Mathematical simulation of impurity distribution in space processing experiments with semiconductors

The effect of natural convection in the melt on impurity distribution is investigated by numerical simulation in the case of uniaxial growth of semiconductor crystals at low gravity conditions.     

Melt temperature fluctuations: Causes and response of the solidification front

It is well understood that temperature oscillations and fluctuations during melt growth give rise to fluctuating concentration of solute in the crystal — so-called solute (or impurity) striations. A major source of the temperature fluctuations is the transition to turbulence in the melt resulting from strong buoyancy and/or surface-driven flows. The interaction of these natural convective flows with any imposed rotation is of significance. The major factors causing flow transitions and particularly those which lead to time-dependent flows in Czochralski and float-zone melts will be briefly reviewed and the likely influence of a low-g environment considered. Theoretical analysis and experimental study of the response of the crystal-melt interface to such temperature fluctuations is reviewed and criteria for maximising crystal homogeneity discussed.     

EXPERIMENTAL AND THEORETICAL STUDIES ON VELOCITY FIELD OF BUOYANCY CONVECTION IN KNbO3 MELT

The Schlieren technique coupling with a differential interference microscope was applied to visualize the KNbO3 melt motion in a loop-shaped Pt wire heater. The natural convection in KNbO3 melt was traced by observing the movement of the tiny KNbO3 crystals (～10μm) and the stream velocities of these tracer crystals were measured. In theoretical analysis, the Navier-Stokes equation was solved as a stable field. The general solution for this system of the differential equation was expressed by an approximate power series of azimuth and radius vector. The expression was substituted in the differential equation; a non-trivial solution was obtained exactly.The velocity distribution in the vertical section was obtained which is in qualitative agreement with the experimental result.     

Computational fluid dynamics and material processing (buoyancy and thermocapillary convections in melts during directional crystallization)

Modelisation and solution of heat and mass transfer problems relevant for material processing are generally hard to be handled, as they often involve 3D unsteady flows, viscous mixtures, phase changes, moving liquid-solid fronts, deforming liquid-gas interfaces, etc.… For space applications, material processing benefits of reduced buoyancy convection but can be faced to a strongly increased complexity due to variable g, mainly in manned flight.

Computational techniques used to analyse fluid motions in material processing, accounting for free surface, crystallization front and bulk convection in melt, are reviewed with emphasis to directional crystallization. Hydrodynamics stability and bifurcation analysis are shown to be useful complementary tools for correlating data, and for a better understanding of the physical laws. This last point will be illustrated in the case of the onset of oscillations in metallic melts.     

Convection in melts and crystal growth

Convection plays a significant role in determining the electronic properties of semiconductor crystals grown from the melt. Inhomogeneities (doping striations) in these crystals can be caused by unsteady natural convection. Therefore, the origins of unsteady natural convection, which means fluctuating temperatures in a fluid, are investigated in this paper. Several effects have been found at increasing Rayleigh numbers Ra which cause fluctuating temperatures. But it was also observed, that unsteady convection became again steady if Ra was increased to higher values. This effect, which is called relaminarization, is very interesting for crystal growth and is discussed in this paper.     

Two-component Bénard convection: Interfacial deformation,oscillatory instabilities and the onset of turbulence

Instabilities and convection in binary fluid mixtures (liquids with impurities, binary gas mixtures, etc.) have been the subject of intense research over the past decade. The major finding has been that mere ppm impurity concentration can play a drastic role in the stability of fluid layers subjected to thermal gradients. For layers open to ambient air the impurity cooperates or competes according to the sign of its migration in the thermal fields with the interfacial deformation thus leading to convective flows. For a layer enclosed between copper plates, say, the impurity can interplay with the slightest buoyancy or buoyancy variations in the environment thus amplifying this force and bringing instability under circumstances where with pure fluids no instability is expected. Recent predictions reported here refer to oscillatory instabilities with or without interfacial deformation and the onset of turbulence in the form of chaotic flows which correspond to irregular patterns with decaying correlations and broadband noise in their power spectra.     

NUMERICAL MODELLING OF VELOCITY AND TEMPERATURE DISTRIBUTIONS OF THE BUOYANCY CONVECTION EFFECT IN KNbO3 MELT

Numerical modelling of velocity and temperature fields in high-temperature KNbO3 melt of a loop-shaped Pt wire heater is carried out by using the commercial com putational code ANSYS for the mathematical solution of the governing equations.Based on the experimental boundary conditions and the Boussinesq approximation,the numerical modelling of a steady and two-dimensional model is applied to study the process under consideration of the buoyancy-driven convection condition. The result is compared with the previous experimental and theoretical data obtained in our laboratory, and the former is in agreement with the latter. Thus a theoretical guide for reasonable growth conditions is provided by studying in depth the real fluid flow effects in the crystal growth from the melt.     

Solidification and Crystal Growth on the SJ-10 Recoverable Scientific Experiment Satellite

The low-gravity environment aboard the space provides a unique platform for understanding crystal-growth-related phenomena that are masked by gravity on the Earth and for exploring new crystal growth techniques. We have characterized the wetting behavior of metal alloys and carried out melt growth of compound semiconductors under the support of materials science program in the SJ-10 recoverable satellite. We found that interfacial reaction plays a significant role in the interfacial evolution of Sn-based alloys. Detached growth of InAsSb was realized under microgravity, whereas during the terrestrial experiment the crystal and the crucible wall contact with each other. Moreover, the suppression of buoyancy-driven convection results in a more uniform composition distribution in the InGaSb and Bi₂Te₃-based semiconductor alloys.      

Observations of magnetospheric convection from low altitudes

Some of the observations and interpretive models that have provided a substantial increase in our knowledge of magnetospheric and ionospheric convection are discussed. While a two-cell convection pattern may be generally consistent with many ionospheric measurements, it is now clear that some significant departures from such a pattern must be considered. We can now specify more accurately the number of convection cells and their shape as well as the electrostatic potential distribution within the cells. All these factors can be shown to be sensitive functions of the interplanetary magnetic field (IMF). Interpretation of these findings in terms of the interaction of the earth's magnetosphere with the interplanetary medium has led to detailed consideration of the location of magnetic merging regions and the magnetic field topology of the outer magnetosphere. In addition, the relative importance of merging, viscous interaction and ionospheric processes in providing the driving force for convection has been considered. In general, the bulk of the driving force is magnetic reconnection; however, viscous processes play a significant role in times of northward interplanetary magnetic fields, and thermospheric drag may contribute to the maintainence of a convection pattern for several hours after such a northward turning.     

冕洞网络的大气模型

本文采用非径向磁流管位形的假设,计算了太阳冕洞网络部分的色球-日冕过渡区的能量平衡模型。所考虑的能量流包括辐射、传导、对流和机械波加热（如阿尔芬波）,计算结果表明在冕洞网络部分的过渡区中,电子温度T和密度N分别比宁静太阳中的值低60%和2倍,而其过渡区的厚度比宁静太阳中的大4倍。这种大气模型可满意地解释T≥105K范围的远紫外观测发射量度的分布。另外我们也发现在冕洞大气的过渡区中,阿尔芬波加热似乎不能忽略,尤其是在冕洞的过渡区底部,它的加热作用可能会超过热传导。在冕洞大气中,由于波动量的淀积而产生的对流能损耗也是重要的,在过渡区底部650km以上,对流能损耗逐渐超过辐射损耗。      

THE CONVECTIVE EFFECT ON THE MORPHOLOGICAL INSTABILITY OF KNbO3 CRYSTALS

Experimentally, it was observed that there were various morphologies of KNbO3 crystals in different regions of the melt of Li2B4O7 and KNbO3 mixture in Pt loop heater. Dendrites grew in the central area of the melt, the diffusive-advective region,in which the temperature gradient is negligible; whereas crystals with smooth sur face were observed in the marginal area, the diffusive-convective region, with large temperature gradient. Based on the solute concentration over the KNbO3 crystal surface examined by electronic probe analysis, it was proved that the combinative effect of buoyancy and surface tension convection induced by temperature gradient enhanced the homogeneity of the solute concentration around KNbO3 crystals and thus their morphological stability.     

贮箱内低温推进剂汽化过程的CFD数值仿真

为研究贮箱内低温推进剂相变对推进剂温度和贮箱压力的影响,对贮箱内的传热传质过程进行了仿真.仿真涉及的物理过程包括贮箱与外界环境的换热、推进剂的自然对流、推进剂与贮箱内壁面的换热以及低温推进剂的相变过程等.根据热力学平衡原理建立了低温推进剂相变模型,使用CFD(Computational Fluid Dynamic)方法对处于地面常压停放状态的液氢贮箱进行了450 s的仿真.研究表明随着贮箱壁面传热过程的稳定,推进剂的温度分布、流动状态以及相变情况会趋于稳定;通过仿真获得了推进剂单位时间的汽化量;影响相变的主要因素是贮箱壁面漏热以及推进剂自身的对流运动.     

Liquid phase sintering of tungsten composites in space: Results of tests performed in Texus

Tungsten-nickel-iron composites are commersially fabricated from powders by liquid phase sintering. They consist of almost spherical tungsten particles in a matrix of nickel-iron-tungsten. A way to contribute to the understanding of the sintering mechanism and the mechanical properties is to study composites with a low amount of tungsten particles. Depending on the great difference in density between the particles and the matrix, this can only be done under microgravity. A primary sintering test of the tungsten composite was done in space using the Texus 10 modul. Prealloys were fabricated from metal powder mixtures, which were hot isostatic pressed. Liquid phase sintering of the two tungsten composites under microgravity has shown that the particles are evenly distributed and that no segregation occured due to convection. Despite an uneven distribution of the particles in the preformed specimens and the short melting period the patricle distribution has become even. Compared to short time sintering tests made on four alloys in the laboratory, the growth and separation of the particles was fast.     

纵向非均匀多孔介质Marangoni对流不稳定性

理论研究了纵向非均匀多孔介质中流体表面张力驱动的对流不稳定性.充满液体的多孔介质层从下方加热,上方自由表面冷却,形成可引起多孔介质液层Marangoni-Benaxd对流流动的纵向温度梯度.采用线性化的Brinkman-Forchheimier方程作为控制方程组,对孔隙率分别为线性函数、正弦三角函数分布的非均匀多孔介质液层的Marangoni-Benaxd问题进行了线性稳定性分析.通过采用Chebyshev-Tau谱方法求解广义特征值问题,得到了系统临界Maxangoni数随无量纲波数变化的中性稳定性曲线,分析和比较了孔隙率的变化对液层对流稳定性和流场结构的影响,获得了纵向非均匀多孔介质液层不稳定性现象的新特征.      

微重力环境下蒸发液层热毛细对流的数值模拟

提出了一种新模型来研究由单一物质构成的液层在其纯蒸气中的蒸发.液层置于微重力环境中并且受到水平方向温度梯度的作用,液层的热毛细对流和蒸发耦合在一起,使得气液界面的传热传质规律更加复杂.用理论分析的方法求解了不考虑热毛细效应的纯蒸发模型,得出温度场分布和界面质量流量的解析表达式.对于热毛细对流和蒸发耦合情况,采用有限差分的投影算法同时求解Navier-Stokes方程和能量方程,得到了不同蒸发Biot数和Marangoni数下流场和温度场的稳态数值解.论述了蒸发Biot数和Marangoni数对界面传热传质的影响,提出并解释了蒸发和热毛细对流耦合的三种模式.      

Laboratory experiments and space phenomena

Two types of convection were observed in the laboratory model of the magnetosphere: viscous convection and convection due to field lines common to both the magnetosphere and artificial solar wind. With a southward field component in the solar wind, convection from the Sun is observed in the polar cap, while with a large northward component, convection is directed toward the Sun. Merging of the field lines occurs in the cleft. With the southward component, a visor appears in front of the magnetosphere boundary. The decay of the visor into small magnetic structure is observed. The formation of an induced magnetosphere with a magnetic tail is shown in the experiments of the simulated conditions near non-magnetic bodies with a plasma shell (Venus, comets). A combined induced-intrinsic magnetosphere also was investigated.     

电导率分布、对流电场转向区与场向电流形态(模式分析)

本文利用一些简单模式讨论对流转向区形态、电离层电导率的分布变化对场向电流形态的影响。结果表明,一区场向电流是最基本的,与对流转向区直接相联。二区场向电流的产生不仅与对流电场的屏蔽相联,也与电导率变化有关。电导率的变化还可产生一区电流高纬侧的零区电流和二区电流低纬侧的反向电流。此外,剪切转向区和旋转转向区所对应的场向电流分布也有所不同。本文结果有助于理解观测的场向电流之复杂形态,也可以解释同样的行星际磁场状况下,场向电流的不同变化。      

轴向通流旋转盘腔流动换热稳态实验与数值模拟

通过开展稳态实验及数值模拟探究了轴向通流旋转盘腔的流动结构与换热特性。通过改变流量系数、旋转雷诺数等参数,探究不同工况下旋转盘两侧及盘罩内侧壁面温度和努塞尔数的径向分布规律。结果表明:在轮缘加热的状态下,旋转盘两侧温度径向分布均呈凹函数形态,且旋转盘迎风面换热强度普遍高于背风面;后轴颈盘罩向两端旋转盘导热,其壁面温度径向分布呈"中间高、两侧低"的状态;随着轴向流量系数的增大,盘腔内部气体对流加剧,径向臂及涡对结构更加明显,旋转盘及轴颈表面换热效果增强;旋转盘腔内的流动换热特性受强迫对流和类Rayleigh-Benard对流2种机理的共同影响。      

A sounding rocket experiment on the marangoni convection

During a 6-minutes free flight of a sounding rocket an experiment on the thermal Marangoni convection in a right circular cylindric floating zone was carried out to verify the thermal Marangoni convection by flow visualisation for the first time at 10^?4 g. From the motion picture analysis the velocity distributions are obtained. The interdependence between the two velocity maxima and the S-shaped temperature distribution on the free surface is discussed. The influence of the heat transfer caused by the flow of the surrounding air induced by the thermal Marangoni convection itself is considered briefly.     

临近空间环境下封闭方腔内耦合换热特性

以临近空间浮空器载荷舱为应用背景,对复杂热边界条件下含热源的三维封闭方腔内自然对流、表面辐射和导热的耦合问题进行了数值模拟。综合考虑对流换热、长波辐射、太阳辐射等因素的影响,建立了临近空间热环境模型。通过Fluent软件用户自定义函数（UDF）引入外部非定常的辐射-对流耦合热边界条件,对腔内换热特性的昼夜变化进行研究,并分析了腔壁厚度、发射率和导热系数对其的影响。数值结果表明,腔内平均温度昼夜变化很小,约为12.9 K,但温度场分布随太阳方位变化而变化;腔内对流换热较弱,同一时刻最大温差约为71.3 K;腔壁热阻和发射率增加会削弱自然对流的强度。