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.     

Three-dimensional thermocapillary and buoyancy convections and interface shape in horizontal Bridgman crystal growth

Computer simulation is conducted to study three-dimensional (3D) thermocapillary and buoyancy convections and their effects on the growth interface for horizontal Bridgman crystal growth. The free-boundary model is based on a finite volume approximation of continuity, momentum, and energy equations on a collocated grid. Crystal growth of GaAs is used as an example. From calculated results, it is observed that the effect of buoyancy convection on the growth interface is significant. With the thermocapillary effect, the 3D flow structures are not changed much, but its effect on the growth interface is not trivial. Due to the convections, the growth interface is always concave, and its deflection is affected significantly by the growth rate and thermal environment. A simple strategy of interface control is illustrated. Furthermore, slight crucible tilting can also affect the 3D flows leading to an asymmetric growth interface.     

Study of the hydrodynamic instabilities in a differentially heated horizontal circular cylinder corresponding to a Bridgman growth configuration

We are interested in determining the origin of the instabilities occurring in a metallic liquid (Prandtl number Pr=0.026) contained in horizontal circular cylinders heated from the end-walls. Our approach by direct numerical simulation (DNS) allows the determination of the transition thresholds for different aspect ratios varying from 1.5 to 10 as well as a precise characterization of the nature and structure of the new flow regimes close to the thresholds. In order to understand the mechanisms of flow transition, fluctuating energy analyses close to the threshold have been performed. The main contributions have been determined and localized in the cavity: shear has been found as the main instability factor but the way it acts is different according to the aspect ratio.     

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.     

Bridgman growth and characterization of birefringent crystal NaNO3

With a bigger birefringence than calcite, sodium nitrate (NaNO₃) single crystal might have potential applications in fiber‐optic polarizer, opto‐isolators and polarizing prisms. However, it is difficult to grow large‐size NaNO₃ crystals for their thermal conductivity anisotropy and phase transition at 275°C. In this paper, crack‐free NaNO₃ crystals with size of Φ20×100 mm³ were prepared by Bridgman method with lower growth rate and lower interface temperature gradient. The dependence of the transmittance on the sample exposure time was measured and studied. The principal refractive indices of NaNO₃ crystal at the wavelengths 0.4730, 0.5320, 0.6328, 1.064 and 1.338 μm were measured by auto‐collimation method. From which, we calculated and obtained the Sellmeier's equation of NaNO₃ crystal. Moreover, the photoluminescence spectra were detected under the excitation at 240 nm, and NaNO₃ crystal presented its fluorescence around 416 nm.     

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.     

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal

Computational analysis of three-dimensional flow and mass transfer in a non-standard configuration for growth of a KDP crystal was conducted. The results show that the surface shear stress is mainly affected by the inlet velocity, and the distribution of the surface supersaturation is determined by the bulk supersaturation and the inlet velocity. By adjusting the inlet velocity, the homogeneity of surface supersaturation can be improved, which is helpful for reducing the occurrence of inclusions and enhancing the crystal quality. The thickness of solute boundary layer is closely related to the flow intensity, but it is almost free from the impact of the bulk supersaturation.     

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.     

Solutal convection in crystal growth: effect of interface curvature on flow structuration in a three-dimensional cylindrical configuration

Due to temperature and concentration gradients in the molten phase, it is well known that convective flows can develop in the bulk under normal conditions of gravity. These motions modify the shape of the growing interface and the concentration distribution along it. This study will only focus on the case of pure solutal convection and the effect of a given interface curvature on the flow. In particular, the transition from a 3D-flow to a 2D one as a function of the interface curvature is examined in order to investigate possible values of the operating parameters and fluid properties. The main aim is to justify the use of 2D-simulation tools for predicting the convective transport in cylindrical crystal growth ampoules.     

Applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic field

To examine the applicability of LES turbulence modeling for CZ silicon crystal growth systems with traveling magnetic fields, LES calculations with Smagorinsky–Lilly turbulence model and van Driest damping at the solid walls are carried out. The program package for the calculations was developed on the basis of the open-source code library OpenFOAM^®${\mathrm{OpenFOAM}}^{\circledR }$. A previously published laboratory model with low temperature melt InGaSn, a 20” crucible, and process parameters corresponding to industrial Czochralski silicon systems is considered. Flow regimes with two crystal and crucible rotation rates and with different strengths of the traveling magnetic field “down” are analyzed. The calculated distributions of averaged temperature and standard temperature deviations are compared with measured ones in the laboratory system, and a relatively good agreement between them is shown. The influence of chosen time steps and grid sizes is analyzed by comparing Fourier spectra of temperature time-autocorrelation functions and temperature spatial distributions, and it is shown that the used moderate meshes of few hundred thousand cells can be applied for practical calculations.     

Effect of a vertical magnetic field on the dendrite morphology during Bridgman crystal growth of Al–4.5 wt% Cu

The effect of a vertical high magnetic field (up to 10 T) on the dendrite morphology has been investigated during Bridgman growth of Al–4.5 wt%Cu alloys experimentally. It is found that the field causes disorder in dendrites and their tilt in orientation. Along with the increase of the magnetic field and decrease of the growth velocity, the dendrites became broken and orientated in 1 1 1 along the direction of solidification instead of 1 0 0. The field also enlarged the primary dendrite spacing and promoted the branching of the dendrites to form high-order arms. Above phenomena are attributed to the thermoelectromagnetic convection effect and orientation caused by the high magnetic field.     

The effects of argon gas flow rate and furnace pressure on oxygen concentration in Czochralski silicon single crystals grown in a transverse magnetic field

The effects of the argon gas flow rate and furnace pressure on the oxygen concentration in a transverse magnetic field applied Czochralski (TMCZ) silicon single crystals were examined through experimental crystal growth. A gas controller which had been proposed by Zulehner was used for this series of experiments. In the TMCZ gas-controlled crystals, a decrease in the oxygen concentration with a decrease in furnace pressure was found. A clear relationship between the oxygen concentration and the argon gas flow rate was not obtained due to the limited experimental conditions. The relationships between the oxygen concentration and the furnace pressure and the argon gas flow rate previously observed for Czochralski (CZ) crystals by a similar gas controller were confirmed by the present gas controller. The oxygen concentration changes in the TMCZ and the CZ crystals were analyzed in terms of the calculated flow velocity of the argon gas between the gas controller and the silicon melt surface. In contrast with the CZ gas-controlled crystals, the oxygen concentration was decreased with an increase in the flow velocity of argon gas in the TMCZ gas-controlled crystals. The surface temperature model and the melt flow pattern model which had been proposed in the previous report are discussed again in light of the present experimental results.     

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.     

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.     

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.     

Effect of steady ampoule rotation on radial dopant segregation in vertical Bridgman growth of GaSe

For vertical Bridgman growth of the nonlinear optical material GaSe in an ampoule sufficiently long that flow and dopant transport are not significantly influenced by the upper free surface, we show computationally that steady rotation about the ampoule axis strongly affects the flow and radial solid-phase dopant segregation. Radial segregation depends strongly on both growth rate U and rotation rate Ω over the ranges 0.25 μms⁻¹U3.0 μms⁻¹ and 0Ω270 rpm. For each growth rate considered, the overall radial segregation passes through two local maxima as Ω increases, before ultimately decreasing at large Ω. Rotation has only modest effects on interface deflection. Radial segregation computed using a model with isotropic conductivity (one-third the trace of the conductivity tensor) predicts much less radial segregation than the “correct” model using the anisotropic conductivity, with the segregation decreasing monotonically with Ω. Consideration of a model in which centrifugal acceleration is deliberately omitted shows that, as Ω increases, diminution and ultimately disappearance of the “secondary” vortex lying immediately above the interface is due to centrifugal buoyancy, while axial distension of the larger “primary” vortex above is due to Coriolis effects. These results, which are qualitatively different from those accounting for centrifugal buoyancy, suggest that several earlier computational and analytical predictions of rotating vertical Bridgman growth are either limited to rotation rates sufficiently low that centrifugal buoyancy is unimportant, or are artifacts associated with its neglect. The overall radial segregation depends approximately linearly on the product of and the growth rate U for the conditions considered, where is the segregation coefficient.     

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.     

Thermal convection and related instabilities in models of crystal growth from the melt on earth and in microgravity: Past history and current status

The paper presents a comparative study of a number of theoretical/experimental/numerical results concerning the dynamics of natural (gravitational), Marangoni and related mixed convection in various geometrical models of widely‐used technologies for the production of single‐crystalline materials (Horizontal and vertical Bridgman growth, Czochralski method, Floating Zone Technique). Emphasis is given to fundamental knowledge provided over the years by landmark analyses as well as to very recent contributions. Such a knowledge is of paramount importance since it is validating new, more complex models, accelerating the current trend towards predictable and reproducible phenomena and finally providing an adequate scientific foundation to industrial processes which are still conducted on a largely empirical basis. A deductive approach is followed with fluid‐dynamic systems of growing complexity being treated as the discussion progresses. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Protein crystal growth in gels and stationary magnetic fields

Thaumatin, lysozyme, and ferritin single crystals were grown in solutions and gels without and with surrounding strong stationary magnetic fields. The crystal size, number and alignment in dependence on the induction force were analysed. The crystal quality, like mosaicity, as function of the magnetic force is discussed by using synchrotron X‐ray diffraction analysis. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.