Numerical investigation of heat transport and fluid flow during the seeding process of oxide Czochralski crystal growth Part 2: rotating seed

In this paper, the role of seed rotation on the characteristics of the two‐dimensional temperature and flow field in the oxide Czochralski crystal growth system has been studied numerically for the seeding process. Based on the finite element method, a set of two‐dimensional quasi‐steady state numerical simulations were carried out to analyze the seed‐melt interface shape and heat transfer mechanism in a Czochralski furnace with different seed rotation rates: ω_seed = 5‐30 rpm. The results presented here demonstrate the important role played by the seed rotation for influencing the shape of the seed‐melt interface during the seeding process. The seed‐melt interface shape is quite sensitive to the convective heat transfer in the melt and gaseous domain. When the local flow close to the seed‐melt interface is formed mainly due to the natural convection and the Marangoni effect, the interface becomes convex towards the melt. When the local flow under the seed‐melt interface is of forced convection flow type (seed rotation), the interface becomes more concave towards the melt as the seed rotation rate (ω_seed) is increased. A linear variation of the interface deflection with respect to the seed rotation rate has been found, too. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three‐dimensional unsteady thermocapillary flow under rotating magnetic field

Under a rotating magnetic filed (RMF), the instability of thermocapillary flow and its evolution with increasing Marangoni number (Ma) for semiconductor melt (Pr = 0.01) in a floating liquid bridge model (As = 1) are investigated numerically. Under 5 mT RMF, the thermocapillary flow is steady and axisymmetric with Ma < Ma_c, and the critical Marangoni number Ma_c for convection instability is 29.5, which is obtained by the direct numerical simulation. When the Ma is a little bit beyond the Ma_c, the thermocapillary flow loses stability to become a three‐dimensional rotating oscillatory convection, and a periodic oscillation is confirmed by the fast Fourier transform analysis, the oscillatory main frequency decays with increasing Ma. Under 1 mT–6 mT RMF, the Ma_c increases roughly with the magnetic strength except the Ma_c at 4 mT, where the corresponding change of flow mode after the instability is observed. The oscillatory convection occurs with a smaller Ma in the RMF than that without magnetic field. In addition, no instability toward a three‐dimensional steady convection, which is the state of thermocapillary flow without magnetic field after the first instability, is observed under the RMF.     

The Characteristics of GaP Window Layer Grown by Indium‐added Liquid Phase Epitaxy

The effects of added Indium on the growth characteristics of GaP were systematically studied using conventional liquid phase epitaxy technique with Ga‐rich GaP source melt. The GaP growth rate uniformly increase with the source melt of increasing Indium addition against Gallium solvent. These epilayers have mirror‐like surface morphology examined by optical microscope except several grown films with large amount of Indium addition meet a terrible interface. The surface morphologies examined by AFM showed the ripples in samples of R_0.05 and R_0.4 and distinct islands with elliptical base shape in the sample of R_0.7 (R‐In ratio). The epitaxial layer with incorporation of Indium addition during growth had good performance on the carrier concentrations and resistivity. The composition of compound semiconductor become to InGaP at higher amount of In addition to Ga was examined by double‐crystal X‐ray diffraction and the distribution of Indium examined by SIMS also provided the evidences in sample of R_0.7.     

Chemical Segregation in Vertical Bridgman Growth of GaInSb Alloys

A set of experiments on the solidification of Ga _1-x In _x Sb alloys with a large variation of the sample diameter (from 1mm to 10mm), of the growth rate (from 0.7 to 7 μm/s) and of the concentration (from x=0.01 to x= 0.1) is described. The associated radial and longitudinal segregation of the In have been analysed by SIMS or electron microprobe. Numerical simulation of the experiments, taking into account thermal, hydrodynamic and chemical behaviour has been carried out with the help of FIDAP. It is shown from these numerical results that a plateau of concentration can be reached even if a convective loop is present close to the interface, provided that the convection does not extend into the bulk of the liquid. This is in full agreement with the experimental results obtained. Supporting this analysis, in some experiments, a defect in term of verticality of the crucible led to complex 3-D convection involving the whole liquid, and in that case no plateau was obtained. For the radial segregation ΔC_R, three regimes of transport are found, characterised by the convective level: - A diffusive one, with a low, constant, ΔC_R related to the interface curvature. - A quasi-diffusive one (weak convection) in which ΔC_R increases with convection. - A convective one in which it decreases. Measured radial segregations are in good agreement with predictions from the numerical simulations.     

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.     

Influence of transverse magnetic field on thermocapillary flow in liquid bridge

For exploring the optimizing convection control technique by external magnetic field in floating zone crystal growth of semiconductor under microgravity, thermocapillary flow in a floating half‐zone model is simulated numerically, and the influences of both the transversal uniform magnetic field and the magnetic field generated by transversal four coils on thermocapillary flow are investigated. The results indicate that the transversal uniform magnetic field is likely to break the axisymmetrical structure of thermocapillary flow, which is unfavorable to the growth of high‐quality crystal; under the magnetic field generated by transversal four coils, both the mean and the maximum velocities increase with the increment of the distance between coils or the decrement of coil radius; and the convection tends to be more axisymmetrical with increasing coil radius. Compared to the transversal uniform magnetic field, the magnetic field generated by transversal four coils of appropriate radius and relative distance may not only suppress convection, but also enhance the axisymmetry of convection at the same time, and finally, the better convection control can be achieved. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermocapillary‐buoyancy flow of silicon melt in a shallow annular pool

In order to understand the nature of surface spoke patterns on silicon melt in industrial Czochralski furnaces, a series of unsteady three‐dimensional numerical simulations were conducted for thermocapillary‐buoyancy flow of silicon melt in annular pool (inner radius r_i = 15 mm, outer radius r_o = 50 mm, depth d = 3 mm). The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces either are adiabatic or allow heat transfer in the vertical direction. Results show that a small temperature difference in the radial direction generates steady roll‐cell thermocapillary‐buoyancy flow. With large temperature difference, the simulation can predict three‐dimensional oscillatory flow, which is characterized by spoke patterns traveling in the azimuthal direction. The small vertical heat flux (3 W/cm²) does not have significant effects on the characteristics of this oscillatory flow. Details of the flow and temperature disturbances are discussed and the critical conditions for the onset of the oscillatory flow are determined. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heat transfer and convection in Czochralski growth of large BGO Crystals

In the present work, numerical modeling has been performed to analyze heat transfer and melt convection during bismuth germanate Bi₄Ge₃O₁₂ (BGO) crystal growth by the Czochralski growth method. In addition to global heat-transfer modeling, the suggested model accounts for the radiative heat exchange in the crystal and melt convection together with the crystallization front formation. The model helped to analyze the modification of the growth setup made by including additional heater. The numerical predictions obtained with CGSim software agree well with available experimental data.     

Effects on the structural and magnetic properties of amorphous ribbons of (Co0.94Fe0.06)72.5Si12.5B15 caused by 4 MeV Cl2+ ion irradiation

The use of energetic ion irradiation to modify magnetic materials has attracted increasing interest in recent years. The possibility of patterning surfaces on these materials offers a wide range of potential applications particularly in technologies related to magnetic storage media, sensing devices and electromagnetic shielding materials. In this work, ultrasoft non-magnetostrictive (Co_0.94Fe_0.06)72.5Si_12.5B₁₅ amorphous ribbons, 50 μm thick and 0.85 mm wide, fabricated by the chilly block melt spinning technique are irradiated, in their amorphous state, by 4 MeV Cl²⁺ ions with a fluence of 5 × 10¹³ cm⁻². The hysteresis properties of both irradiated and non-irradiated samples are characterized by means of a vibrating sample magnetometer while surface magnetic domain structure is observed by Bitter technique. The presence of an induced magnetic anisotropy in irradiated samples is ascribed to the local damage, caused by ion irradiation treatment, which results in modified coercive field and permeability of the samples. X-ray diffraction results are presented to confirm the amorphicity of the structure even after irradiation with ions.     

Measurements of dendrite tip growth and sidebranching in succinonitrile–acetone alloys

Experiments are carried to investigate free dendritic growth of succinonitrile–acetone alloys in an undercooled melt. The measurements include the steady dendrite tip velocity and radius, the non-axisymmetric amplitude coefficient of the fins near the tip, and the envelope width, projection area, and contour length of the sidebranch structure far from the tip. It is found that the measured dendrite tip growth Péclet numbers agree well with the predictions from a stagnant film model that accounts for thermosolutal convection in the melt. The measured tip selection parameter, σ^?, is verified to be independent of the alloy composition, but shows a strong dependence on the imposed undercooling. The universal amplitude coefficient, A₄, is measured to be equal to 0.004, independent of the undercooling, but the early onset of sidebranching prevents its accurate determination for more concentrated alloys. For the self-similar sidebranch structure far from the tip, scaling laws are obtained for the measured geometrical parameters. While melt convection causes some widening of the sidebranch envelope, and the early onset of sidebranching for alloy dendrites results in a 25% upward shift of the envelope width, the projection area and, hence, the mean width of a sidebranching dendrite, as well as its contour length in the sidebranch plane, obey universal power laws that are independent of the convection intensity and the alloy composition.     

Magnetic studies of intermetallic compounds Al3R (Al11R3) both in the solid and liquid states

The magnetic susceptibility of Al₃R and Al₁₁R₃ (R = Ce, Pr, Sm, Gd, Dy, Ho, Yb) compounds is investigated over wide temperature (300–1900 K) and field (0.2–1.2 T) ranges. It is found that microinclusions of Al₂R can exist in the samples. They are not detectable in ordinary X-ray diffraction but give a significant contribution to the magnetic properties. The average effective magnetic moment per rare-earth atom changes through the rare-earth metals line reaching its maximum for holmium but rather lower than for the pure rare-earth metals. It means that rare-earth elements form covalent bonds with aluminum. These bonds remain in the liquid phase and begin to break down after melting point of Al₂R only. The transition into a true solution state of the melt is somewhere above 1900 K.     

Nanostructured crystals of Sr1?xRxF2+x fluorite phases and their ordering: 6. Microindentation analysis of crystals

Hardness, crack resistance, brittleness, and effective fracture energy have been studied for crystals of 24 fluorite phases Sr_{1 − x} R _x F_{2 + x} (R are 14 rare earth elements (REEs); 0 < x ≤ 0.5) and SrF2 grown by the Bridgman method from a melt. These characteristics change nonlinearly with an increase in the REE content for Sr_{1 − x} R _x F_{2 + x} (0 < x ≤ 0.5) with R = La, Nd, Sm, Gd, and Lu; it is maximum in the range x < 0.1 for all REEs. The changes in a number of REEs have been traced for an isoconcentration series of Sr_0.90 R _0.10F_2.10 crystals (R = La, Nd, Sm, Gd, Ho, Er-Lu, or Y) and crystals (similar in composition) with R = Tb and Dy. The hardness of Sr_{1 − x} R _x F_{2 + x} crystals is higher by a factor of ∼2–3 than that of SrF2. The effect of decrease in microstresses in SrF₂ crystals is confirmed by the isomorphic introduction of R ³⁺ ions into this crystalline matrix.     

3D simulation of the effects of growth parameters on the growth of sapphire crystals using heat exchanger method

3D simulations using the commercial CFDRC and FIDAP code, which are based on finite element techniques, were performed to investigate the effects of anisotropic conductivity on the convexity of the melt–crystal interface and the hot spots of sapphire crystal in a heat‐exchanger‐method crystal growth system. The convection boundary conditions of both the energy input to the crucible by the radiation as well as convection inside the furnace and the energy output through the heat exchanger are modeled. The cross‐sectional flow pattern and the shape of the melt–crystal interface are confirmed by comparing the 3‐D modeling results with previous 2D simulation results. In the 3D model, the “hot spots” in the corners of the crucible are donut shaped, and the shape changes with the value of the conductivity of anisotropic crystal. The outline of the crystal becomes more convex as the conductivity in the z direction (k_sz) increases. The outline of melt–crystal interface is elliptical when the anisotropic conductivity is moving in the radial direction (k_sx and k_sy). The portion at the outline touching the bottom of the crucible is smaller than the maximum outline of the crystal, meaning that the shape at the “hot spot”, changes with the value of the conductivities of anisotropic crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical and analytical modelling of the MHD buoyancy-driven flow in a Bridgman crystal growth configuration

We present analytical and numerical models of magnetohydrodynamic(MHD) buoyancy-driven flow within the liquid pool of a horizontal Bridgman crystal growth furnace, under the influence of a uniform vertical magnetic field B₀. A horizontal differentially heated cylinder, whose aspect ratio (radius to length) is small enough for a fully developed regime to be established in the central core, is considered. With Hartmann layers remaining electrically inactive, a modified Rayleigh number Ra_G, which is the ration of the ordinary Rayleigh number to the square of the Hartmann number, is found to control the MHD reorganisation of the flow. This modified Rayleigh number is a measure of the importance of thermal convection relative to diffusion if velocity is estimated from the balance between the torques of buoyancy and the Laplace force. When Ra_G is much smaller than unity (quasi-diffusive regime), an analytical modelling of the flow, based on a power series of Ra_G, demonstrates that this balance requires secondary vortices within vertical mid-planes of the cylinder, both within the core flow and near the end walls. A 3-D numerical calculation of the flow provides evidence of the transition from a convective MHD flow (when Ra_G is still of the order of unity) to the quasi-diffusive flow, analytically studied. Indeed, this transition takes the form of a rather complex 3-D MHD organisation of the flow which is due to the nonuniformity of the axial temperature gradient along the cylinder.     

The growth and defect structure of CdF2 and nonstoichiometric Cd1 ? xRxF2 + x phases (R are rare earth elements or in): Part VI. The optical properties of Cd0.9R0.1F2.1 crystals

The optical properties of the isoconcentration series of Cd_0.9 R _0.1F_2.1 crystals (R = Y, La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, or Lu) grown from a melt by the Bridgman method have been investigated. The crystals have an anomalous birefringence (∼10⁻⁶) nonuniformly distributed over the sample diameter; the dichroism in them does not exceed 10⁻⁹. Scanning using a spectral modulator showed the nonuniform distribution of rare earth elements over the crystal diameter. The refractive indices n have been measured at wave-lengths of 0.436, 0.546, and 0.589 μm. The character of change in n along the rare-earth series is nonuniform and similar to the change in n in Sr_0.9 R _0.1F_2.1 crystals. It is shown that the refractive indices in Cd_{1 − x} R _x F_{2 + x} crystals, depending on the RF₃ content, can be estimated using the method of molecular refraction additivity. Original Russian Text ? A.F. Konstantinova, T.M. Glushkova, I.I. Buchinskaya, E.A. Krivandina, B.P. Sobolev, 2009, published in Kristallografiya, 2009, Vol. 54, No. 4, pp. 648–651.     

Structure,microstructure and magnetic properties of mixed rare earth oxide (Dy1‐xErx)2O3

The mixed rare earth oxide (Dy_1‐xEr_x)₂O₃ (0.0 ≤ x ≤ 1.0) were synthesized by a sol–gel process. X‐ray and neutron diffraction data were collected and crystal structure and microstructure analyses were performed using Rietveld refinement method. All samples were found to have the same crystal structure and formed solid solutions over the whole range of x. Preferential cationic distribution is found for all samples but with different extent with Dy³⁺ preferring the 8b among the two non‐equivalent sites 8b and 24d of the space group Ia3. The lattice parameter is found to vary linearly with the composition x and a systematic variation is found in the r.m.s microstrain . Magnetization measurements were done in the temperature range 5‐300 K and a behavior in accordance with Curie‐Weiss law was found. Anomalous concentration dependence is found in magnetic susceptibility which is ascribed to the concentration dependence of effective crystal field combined with the contribution of ⁴I_15/2 and ⁶H_15/2 manifold at elevated temperature. The effective magnetic moments μ_eff is found to decrease linearly with composition parameter x, except for sample x=0.5 where the magnetization is enhanced. The Curie‐Weiss paramagnetic temperatures indicated antiferromagnetic interaction. These magnetic results are discussed in view of the cationic distribution. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three dimensional simulation of melt flow in Czochralski crystal growth with steady magnetic fields

Three-dimensional transient numerical simulations were carried out to investigate the melt convection and temperature fluctuations within an industrial Czochralski crucible. To study the magnetic damping effects on the growth process, a vertical magnetic field and a cusp magnetic field were considered. Due to our special interest in the melt convection, only local simulation was conducted. The melt flow was calculated by large-eddy simulation (LES) and the magnetic forces were implemented in the CFD code by solving a set of user-defined scalar (UDS) functions. In the absence of magnetic fields, the numerical results show that the buoyant plumes rise from the crucible to the free surface and the crystal–melt interface, which indicates that the heat and mass transfer phenomena in Si melt can be characterized by the turbulent flow patterns. In the presence of a vertical magnetic field, the temperature fluctuations in the melt are significantly damped, with the buoyant plumes forming regular cylindrical geometries. The cusp magnetic field could also markedly reduce the temperature fluctuations, but the buoyant plumes would break into smaller vortical structures, which gather around the crystal as well as in the center of the crucible bottom. With the present crucible configurations, it is found that the vertical magnetic field with an intensity of 128 mT can damp the temperature fluctuations more effectively than the 40 mT cusp magnetic field, especially in the region near the growing crystal.     

Crystallization of a germanium melt in an external electric field

Data are presented on experimental studies of the influence of an external electric field on crystallization of a germanium melt under the layer of a B₂O₃ flux. It has been found out that with the field supercoolings of the melt sharply change. This effect is due to the change of the number of active nucleation centres at the germanium – B₂O₃ flux interface. The maximum supercoolings of the germanium melt ΔT⁻ = 190 K were obtained when a negative potential was connected to germanium. The dependences of supercooling on preliminary melt overheating were measured.     

Concentration dependences of the unit-cell parameters of nonstoichiometric fluorite-type Na0.5 − x R 0.5 + x F2 + 2x phases (R = rare-earth elements)

Unit-cell parameter a of the cubic phases with a varying composition Na_{0.5 ? x} R _{0.5 + x} F_{2 + 2x} (R = Gd-Lu and Y) and with a fluorite-type structure, is described within an accuracy of ±0.003 Å, by the formula a = 4.454 + 0.874r ₃ + x(6.7238r ₃ ? 7.259) where r ₃ is the Shannon “crystal ionic radius” R ³⁺ at c.n. = 8.