旋转磁场对空间浮区内流场及浓度场的影响

采用全浮区模型数值研究了旋转磁场作用下熔区内热毛细对流流动特性,分析了磁场强度对流场及浓度场的影响.研究发现,无磁场时,熔体内杂质浓度场和流场呈现三涡胞对称振荡特征;温度场主要由扩散作用决定,呈对称分布.旋转磁场作用下,Ma数基本保持不变.当磁场强度B0≤1 mT时,熔体内杂质浓度场和流场与无磁场时结构类似,但旋转磁场的搅拌作用使得熔体内周期性振荡提前出现,且当旋转磁场产生的洛伦兹力相对较大时,表面张力产生的三维振荡对流得到很好地抑制.B0=5 mT时,周向波动被完全抑制,熔区内流场和浓度场呈二维轴对称分布.旋转磁场对熔体流动产生的轴向抑制作用和周向搅拌作用,都有助于熔体流动的稳定性、浓度分布以及温度分布的均匀性,从而有利于高质量晶体的生长.     

Modification of Fluid Flow and Heat Transport in Vertical Bridgman Configurations by Rotating Magnetic Fields

Applying a rotating magnetic field to an electrically conducting liquid, a Lorentz force is induced which generates a melt rotation of a certain angular velocity. A cylindrical gallium melt (aspect ratio 2.5) has been used as a model liquid. The melt has been heated from the bottom (Ra = 10⁶) or from the top (Ra = −10⁶) and the resulting temperature fluctuations in the melt have been measured in dependence on the rotating field strength (B_max = 30 mT). In the case of the unstable gradient 0.8 mT are sufficient to dominate the buoyancy driven convection and to reduce the amplitude of the buoyancy caused temperature oscillations for more than one order of magnitude. At the same time, the fluctuation frequency increases with the field strength. In the case of the stabilizing temperature gradient, low amplitude/high frequency temperature fluctuations are generated by the rotating magnetic field, indicating the transition to a time-dependent flow. In both cases we see an increase of the convective heat transport for magnetic inductions higher than approximately 5 m T. Applying the rotating magnetic field to the Bridgman growth of gallium doped germanium, the same behavior can be seen: Growing with a top-seeded arrangement, the intensity of the dopant striations is decreased and their frequency is increased. Growing with a bottom-seeded arrangement, the interface curvature changes from concave to convex and the flow becomes time-dependent.     

Numerical simulation of MHD rotator action on hydrodynamics and heat transfer in single crystal growth processes

The article presents the results of the mathematical and physical simulations of the influence of a rotating magnetic field (RMF) on the hydrodynamics and heat transfer in processes of large semiconductor single crystal growth in ampoules. Different versions of the RMF are considered, in particular, for symmetric and asymmetric positions of a RMF inductor with regard to the melt in the ampoule, for two counter-rotating magnetic fields, for different geometrical ratios in the “RMF inductor - liquid melt” system, and for different electrical conductivities of the hard walls at their contact with the melt. The interconnection between the distribution of the electromagnetic forces in the liquid volume and the formed velocity patterns, temperature distribution and shape of the solidification front is studied. An original method for the definition of the electromagnetic forces, which considers finite dimensions of the RMF inductor and melt, was used to calculate real conditions of the RMF influence on growth processes. The numerical results obtained are compared to the data of model experiments. Their satisfactory agreement permits us to propose this calculation method for the definition of the optimal parameters of a growth process under specific conditions and to select the most rational type of RMF influence.     

Application of rotating magnetic fields in Czochralski crystal growth

The physical principles of electromagnetic stirring with a rotating magnetic field are explained and a mathematical model to calculate the electromagnetic volume force, the fluid flow and the transport of heat and solutes is outlined. For the electromagnetic volume force and for the order of magnitude of the flow velocities approximative analytical expressions are given. A high flexibility in configuring the volume force in order to achieve a desired flow distribution is obtained by multi-frequency stirring that is by superposition of two or several magnetic fields with different frequencies and/or sense of rotation. Results of experimental investigation and mathematical simulation of multi-frequency stirring are given. Numerical simulation of the fluid flow, the temperature and the oxygen distribution in a Czochralski process crucible was performed including the effect of single mode and multi-frequency stirring. The results indicate that electromagnetic stirring should offer large potentials for the optimization of the flow configuration in a Czochralski process crucible. Finally examples from literature of practical application of rotating magnetic fields in crystal growth are presented.     

Modelling of the isothermal melt flow due to rotating magnetic fields in crystal growth

The use of a rotating magnetic field promises the feature of a contactless flow control in crystal growth especially for configurations where an increase of the material transport in a definite way is desired. This paper gives the comparison of numerically calculated and experimentally obtained results on the flow due to a rotating magnetic field as well as numerical results on the influence of the field parameters (frequency, amplitude) on the fluid flow in the melt.     

不同工艺参数及喷淋板结构下PECVD热流场分析

建立了PECVD腔室的连续流体和传热模型,通过仿真实验来分析工艺参数和喷淋板结构对PECVD腔室热流场的影响.在典型工艺的基础上,根据单变量原则设计不同的仿真实验来研究工艺参数对晶圆片上方流速、压力及温度分布的影响,结果显示在不同的工艺参数下,流速分布都能够保持线性分布;温度分布波动很小,表现良好的稳定性;压力随径向近似抛物线分布,中心压力高边缘压力低.另外本文设计了两组仿真实验,研究喷淋板不同的流阻分布对热流场的影响,结果显示喷淋板流阻的分布对流速分布有明显的影响,在不同的流阻分布下,加热盘边缘处的流速保持不变,但是流速分布存在一个拐点,拐点前和拐点后流速都近似于直线分布;结果说明能够通过改变喷淋板流阻的分布来调控晶圆上方流速的分布从而获得更高的薄膜工艺均匀性.     

Mathematical modeling of impurity distribution in the melt meniscus in the growth of profiled sapphire crystals

The distribution of impurities in the growth of profiled sapphire crystals is simulated. The distribution of impurities was calculated with the use of the diffusion equation with convective terms. The melt flow was found by solving the Navier-Stokes equation. The distributions of impurities over the melt meniscus are obtained at different crystallization rates. The maximum concentration supersaturation in the meniscus is studied as a function of its geometric parameters.     

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)     

Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 1: non‐rotating seed

For the seeding process of oxide Czochralski crystal growth, the flow and temperature field of the system as well as the seed‐melt interface shape have been studied numerically using the finite element method. The configuration usually used initially in a real Czochralski crystal growth process consists of a crucible, active afterheater, induction coil with two parts, insulation, melt, gas and non‐rotating 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 source the fluid flow and temperature field were determined in the whole system. We have considered two cases with respect to the seed position: (1) before and (2) after seed touch with the melt. It was observed that in the case of no seed rotation (ω_seed = 0), the flow pattern in the bulk melt consists of a single circulation of a slow moving fluid. In the gas domain, there are different types of flow motion related to different positions of the seed crystal. In the case of touched seed, the seed‐melt interface has a deep conic shape towards the melt. It was shown that an active afterheater and its location with respect to the crucible, influences markedly the temperature and flow field of the gas phase in the system and partly in the melt. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

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.     

Use of an inhomogenous magnetic field for silicon crystal growth

The flow of liquid silicon and oxygen transfer during crystal growth under three different types of cusp-shaped magnetic field were clarified using numerical simulation, flow visualization, and infrared measurement of oxygen concentration in grown crystals. Velocity vectors obtained from numerical simulation are almost parallel to cusp-shaped magnetic fields since flow parallel to a magnetic field does not produce a Lorentz force. This parallel flow enhances homogenization of oxygen concentration along the radial direction in grown crystals. Cusp-shaped magnetic fields can control the flow velocity at the top of the melt. Since melt with a low concentration of oxygen at the top of the melt transfers directly from the free surface to the solid-liquid interface, a low concentration of oxygen in crystals can be achieved. Separation of fluid flow between the near surface and bulk can produce a spatial distribution of the concentration in the melt, and therefore a low oxygen concentration can be obtained in grown crystals.     

Control over gas bubble distribution in shaped sapphire crystals

Bubble distribution in shaped sapphire crystals grown by Stepanov technique is found to depend on the field of velocities of the melt flows between the top surface of a die and the crystallization front. A die design defining the flows in the meniscus is a tool for control over the bubble distribution.     

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.     

Effect of magnetic field on melt flow and crystal growth of oxide crystals

The flow in an oxide melt such as LiNbO, and TiO₂ in a high magnetic field was observed by using magnetic-field-applied Czochralski equipment for oxide crystals. It was found that the flows in oxides melts were very much different from these in a semiconductor melt. The single crystals of TiO₂ were grown in a magnetic field by using this equipment.     

Unsteady three-dimensional buoyancy-driven convection in a circular cylindrical cavity and its damping by magnetic field

The oscillatory convection in an electrically conducting liquid-metal confined in a cylindrical cavity of moderate length is investigated using a spectral numerical method involving direct resolution of the Navier-Stokes equations for three-dimensional flows. Time signals, symmetry properties and energy budgets are presented in order to characterize the flow oscillations. The damping of the oscillatory flows by a vertical magnetic field is then studied up to the stabilization to a steady flow.     

Heat and Momentum Transfer Numerical Analysis in a Vertical Bridgman Growth System

In this work the momentum and heat transfer on a Bridgman system for the growth of GaSb has been studied. The main objective was to obtain some information about the role of the different processes like conduction, radiation and convective effects both in the melted material and the surrounding environment. These simulations are based on a 2D axi‐symmetrical model using a finite element method based code. The simulations have been carried out both in steady and transient states. It has been demonstrated that the consideration of a moving environment is important in the distribution of temperatures. The effects of the variations of thermal conductivities and emisivities on the thermal and velocity fields have been investigated. The results show that the key parameters are the thermal conductivities of the different materials present in the system, which produce significant changes in the convective flows inside the melt.     

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)     

Convection in melts and impurity distribution in semiconductor crystals

Impurity distributions in semiconductor melts and crystals grown from these melts are experimentally and numerically studied on an example of Ga-doped Ge crystals. It is shown that inhomogeneous dopant distribution is observed in the form of striations and is caused by the convective flows in the melt and their nonstationary rearrangement in the vicinity of the crystallization front. The character of heat and mass transfer under the microgravity conditions is predicted. The necessity of precision experiments under terrestrial and, especially, space conditions is emphasized.