Effect of a static magnetic field on silicon transport in liquid phase diffusion growth of SiGe

Liquid phase diffusion experiments have been performed without and with the application of a 0.4 T static magnetic field using a three‐zone DC furnace system. SiGe crystals were grown from the germanium side for a period of 72 h. Experiments have led to the growth of single crystal sections varying from 0 to 10 mm thicknesses. Examination of the processed samples (single and polycrystalline sections) has shown that the effect of the applied static magnetic field is significant. It alters the temperature distribution in the system, reduces mass transport in the melt, and leads to a much lower growth rate. The initial curved growth interface was slightly flattened under the effect of magnetic field. There were no growth striations in the single crystal sections of the samples. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct observation and numerical simulation of molten silicon flow during crystal growth under magnetic fields by x-ray radiography and large-scale computation

Control of melt flow during Czochralski (CZ) crystal growth by application of magnetic fields is an important technique for large-diameter (>300 mm) silicon single crystals. Melt convection under magnetic fields is an interesting problem for electromagnetic-hydrodynamics. This paper reviews the effects of a vertical magnetic field and a cusp-shaped magnetic field on melt flow during CZ crystal growth. Melt flow in vertical magnetic fields or cusp-shaped magnetic fields was investigated by the direct observation method based on X-ray radiography and by numerical simulation. The first part of this review shows the result of direct observation of molten silicon flow under magnetic fields. It also compares the results of experimental and numerical simulation. The second part shows the details of the numerical simulation of the behavior of molten silicon in magnetic fields.     

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.     

Levitation of metallic melt by using the simultaneous imposition of the alternating and the static magnetic fields

This study developed a new levitation method, which used the simultaneous imposition of static and alternating magnetic fields. Dynamic behavior was measured for pure Cu and pure Ni melts levitated by the proposed method. The oscillation due to surface tension and convection in levitated Cu melts were hardly observed at static magnetic fields exceeding 1 T. Only the rotation of this axis parallel to the static magnetic field was observed under high static magnetic fields. The proposed method demonstrated that metallic melt could be statically levitated like a solid sphere. It was also found that stable levitation of paramagnetic Ni melt was rather difficult at static magnetic fields exceeding 5 T, because of the magnetization force.     

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.     

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.     

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.     

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)     

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.     

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)     

Crystal growth by the travelling heater method using tapered crucibles and applied rotating magnetic field

Crystal growth experiments were carried out by the Travelling Heater Method using tapered growth ampoules with and without the application of a rotating magnetic field. The objective was to enhance its commercial potential by reducing the size of required seed crystals and increasing the growth rate. To this end, a number of GaSb crystals were grown using either 25 mm diameter straight, or 10 mm to 25 mm tapered growth ampoules. Growth rates of 2 mm/day and 5 mm/day were employed. The effect of rotating magnetic fields of several strengths and frequencies was examined. (© 2010 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.     

Global simulation of a Czochralski furnace for silicon crystal growth against the assumed thermophysical properties

In order to understand the effects of the thermophysical properties of the melt on the transport phenomena in the Czochralski (Cz) furnace for the single crystal growth of silicon, a set of global analyses of momentum, heat and mass transfer in small Cz furnace (crucible diameter: 7.2 cm, crystal diameter: 3.5 cm, operated in a 10 Torr argon flow environment) was carried out using the finite‐element method. The global analysis assumed a pseudosteady axisymmetric state with laminar flow. The results show that different thermophysical properties will bring different variations of the heater power, the deflection of the melt/crystal interface, the axial temperature gradient in the crystal on the center of the melt/crystal interface and the average oxygen concentration along the melt/crystal interface. The application of the axial magnetic field is insensitive to this effect. This analysis reveals the importance of the determination of the thermophysical property in numerical simulation. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

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.     

Combined effects of crucible geometry and Marangoni convection on silicon Czochralski crystal growth

In order to understand the influence of crucible geometry combined with natural convection and Marangoni convection on melt flow pattern, temperature and pressure fields in silicon Czochralski crystal growth process, a set of numerical simulations was conducted. We carry out calculation enable us to determine temperature, pressure and velocity fields in function of Grashof and Marangoni numbers. The essential results show that the hemispherical geometry of crucible seems to be adapted for the growth of a good quality crystal and the pressure field is strongly affected by natural and Marangoni convection and it is more sensitive than temperature. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Earth optimization of space experiment on growth of germanium by floating-zone technique with the use of rotating magnetic fields

The results are considered of the earth experiments on growth of high-purity and Ga-doped germanium single crystals 15 mm in diameter and 60 mm in length, which were performed in a Zona-4 “space furnace” under the technological regimes close to those existing in space orbits. It is shown that the use of a magnetohydrodynamic (MHD) factor [weak (0.15–0.2 mT) rotational (400 Hz) magnetic fields] during crystallization of semiconductors by the floating-zone technique is a very promising method for control of dopant distributions and electrophysical properties in a growing crystal. It is shown that in such magnetic fields, the effective coefficient of Ga distribution in Ge decreases by 10%. The shift of the donor-acceptor balance of the residual dopants in a compensated semiconductor during growth with the MHD-stirring of the melt was first established in growth of undoped germanium single crystals. It was also established that magnetic fields produce different effects on the resistivity microinhomogeneity in undoped and doped crystals. The mechanisms of the MHD effect on the properties of the grown crystals are discussed as well as the perspectives of performing analogous experiments aboard spacecrafts. It is predicted that, under the microgravitation conditions, the effects revealed in terrestrial experiments would be more pronounced.     

The role of inner and internal radiation on the melt growth of sapphire crystal

In this paper, for an inductively heated Czochralski furnace used to grow sapphire single crystal, influence of the inner (wall‐to‐wall) and crystal internal (bulk) radiation on the characteristics of the growth process such as temperature and flow fields, structure of heat transfer and crystal‐melt interface has been studied numerically using the 2D quasi‐steady state finite element method. The obtained results of global analysis demonstrate a strong dependence of thermal field, heat transport structure and crystal‐melt interface on both types of radiative heat transfer within the growth furnace.