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.     

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)     

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.     

A detailed study of gold single crystal growth in a silica gel

Gold single microcrystals have been fabricated by electrochemical growth in a silica gel. Structural characterization of the single crystals by backscatter electron diffraction showed a preferred orientation of Au (1 1 1) and a minor orientation of Au (1 0 0). In addition, the influence of additives on the nucleation and growth of gold microcrystals has been studied. It was found that the inclusion of chemical additives in the growth solutions altered the characteristics of the gold crystals. Possible mechanisms for nucleation and growth of these crystals are discussed.     

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.     

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.     

Optimization of control parameters of cadmium zinc telluride Bridgman single crystal growth

The temperature gradient within a furnace chamber and the crucible pull rate are the key control parameters for cadmium zinc telluride Bridgman single crystal growth. Their effects on the heat and mass transfer in front of the solid‐liquid interface and the solute segregation in the grown crystal were investigated with numerical modeling. With an increase of the temperature gradient, the convection intensity in the melt in front of the solid‐liquid interface increases almost proportionally to the temperature gradient. The interface concavity decreases rapidly at faster crucible pull rates, while it increases at slow pull rates. Moreover, the solute concentration gradient in the melt in front of the solid‐liquid interface decreases significantly, as does the radial solute segregation in the grown crystal. In general, a decrease of the pull rate leads to a strong decrease of the concavity of the solid‐liquid interface and of the radial solute segregation in the grown crystal, while the axial solute segregation in the grown crystal increases slightly. A combination of a low crucible pull rate with a medium temperature gradient within the furnace chamber will make the radial solute segregation of the grown crystal vanish. (© 2007 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.     

ACRT forced convection and its effects on solute segregation and heat and mass transfer during single crystal growth

A numerical simulation study was carried out for CdZnTe vertical Bridgman method crystal growth with the accelerated crucible rotation technique (ACRT). The convection, heat and mass transfer in front of the solid‐liquid interface, and their effects on the solute segregation of the grown crystal can be characterized with the following. ACRT brings about a periodic forced convection in the melt, of which the intensity and the incidence are far above the ones of the natural convection without ACRT. This forced convection is of multiformity due to the changes of the ACRT parameters. It can result in the increases of both the solid‐liquid interface concavity and the temperature gradient of the melt in front of the solid‐liquid interface, of which magnitudes vary from a little to many times as the ACRT wave parameters change. It also enhances the mass transfer in the melt in a great deal, almost results in the complete uniformity of the solute distribution in the melt. With suitable wave parameters, ACRT forced convection decreases the radial solute segregation of the crystal in a great deal, even makes it disappear completely. However, it increases both the axial solute segregation and the radial one notably with bad wave parameters. An excellent single crystal could be gotten, of which the most part is with no segregation, by adjusting both the ACRT wave parameters and the crystal growth control parameters, e.g. the initial temperature of the melt, the temperature gradient, and the crucible withdrawal rate. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Silicon transport under rotating and combined magnetic fields in liquid phase diffusion growth of SiGe

The effect of applied rotating and combined (rotating and static) magnetic fields on silicon transport during the liquid phase diffusion growth of SiGe was experimentally studied. 72‐hour growth periods produced some single crystal sections. Single and polycrystalline sections of the processed samples were examined for silicon composition. Results show that the application of a rotating magnetic field enhances silicon transport in the melt. It also has a slight positive effect on flattening the initial growth interface. For comparison, growth experiments were also conducted under combined (rotating and static) magnetic fields. The processed samples revealed that the addition of static field altered the thermal characteristics of the system significantly and led to a complete melt back of the germanium seed. Silicon transport in the melt was also enhanced under combined fields compared with experiments with no magnetic field. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

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.     

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)     

Synthesis and single crystal growth of SnS by the Bridgman‐Stockbarger technique

SnS is a promising candidate as PV absorber material according to the material properties and the Loferski diagram, but despite the numerous publications on this material, the intrinsic material properties are widely unknown and the theoretical possible values for efficiency are still far away from those achieved in reality. Due to the fact that this material is mostly grown as thin film material, bulk research is rare. The material synthesis and the melt growth of tin monosulfide (SnS) by using Bridgman‐Stockbarger technique have been investigated in this study. After first growth experiments produced polycrystalline SnS, a significant reduction of the growth velocity lead to samples with a high amount of single crystalline material. These samples were investigated in detail regarding the structural and optical properties by using XRD/HRXRD, chemical etching and photoluminescence.     

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.     

Crystallization rate control for alkali halide crystal growth by the VGF technique with a skull layer

This study describes the ability to use the melt‐level control for stabilization of the crystallization rate during NaI crystal growth by the VGF technique with a skull layer. It is shown that a conventional linear decrease of the heater temperature leads to a nonuniform crystallization rate and deterioration of crystal quality. A method and algorithm of temperature control for the stabilization of the crystallization rate during crystal growth is proposed. The series of growth experiments with NaI(Tl) crystals proved the efficiency of this approach and ability to obtain scintillators with high registration efficiency, about 6.3% energy resolution for a ¹³⁷Cs (662 keV) source.     

Three‐dimensional study of the pressure field and advantages of hemispherical crucible in silicon Czochralski crystal growth

The effects of several growth parameters in cylindrical and spherical Czochralski crystal process are studied numerically and particularly, we focus on the influence of the pressure field. We present a set of three‐dimensional computational simulations using the finite volume package Fluent in two different geometries, a new geometry as cylindro‐spherical and the traditional configuration as cylindro‐cylindrical. We found that the evolution of pressure which is has not been studied before; this important function is strongly related to the vorticity in the bulk flow, the free surface and the growth interface. It seems that the pressure is more sensitive to the breaking of symmetry than the other properties that characterize the crystal growth as temperature or velocity fields. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solid mechanics and material strength studies on the melt growth of bulk single crystals

Microdefects such as dislocations and macrocracking should be controlled during the crystal growth process to obtain high-quality bulk single crystals. Solid mechanics and material strength studies on the single crystals are of importance to solve the problems related to the generation and multiplication of dislocations and the cracking of single crystals. The present paper reviews such research activities that comprise the thermal stress analysis during crystal growth process, the dislocation density estimation during crystal growth process, and the cracking of single crystal due to thermal stress.     

Crystal growth and spectral analysis of Dy3+ and Er3+ doped KPb2Cl5 as a mid‐infrared laser crystal

This paper reports crystal growth and optical characteristics of dysprosium (Dy³⁺) and erbium (Er³⁺) doped mid‐infrared laser crystal ternary‐potassium‐lead‐chloride (KPb₂Cl₅). Two transparent crystals with good optical quality have been grown successfully by using the Bridgman technique,the largest crystal size reaches up to ∅︁10×60mm². Measurements of X‐ray diffraction(XRD) and absorption spectra were carried out. Based on Judd‐Ofelt theory, the intensity parameters Ω_t(t=2,4,6), the experimental and theoretical oscillator strengths have been obtained.The intensity parameters Ω_t(t=2,4,6) of Er³⁺:KPb₂Cl₅ were calculated to be Ω₂=5.10×10^‐20 cm², Ω₄=1.25×10^‐20 cm², Ω₆=0.83×10^‐20 cm², and the values for Dy³⁺:KPb₂Cl₅ were calculated to be Ω₂=6.26×10^‐20 cm², Ω₄=2.45×10^‐20 cm², Ω₆=0.04×10^‐20 cm² respectively. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)