Large eddy simulation of Marangoni convection in Czochralski crystal growth

Large eddy simulation model is used to simulate the fluid flow and heat transfer in an industrial Czochralski crystal growth system. The influence of Marangoni convection on the growth process is discussed. The simulation results agree well with experiment, which indicates that large eddy simulation is capable of capturing the temperature fluctuations in the melt. As the Marangoni number increases, the radial velocity along the free surface is strengthened, which makes the flow pattern shift from circumferential to spiral. At the same time, the surface tension reinforces the natural convection and forces the isotherms to curve downwards. It can also be seen from the simulation that a secondary vortex and the Ekman layer are generated. All these physical phenomena induced by Marangoni convection have great impacts on the shape of the growth interface and thus the quality of the crystal. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional numerical study of the effect of large Grashof number on HEM crystal growth

Heat transfer and fluid flow in HEM crystal growth of silicon in cylindrical cavity is studied numerically. The walls of the crucible are heated to a fixed temperature. The exchanger that causes and induces natural convection is seated at the middle‐bottom of the crucible. The finite‐volume method is employed to solve the governing equations with proper boundary conditions. The effects of transport mechanism on the temperature distribution, melt flow, pressure and stream function are presented. We focus our work on the pressure field which has not yet been studied in HEM crucible. Also, we extend our work on a wide range Grashof number and for large numbers until 10¹² not yet studied in HEM furnace. It is found that the onset of flow fluctuations appears at Gr = 10¹⁰. Uniform temperature is observed in the entire melt at high Grashof number with development of a thermal boundary layer close to the exchanger. The thermal boundary layer thickness is calculated for strong buoyancy regime. Besides, for very high Gr number, buoyancy has less effect on temperature and then on melt‐crystal interface shape. During enlarging Gr, pressure evolution is related to temperature variation more than flow pattern.     

紊流模型模拟分析旋转对提拉大直径单晶硅的影响

本文采用紊流模型对提拉大直径单晶硅时,对晶体旋转、坩埚旋转及二者共同作用三种情况下,熔体内的流线、等温线、氧的浓度分布、紊流粘性系数、紊动能等作了数值模拟,发现晶体的旋转能提高氧的径向均匀性,紊流粘性系数和紊动能随着坩埚转速的提高先增加后下降.晶体坩埚同时旋转时并不能有效降低紊流粘性系数,但能使子午面上的流动受到抑制,等温线更为平坦,有利于晶体生长.     

Numerical investigation of magnetic field effect on pressure in cylindrical and hemispherical silicon CZ crystal growth

The effect of axial magnetic field of different intensities on pressure in silicon Czochralski crystal growth is investigated in cylindrical and hemispherical geometries with rotating crystal and crucible and thermocapillary convection. As one important thermodynamic variable, the pressure is found to be more sensitive than temperature to magnetic field with strong dependence upon the vorticity field. The pressure at the triple point is proposed as a convenient parameter to control the homogeneity of the grown crystal. With a gradual increase of the magnetic field intensity the convection effect can be reduced without thermal fluctuations in the silicon melt. An evaluation of the magnetic interaction parameter critical value corresponding to flow, pressure and temperature homogenization leads to the important result that a relatively low axial magnetic field is required for the spherical system comparatively to the cylindrical one.     

ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional simulation of melt flow in Czochralski crystal growth with steady magnetic fields

Three-dimensional transient numerical simulations were carried out to investigate the melt convection and temperature fluctuations within an industrial Czochralski crucible. To study the magnetic damping effects on the growth process, a vertical magnetic field and a cusp magnetic field were considered. Due to our special interest in the melt convection, only local simulation was conducted. The melt flow was calculated by large-eddy simulation (LES) and the magnetic forces were implemented in the CFD code by solving a set of user-defined scalar (UDS) functions. In the absence of magnetic fields, the numerical results show that the buoyant plumes rise from the crucible to the free surface and the crystal–melt interface, which indicates that the heat and mass transfer phenomena in Si melt can be characterized by the turbulent flow patterns. In the presence of a vertical magnetic field, the temperature fluctuations in the melt are significantly damped, with the buoyant plumes forming regular cylindrical geometries. The cusp magnetic field could also markedly reduce the temperature fluctuations, but the buoyant plumes would break into smaller vortical structures, which gather around the crystal as well as in the center of the crucible bottom. With the present crucible configurations, it is found that the vertical magnetic field with an intensity of 128 mT can damp the temperature fluctuations more effectively than the 40 mT cusp magnetic field, especially in the region near the growing crystal.     

Solutocapillary convection in germanium‐silicon melts

Surface tension gradients in free crystal growth melts give rise to convective flow. If these gradients are due to thermal gradients, the well known thermocapillary (Marangoni) convection ensues. Concentration gradients due to segregation at the interface during growth can lead to additional solutocapillary convection. A system with large solutocapillary convection is Ge‐Si due to the pronounced segregation and the strong difference in surface tension; solutal buoyancy convection is also present due to the large density difference between Ge and Si. Solutocapillary convection will oppose thermocapillary convection in the Ge‐Si system since Si, having the higher surface tension, is preferentially incorporated into the crystal. A set of experiments directly proving and partially quantifying the effect has been conducted under microgravity during a parabolic flight campaign by recrystallizing Ge‐Si mixtures of different compositions, between 3% and 9% Si, in a crucible with tracers to visualize the movement. Solutocapillary flow with initial flow rates in excess of 5.5 cm/s at the onset of crystallization was measured. A slight dependence of the flow velocity on the initial Si content has been found. Experiments on the ground showed the same effect but with overall smaller speeds; this difference can be explained by the additional action of solutal buoyancy convection. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rotating magnetic fields: Fluid flow and crystal growth applications

Rotating or alternating magnetic fields are widely used in the industrial steel casting process or in metallurgical manufacturing. For the growth of single crystals, these techniques attracted a rapidly increasing attention within the last years: a well defined melt flow leads to a more homogeneous temperature and concentration distribution in the melt and consequently improves the growth process. Rotating magnetic fields (RMF) might be used instead of crucible and/or crystal rotation avoiding mechanically induced disturbances or might be added to conventional rotation mechanisms to gain a further flow control parameter. Compared to static magnetic fields, rotating ones are distinguished by a much lower energy consumption and technical effort. Furthermore, there are no reports on detrimental effects such as the generation of thermoelectromagnetic convection or coring effects in the grown crystals. One advantage of rotating magnetic fields is the possibility to apply them even to melts with a rather low electrical conductivity like e.g. aqueous solutions. High flow velocities are already generated with moderate fields. Therefore the field strength has to be adjusted with care because otherwise undesirable Taylor vortices might be induced. In the last years, the potential of rotating magnetic fields for crystal growth processes was demonstrated for model arrangements using e.g. gallium or mercury as a test liquid as well as for a variety of growth techniques like Float Zone, Czochralski, Bridgman, or Travelling Heater Methods: Fluctuations of the heat transport due to time-dependent natural convection have could be reduced by more than an order of magnitude or the mass transport could be improved with respect to the a better radial symmetry and/or a more homogeneous microscopic segregation.     

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)     

Numerical simulation of thermal and mass transport during Czochralski crystal growth of sapphire

The thermal and flow transport in an inductively heated Czochralski crystal growth furnace during a crystal growth process is investigated numerically. The temperature and flow fields inside the furnace, coupled with the heat generation in the iridium crucible induced by the electromagnetic field generated by the RF coil, are computed. The results indicate that for an RF coil fixed in position during the growth process, although the maximum value of the magnetic, temperature and velocity fields decrease, the convexity of the crystal‐melt interface increases for longer crystal growth lengths. The convexity of the crystal‐melt interface and the power consumption can be reduced by adjusting the relative position between the crucible and the induction coil during growth. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Marangoni Convective Effect during Crystal Growth in Space

GaSb:Te and GaInSb samples have been solidified under microgravity conditions during the D2 Spacelab mission. Experimental design and parameters are described. Analysis of the thermal data taken during the flight, associated to numerical simulations of heat transfer in the experiment, with the help of FIDAP, gave the experimental conditions (thermal gradients and growth rate). Quantitative chemical analyses of the samples show a chemical segregation characteristic of strong mixing in the melt during crystal growth. Silica crucibles with an internal screw thread groove on the inner wall were used in order to get dewetting of samples from the crucible. It was therefore supposed that Marangoni convection on the free surface associated to the groove might have been the source of convection. This hypothesis has been studied by numerical simulation using FIDAP and the velocity field obtained is in agreement with a strong perturbation of the solutal boundary layer ahead the solid-liquid interface. This can explain the observed chemical segregation.     

Cover Picture: Cryst. Res. Technol. 1/2011

The cover picture shows an isosurface of the difference between instantaneous and averaged temperature, colored by geometric height using a large eddy simulation of Marangoni convection in Czochralski crystal growth. (see pages 14–22) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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.     

数值模拟自然对流对直拉单晶硅的影响

在直拉单晶硅生长的过程中,自然对流对晶体界面的形状、温度场及应力分布影响很大。本文采用二维模型对熔体内自然对流对单晶硅的影响作了数值模拟,在低雷诺数时采用层流模型,高雷诺数时采用紊流模型,Gr的变化范围从3×106到3×1010,这样涵盖了从小尺寸到大尺寸的直拉单晶硅生长系统。数值结果表明熔体的流动状态不仅与熔体的Gr有关,还与熔体高度和坩埚半径的比值密切相关。当Gr>108时,熔体内确实存在紊流现象,层流模型不再适合,随着Gr的增大,紊流现象加剧,轴心处的等温线变得更为陡峭,不利于晶体生长。     

A modified zone growth method for an InGaAs single crystal

We have been developing a zone growth method for an In_xGa_1−xAs single crystal with a uniform InAs composition, using an InGaAs source, InGaAs melt and InGaAs seed charged in a crucible. This time, we modified the zone growth method to increase the length of an InGaAs zone crystal. A gap created between the wall around the InGaAs source and the inner wall of the crucible effectively prevents the interruption in normal zone growth because it changes the directions of heat current in the source. In addition, we found that it is very important for single crystal growth that no rotation of the crucible takes place during zone growth, because the degree of mixing caused by melt convection is reduced. The zone growth region of the obtained InGaAs crystal is almost exclusively of single-crystal-type, and it is about 26 mm long, which is 1.5 times the region length of the zone single crystal reported previously. We believe that a longer growth period could have further increased the length of our zone crystal, because some of the source remained. The InAs composition (x) of the zone crystal is greater than 0.3, and the crystal diameter is 15 mm.     

Gas bubbles in shaped sapphire

Shaped sapphire single crystals almost always contain a typical defect: small bubbles also known as “micro-voids”. The goal of this paper is to review the existing literature and give a survey of our recent work on this specific defect. As a conclusion to our review we propose a mechanism for bubble formation and its occurrence and distribution in shaped sapphire.The bubbles contain CO which originates as a result of complex reactions between the molten alumina, Mo crucible and graphite pieces. The CO dissolves in the molten alumina and is probably present as a saturated solution whatever the growth conditions. Then the dissolved gas is rejected at the solid–liquid interface and bubble nucleation occurs where the concentration of CO is highest. Therefore, the location of the bubbles in the crystal is governed by the hydrodynamics in the meniscus, which include Marangoni convection. The bubble is finally incorporated in the crystal when it reaches a critical size which depends only on the growth rate.When a central capillary channel is used, the bubbles are located in a layer close to the surface of the crystal from where they can be easily removed by polishing. Also, all the literature agrees on the fact that interface destabilization at high velocity results in the presence of bubbles throughout the entire crystal and should be avoided.     

Numerical modelling of heat transfer in GaSb Czochralski crystal growth (CZ and LEC)

By the hand of a system-oriented steady-state model of the GaSb crystal growth (CZ and LEC) the crystal-melt interface, the heat losses due to cooling, and the required crucible temperatures are calculated as a response to the boundary conditions for temperature and heat flows, and to the chosen geometry. Of special interest is a phantom of an after-heater influencing the cooling of the crystal.     

Melt stirring effect of a weak magnetic field on crystal growth

Melt stirring effect of a weak magnetic field for the natural convection of liquid metal in an electrically adiabatic cubic enclosure heated from one vertical wall and cooled from an opposing wall was studied by a fully transient three-dimensional numerical analyses and the reasoning for melt stirring effect was clarified from the numerical results. Similar techniques were applied for the melt convection in a cylindrical Czochralski crystal growing crucible with an application of a vertical magnetic field. In a static crucible, central fluid column rotated in a magnetic field and in a rotating crucible, central fluid column did not rotate in a magnetic field. These peculiar characteristics could have been explained due to the Lorentz force.     

单晶炉导流筒、热屏及炭毡对单晶硅生长影响的优化模拟

在CZ法生长太阳能级单晶硅中,单晶炉的导流筒、热屏和炭毡对晶体生长有很大影响.通过对上述三个部件进行改进优化,并通过数值模拟对优化前后晶体和熔体的热场、热屏外表面与石英坩埚内壁面之间的氩气流场以及晶体中的热应力进行分析,得出以下结论:石墨导流筒的引入减少了炉体上部的氩气流动涡胞,进而减少了SiO在单晶炉上部的沉积;优化后的热屏减少了加热器对晶体的烘烤,使结晶速率加快;优化后的侧壁炭毡阻止了加热器向上部的热损失.优化后在加热器功耗不变时,结晶速率至少可提高35;,而不增加宏观位错的发生概率.