

Strontium titanate single crystals 15–20 mm in diameter and 40–80 mm in length were grown by a floating zone method with radiation heating. Additional crystal heating just below the molten zone by an in-growth annealing furnace was applied in order to lower the temperature gradients and to achieve slower cooling of the grown crystal. The crystal perfection was studied with X-ray topography and double-crystal diffractometry. The most perfect crystals were grown in [0 0 1] direction with single grain rocking curve widths of about 30″ and subgrain misorientations of 1′–3′ over 10×10 mm² areas of the boule cross-section for both (0 0 1)-, (1 1 0)- and (1 1 1)-oriented slices. Such high-quality crystal can be grown reproducibly with starting materials of 4N grade quality.     

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.     

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.     

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)     

Experimental Study of Interface Inversion of Tb3ScxAl5‐xO12 Single Crystals Grown by the Czochralski Method

Thermal conditions and rotation rate were examined experimentally for obtaining a flat interface growth of high melting‐point oxide (Tb₃Sc_xAl_5‐xO₁₂ ‐ TSAG) by the Czochralski method. The critical crystal rotation rate can be significantly reduced, of about twice at low and very low temperature gradients comparing to medium temperature gradients in the melt and surroundings of the crystal. The interface shape of TSAG crystals is not very sensitive on crystal rotation rate at small rotations and becomes very sensitive at higher rotations, when the interface transition takes place. The range of crystal rotation rates during the interface transition from convex to concave decreases with a decrease of temperature gradients. At low temperature gradients interface inversion crystals takes place in very narrow range of rotation rates, which does not allow one to growth such crystals with the flat interface. Even changing crystal rotation rate during the growth process in a suitable manner did not prevent the interface inversion from convex to concave and thus did not allow to obtain and maintain the flat interface.     

Anomalous effects in dopant distribution in Ge single crystals grown by the floating zone technique aboard spacecrafts

Specific features of Ga-dopant distribution in Ge single crystals grown by the floating zone technique from lightly and heavily Ga-doped Ge melts aboard the Photon spacecrafts have been studied. An anomalously strong concentration dependence of the effective coefficient of Ga distribution in Ge crystallized from melts with a well-developed free surface, which has no analogues under the terrestrial conditions, has been established for the first time. This anomaly is interpreted as a consequence of specific concentration-dependent processes of heat and mass transfer in the molten zone, and, first of all, the intensification of the concentration-capillary convection with an increase of the doping level. The quantitative characteristics of the crystallization parameters necessary for the construction and verification of hydrodynamic models are obtained experimentally. The effect of the observed phenomena on the electrophysical homogeneity of the grown single crystals and possible methods for the control of dopant distribution in such crystals are discussed.     

Resistivity distribution of silicon single crystals using codoping

Numerous studies including continuous Czochralski method and double crucible technique have been reported on the control of macroscopic axial resistivity distribution in bulk crystal growth. The simple codoping method for improving the productivity of silicon single-crystal growth by controlling axial specific resistivity distribution was proposed by Wang [Jpn. J. Appl. Phys. 43 (2004) 4079]. Wang [J. Crystal Growth 275 (2005) e73] demonstrated using numerical analysis and by experimental results that the axial specific resistivity distribution can be modified in melt growth of silicon crystals and relatively uniform profile is possible by B–P codoping method. In this work, the basic characteristic of 8 in silicon single crystal grown using codoping method is studied and whether proposed method has advantage for the silicon crystal growth is discussed.     

Growth and characterization of CdSe single crystals by modified vertical vapor phase method

Good quality, large single crystals of CdSe were grown by the modified growth method (i.e., vertical unseeded vapor phase growth with multi-step purification of the starting material in the same quartz ampoule without any manual transfer between the steps). Lower temperature gradients (8–9°C/cm) at the growth interface were used for the crystal growth. As-grown CdSe crystals was characterized by X-ray diffraction, scanning electron microscopy, energy dispersive analyzer of X-rays, high-resistance instrument measurement, and etch-pit observation. It is found that there are two cleavage faces of (1 0 0) and (1 1 0) orientations on the crystal, the resistivity is about 10⁸ Ω cm, and the density of etch pits is about 10^3–4/cm². The crystal was cut into wafers and was fabricated into detectors. The detectors were tested using an ²⁴¹Am radiation source. γ-ray spectra at 59.5 keV were obtained. The results demonstrated that the quality of the as-grown crystals was good. The crystals were useful for fabrication of room-temperature-operating nuclear radiation detectors. Therefore, the modified growth technique is a promising, convenient, new method for the growth of high-quality CdSe single crystals.     

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)     

半导体单晶生长过程中的位错研究

阐述了现有的半导体单晶位错模型,即临界切应力模型和粘塑性模型的基本理论及应用状况.分析了熔体法单晶生长过程中影响位错产生、增殖的各种因素,以及抑制位错增殖的措施.与熔体不润湿、与晶体热膨胀系数相近的坩埚材料,低位错密度的籽晶可有效地抑制生长晶体的位错密度;固液界面的形状及晶体内的温度梯度是降低位错密度的关键控制因素,而两因素又受到炉膛温度梯度、长晶速率、气体和熔体对流等晶体生长工艺参数的影响.最后,对熔体单晶生长过程的位错研究进行了展望.     

Static magnetic fields in semiconductor floating-zone growth

Heat and mass transfer in semiconductor float-zone processing are strongly influenced by convective flows in the zone, originating from sources such as buoyancy convection, thermocapillary (Marangoni) convection, differential rotation, or radio frequency heating. Because semiconductor melts are conducting, flows can be damped by the use of static magnetic fields to influence the interface shape and the segregation of dopants and impurities. An important objective is often the suppression of time-dependent flows and the ensuing dopant striations. In RF-heated Si-FZ-crystals, fields up to 0.5Tesla show some flattening of the interface curvature and a reduction of striation amplitudes. In radiation-heated (small-scale) Si-FZ crystals, fields of 0.2–0.5Tesla already suppress the majority of the dopant striations. The uniformity of the radial segregation is often compromised by using a magnetic field, due to the directional nature of the damping. Transverse fields lead to an asymmetric interface shape and thus require crystal rotation (resulting in rotational dopant striations) to achieve a radially symmetric interface, whereas axial fields introduce a coring effect. A complete suppression of dopant striations and a reduction of the coring to insignificant values, combined with a shift of the axial segregation profile towards a more diffusionlimited case, are possible with axial static fields in excess of 1Tesla. Strong static magnetic fields, however, can also lead to the appearance of thermoelectromagnetic convection, caused by the interaction of thermoelectric currents with the magnetic field.     

Optimization of control parameters of cadmium zinc telluride Bridgman single crystal growth

The temperature gradient within a furnace chamber and the crucible pull rate are the key control parameters for cadmium zinc telluride Bridgman single crystal growth. Their effects on the heat and mass transfer in front of the solid‐liquid interface and the solute segregation in the grown crystal were investigated with numerical modeling. With an increase of the temperature gradient, the convection intensity in the melt in front of the solid‐liquid interface increases almost proportionally to the temperature gradient. The interface concavity decreases rapidly at faster crucible pull rates, while it increases at slow pull rates. Moreover, the solute concentration gradient in the melt in front of the solid‐liquid interface decreases significantly, as does the radial solute segregation in the grown crystal. In general, a decrease of the pull rate leads to a strong decrease of the concavity of the solid‐liquid interface and of the radial solute segregation in the grown crystal, while the axial solute segregation in the grown crystal increases slightly. A combination of a low crucible pull rate with a medium temperature gradient within the furnace chamber will make the radial solute segregation of the grown crystal vanish. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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。     

Floating zone growth and high-temperature hardness of CrB2 single crystals

Single crystals of CrB₂ were prepared by the floating zone method. The crystal quality was improved by controlling the molten zone composition. The crystals preferentially grew normal to the plane which has the lowest Vickers hardness, similar to the other refractory boride crystals. On the growth plane, the direction of the a-plane, which longitudinally exists along the crystal rod, was controlled without the seed crystal by the position of the lower sintered rod. The anisotropy in the hardness was also consistent with morphology of the crystals prepared by the flux growth. In addition, the hardness measurement was useful for estimating the quality of refractory crystals in the floating zone growth.