微重力下静态磁场对浮区法硅单晶生长的影响

考虑晶体生长界面的变形,利用有限体积方法对侧面加热的空间全浮区法硅单晶生长中熔区内的热质传输、流场及晶体生长界面位置和形态特征进行了数值研究.应用不同中等强度的轴向磁场和勾型磁场对硅熔体内的热毛细对流进行抑制.分析了静态磁场不同强度下熔区中的对流模式,研究表明,轴向和勾型磁场均能有效抑制熔体内的对流,并将热毛细对流挤压到自由表面附近.轴向磁场可有效抑制熔体的径向流动,但难以有效抑制轴向对流;勾型磁场则可以达到更好的控制熔体对流的效果.对不同强度下的固液面形态及位置分析发现:轴向磁场下固液面基本和无磁场时的重合,但磁场强度较小时固液面在自由表面边缘处向单晶侧有个凸起;勾型磁场作用下的固液面比较平滑,其中心区域较无磁场时整体向z轴正向偏移.研究结果可对浮区法晶体生长中获得高质量晶体提供帮助.     

勾形磁场下提拉法生产单晶硅的数值模拟

本文给出了提拉单晶硅时,勾形磁场强度的计算公式,并对单晶硅在有无勾形磁场情况下熔体内流场和氧的浓度分布进行了数值模拟,计算出磁场作用下磁场强度和洛伦兹力及有无磁场时流函数、垂直截面处的速度场和氧的浓度分布.通过分析表明,勾形磁场能使流动更为平稳,能有效地降低熔体内及生长界面氧的浓度,并对产生这一现象的机理作了理论分析.     

不同磁场对大直径单晶硅生长中的动量与热量输运影响的数值分析

本文采用紊流模型对大直径单晶硅在垂直磁场及勾形磁场作用时熔体内动量及热量输运作了数值模拟.采用有限体积法离散控制方程,采用SIMPLE((Semi-implicit Method for Pressure Linked Equations)算法耦合压力和速度场.对无磁场、垂直磁场及勾形磁场作用下熔体内的传输特性进行了比较.数值计算结果表明,垂直磁场对动量及热量的分布具有双重效应.垂直磁场强度过大,不利于晶体生长.随着勾形磁场强度的增加,熔体内子午面上的流动减弱,并且紊流强度也相应降低.     

轴向磁场作用下Czochralski浅液池内热对流特性研究

为了有效抑制熔体热对流并提高晶体的生长质量,采用三维数值模拟方法研究了轴向磁场对双向温差作用下Czochralski浅液池内Marangoni-热毛细对流的影响.在一个给定的底部热流密度条件下,探讨了轴向磁场对稳态流动和非稳态流动的影响,确定了不同磁场强度下流动由三维稳态流动向三维非稳态流动转变的临界Macri.结果表明:随着磁场强度的增大,临界Macri不断增大.轴向磁场对液池内稳态和非稳态Marangoni-热毛细对流均具有较好的抑制效果.对于稳态流动,磁场的引入会使自由表面温度波动幅值受到削弱,波数减少;对于非稳态流动,监测点P处的温度振荡随着磁场强度的增加不断逐渐减弱直至消失,流动由三维非稳态过渡为三维稳态,相应地,温度波动结构也会发生转变.     

微重力条件下Marangoni数对分离结晶过程的影响

为了了解微重力条件下新型分离结晶生长过程中熔体热毛细对流的基本特征,利用有限差分法进行了三维数值模拟.当熔体顶部分别为自由表面及固壁边界条件时,得到了新型分离结晶Bridgrnan生长过程中熔体热毛细对流的速度分布和温度分布.结果表明:熔体顶部为自由表面时,当Marangoni数较小时,在上自由表面和下部狭缝处自由表面的表面张力的驱动下,熔体内部产生了逆时针和顺时针两个流动方向相反的流胞,此时熔体内的流动状态为稳态;随着Marangoni数进一步的增大,流胞的流动逐渐增强并逐步向熔体内部扩展,熔体内部温度分布非线性增强,上自由表面和下部狭缝处自由表面处速度增大;当Marangoni数超过某一临界值后,流动转化为非稳态流动.当熔体顶部为固壁时,与熔体顶部为自由表面时相比,临界Marangoni数增大.流动失稳的物理机制是流速的变化和阻力的变化之间存在滞后.     

轴向磁场对环形浅液池内硅熔体热毛细对流的影响

为了更好地了解轴向磁场对温度梯度作用下Marangoni-热毛细对流的影响,采用有限差分法对环形浅液池内硅熔体制单晶的流动进行了数值模拟.研究了三种不同边界条件下,Ha数分别为0、10、20、30对应下硅熔体内部流动强度和自由表面速度.结果表明,轴向磁场对浅液池内的Marangoni对流、热毛细对流和耦合的Marangoni-热毛细对流都有较好的抑制作用,且随着磁场强度的增强,抑制作用增加,更有利于提高晶体的结晶质量.当磁场强度和底部热流密度一定时,随着水平温度梯度的增加,靠近内壁的流动得到增强,外壁附近流动反而减弱.     

感应加热制备太阳能级铸造准单晶硅熔体流动行为研究

用专业晶体生长软件(CG-Sim)对制备太阳能级准单晶硅用真空感应铸锭炉的热场结构以及在熔炼过程中硅熔体的流动行为进行了研究.结果表明,熔体中电磁力是熔体流动的驱动力之一,并且感应线圈与熔体高度的比值(k)对熔体内电磁力的大小和分布具有很大的影响,当k值为1.2时,熔体内形成一个上下贯通的涡流,有利于杂质的挥发.同时,当感应线圈频率在3000～5000 Hz范围时,熔体对流强度较低,可以增加坩埚-熔体边界层的厚度,降低熔体中的氧含量.     

水平磁场下硅熔体的有效粘度

用钕铁硼(NdFeB)永磁材料构建"魔环"结构的永磁体,向直拉硅生长的熔体所在空间引入磁感应强度,采用回转振荡法测量不同磁场强度下硅熔体的磁粘度(有效粘度).在温度一定时,粘度随着磁场强度的增加而增加,二者呈抛物线关系.熔硅温度升高,磁场影响加剧,抛物线更加陡峭.1510～1590℃温度区间内,粘度有异常变化.     

磁场结构对Ф300 mm直拉单晶硅碳杂质的影响研究

本文利用CGSim晶体生长软件分析了不同磁场结构对直拉单晶硅中碳杂质含量的影响。结果表明,气氛中的碳原子主要通过熔体自由表面上靠近坩埚壁一侧区域扩散进熔体。通过调节对称磁场和非对称磁场的结构参数来抑制碳原子掺入区域的对流强度,增大碳原子扩散层的厚度,进而降低熔体中的碳原子浓度,最终获得低碳含量的直拉单晶硅。     

勾形磁场对分离结晶法生长CdZnTe晶体过程中液层热毛细-浮力对流的影响

借助数值模拟手段研究了常重力条件下分离结晶法生长CdZnTe晶体过程中液层热毛细-浮力对流,探讨了不同勾形磁场强度和狭缝宽度对流动的影响.计算选取液层的高径比A为1,狭缝宽度S分别为0.05、0.075以及0.1,磁场Hartmann数分别为45、90及135.结果表明:勾形磁场能够对液层内热毛细-浮力对流起到抑制的作用,且随着磁场强度的增加,流动失稳的临界Marangoni数增大;随着狭缝宽度S的增大,液层内部流动减弱.     

Three‐dimensional unsteady thermocapillary flow under rotating magnetic field

Under a rotating magnetic filed (RMF), the instability of thermocapillary flow and its evolution with increasing Marangoni number (Ma) for semiconductor melt (Pr = 0.01) in a floating liquid bridge model (As = 1) are investigated numerically. Under 5 mT RMF, the thermocapillary flow is steady and axisymmetric with Ma < Ma_c, and the critical Marangoni number Ma_c for convection instability is 29.5, which is obtained by the direct numerical simulation. When the Ma is a little bit beyond the Ma_c, the thermocapillary flow loses stability to become a three‐dimensional rotating oscillatory convection, and a periodic oscillation is confirmed by the fast Fourier transform analysis, the oscillatory main frequency decays with increasing Ma. Under 1 mT–6 mT RMF, the Ma_c increases roughly with the magnetic strength except the Ma_c at 4 mT, where the corresponding change of flow mode after the instability is observed. The oscillatory convection occurs with a smaller Ma in the RMF than that without magnetic field. In addition, no instability toward a three‐dimensional steady convection, which is the state of thermocapillary flow without magnetic field after the first instability, is observed under the RMF.     

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.     

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.     

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.     

Axial macrosegregation in Ga‐doped germanium grown by the vertical gradient freeze technique with a rotating magnetic field

The impact of a rotating magnetic field (RMF) on the axial segregation in Vertical Gradient Freeze (VGF) grown, Ga doped germanium is investigated. Growth experiments were performed using the VGF‐RMF as well as the conventional VGF technique. Carrier concentration profiles characterising the Ga segregation were measured by the Spreading Resistance method and calibrated using Hall values of carrier concentration and mobility. The Ga concentration rises more gradually under RMF action, i.e., the dopant segregation is significantly reduced by the rotating field. This effect is attributed to a better mixing of the melt. Numerical results on the flow velocity confirm this explanation. The RMF induced flow is much more intense than the natural buoyant convection due to the radial temperature gradient and leads to a pronounced decrease of the effective partition coefficient k_eff. In the early stages of growth a k_eff value close to k₀ was obtained, i.e., the gallium was almost homogeneously distributed within the melt. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Experiments on the oscillatory convection of low Prandtl number liquid in Czochralski configuration for crystal growth with cusp magnetic field

This paper presents results of experiments on the oscillatory convection of mercury in a Czochralski configuration with cusp magnetic field. Temperature fluctuation measurements are carried out to determine the critical Rayleigh number for the onset of time dependent natural convection. The effects of a cusp magnetic field on the supercritical natural convection coupled with rotation of crystal disk are investigated. In the presence of a rotating flow it is found that a cusp magnetic field can induce a new long wave instability and can amplify the temperature fluctuation depending on the magnitude of the relevant flow similarity parameters and the melt aspect ratios. A flow regime diagram for the amplification and damping of the temperature fluctuations is presented to provide an experimental data base for finding optimum growth conditions in the cusp magnetic field Czochralski process.     

The influence of melt stirring intensity on the axial impurity distribution in proustite single crystals grown by the Stockbarger method using ACRT

The influence of modulated crucible rotation on the axial distribution of Cu, Mg and Si impurities in proustite single crystals grown by the Stockbarger method using ACRT is studied in a wide range of Taylor numbers (1.9·10⁵ < Ta < 7.12·10⁷). The impurity content in the upper part and in the tail portion of the grown crystals is measured using X‐ray‐phase analysis. Micro and macrostriations are observed in the grown crystals. The wavelengths of impurity content fluctuations have been determined. The microfluctuations of axial impurity content are caused by modulated crucible rotation. The studies have revealed that the ACRT provides an effective removal of impurities from the main part of the grown crystal at high intensity of melt stirring, and consequently, the ACRT can be applied validly to decrease the impurity content during the growing of high‐quality proustite single crystals. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)