Czochralski Melt Research Articles

Single crystal growth of 4-aminobenzophenone (ABP) by micro-capillary Czochralski melt technique for second harmonic generation (SHG) applications

Single crystal of 4-aminobenzophenone (ABP) was grown by micro-capillary Czochralski (mc-CzT) pulling technique from melt using a laboratory designed mini-Czochralski crystal puller set-up with its seed-rod attached with micro-capillary tube. The capillary action of the melt at the tip of the micro tube was carefully controlled in such a way that a single crystal nucleation was induced at the melt interface. Optimization of the melt temperature along with successive control of the rotation and upward pulling rates of the micro-capillary tube led to a successful single crystal growth of ABP. Crystal structure of the grown ABP was confirmed by single crystal X-ray diffraction (SCXRD) structural refinement and the molecular packing stability in the unit cell was studied through intermolecular hydrogen bonding interactions via theoretical means. Further, powder X-ray diffraction (PXRD), UV–visible-near IR (UV–vis-NIR), Fourier-transform infrared (FTIR) spectroscopy and differential scanning calorimetry (DSC) analyses were carried out to confirm the crystalline purity, optical transparency, modes of molecular vibrations and thermal stability of the grown crystal. Kurtz and Perry technique was used to study second harmonic generation (SHG) ability of the grown ABP crystal and found that the SHG efficiency was about 15 times that of potassium dihydrogen phosphate (KDP) and 5 times that of urea.

Thermofluid Characteristics of Czochralski Melt Convection Using 3D URANS Computations

Turbulent characteristics of Czochralski melt flow are presented using the unsteady Reynolds-averaged Navier–Stokes (URANS) turbulence modeling approach. Three-dimensional, transient computations were performed using the Launder and Sharma low-Re k-ε model and Menter shear stress transport (SST) k-ω model on an idealized Czochralski setup with counterrotating crystal and crucible. A comparative assessment is performed between these two Reynolds-averaged Navier–Stokes (RANS) models in capturing turbulent thermal and flow behaviors. It was observed that the SST k-ω model predicted a better resolution of the Czochralski melt flow capturing the near wall thermal gradients, resolving stronger convective flow at the melt free surface, deciphering more number of characteristics Czochralski recirculating cells along with predicting large number of coherent eddy structures and vortex cores distributed in the melt and hence a larger level of turbulent intensity in the Czochralski melt compared with that by Launder and Sharma low-Re k-ε model.

A study of thermo-fluid characteristics of Czochralski melt using rotation and curvature corrected Partially-Averaged Navier-Stokes (PANS) turbulence models

A Czochralski melt flow encounters the effects of anisotropic body forces owing to the system rotation as well as significant streamline curvature due to inherent vortical structures and flow past curved surfaces. Two-equation eddy-viscosity models lack the ability to capture the flow anisotropy and curvature effects. Here we present the first study on the thermo-fluid characteristics of Czochralski melt using rotation and streamline curvature corrected Partially-Averaged Navier-Stokes (PANS) adaptations of the low-Re k-ε and SST k-ω models. The paper presents physical insights to the new PANS turbulence modelling approach highlighting improvements in the predicting capability of PANS models with the incorporation of rotation and curvature corrections. The PANS models showed good agreement with the results available in the literature (both experimental and computational). In addition for the PANS low-Re k-ε model it was observed that the prediction of the typical Czochralski melt flow structure in terms of shape, relative size and orientation of the characteristic cells improved with rotation and curvature corrections. Further thermal fluctuations and vortex cores also reduced in the melt in the case of the PANS low-Re k-ε model showing stabilization of flow. The corresponding rotation and curvature modification to the PANS SST k-ω model corrected the flow dynamics from a buoyancy dominated to rotationally driven along with an increase in the thermal fluctuations and vortex cores in the Czochralski melt resulting in a destabilization of the melt flow.

Deciphering the flow structure of Czochralski melt using Partially Averaged Navier–Stokes (PANS) method

Czochralski melt flow is an outcome of complex interactions of centrifugal, buoyancy, coriolis and surface tension forces, which act at different length and time scales. As a consequence, the characteristic flow structures that develop in the melt are delineated in terms of recirculating flow cells typical of rotating Bénard–Marangoni convection. In the present study, Partially Averaged Navier–Stokes (PANS) method is used for the first time to study an idealized Czochralski crystal growth set-up. It is observed that with a reduction in the PANS filter width, more turbulent scales are resolved and the present PANS model is able to resolve almost all the characteristic flow structures in the Czochralski flow at a comparatively lower computational cost compared with more advanced turbulence modelling tools, such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES).

Partially-Averaged Navier-Stokes (PANS) approach for study of fluid flow and heat transfer characteristics in Czochralski melt

The Partially-Averaged Navier-Stokes (PANS) approach has been applied for the first time to model turbulent flow and heat transfer in an ideal Czochralski set up with the realistic boundary conditions. This method provides variable level of resolution ranging from the Reynolds-Averaged Navier-Stokes (RANS) modelling to Direct Numerical Simulation (DNS) based on the filter control parameter. For the present case, a low-Re PANS model has been developed for Czochralski melt flow, which includes the effect of coriolis, centrifugal, buoyant and surface tension induced forces. The aim of the present study is to assess improvement in results on switching to PANS modelling from unsteady RANS (URANS) approach on the same computational mesh. The PANS computed results were found to be in good agreement with the reported experimental, DNS and Large Eddy Simulation (LES) data. A clear improvement in computational accuracy is observed in switching from the URANS approach to the PANS methodology. The computed results further improved with a reduction in the PANS filter width. Further the capability of the PANS model to capture key characteristics of the Czochralski crystal growth is also highlighted. It was observed that the PANS model was able to resolve the three-dimensional turbulent nature of the melt, characteristic flow structures arising due to flow instabilities and generation of thermal plumes and vortices in the Czochralski melt.

Effect of the capillary meniscus height on the instability of large Prandtl number Czochralski melt flow

Effect of the capillary meniscus on the instability of large Prandtl number Czochralski melt flow is studied experimentally. The measurements are conducted in two experimental facilities by two independent non-intrusive optical techniques. The quantitative results are presented as dependencies of the critical Grashof number (critical temperature difference) on the meniscus height for different Prandtl numbers, radii and aspect ratios. The results show that with increase of the meniscus height the critical temperature difference noticeably grows and sometimes doubles. Recently reported parametric relations for the critical Grashof number and oscillations frequency are extended to include parameters of the meniscus.

Rotationally-driven axisymmetric oscillatory convection in a semitransparent Czochralski melt model

A numerical study was carried out to investigate the effect of surface tension-driven convection on the transition of flow modes in an axisymmetric Czochralski oxide melt model. Computational results were obtained over a reasonably wide range of the crystal dummy rotation rate for the cases with and without Marangoni effect. The transition of the flow from steady-state to an axisymmetric oscillatory one was found to be occurred at a threshold value of the ratio between buoyancy and the rotationally-driven forces, which is considerably smaller in the presence of the Marangoni flow. This was shown that, in the presence of thermocapillary forces, the descending cold plume has a larger impact on the thermal field if compared to the case in which the Marangoni effect was ignored. Depending on the circumstances, each of the two different mechanisms, i.e., the rotating Rayleigh–Benard instability and the baroclinic instability, may play a dominant role in the steady-oscillatory flow transition. Thermocapillary effect on the mechanism of instability giving rise to the transition of the convective flow was studied.

Experimental study of cold plume instability in large Prandtl number Czochralski melt: Parametric dependences and scaling laws

A parametric experimental study of the cold plume instability that appears in the large-Prandtl-number Czochralski melt flows is reported. The critical temperature difference (the critical Grashof number) and the frequency of appearing oscillations were measured for varying Prandtl numbers, aspect ratios of the melt, and crystal/crucible radii ratio. The measurements were carried out by two independent and fully non-intrusive experimental techniques. The results are reported as dimensional and dimensionless parametric dependences, and then are joined into relatively simple empirical relations showing how the critical Grashof number and the frequency of emerging oscillations depend on other parameters.

Convective Interactions and Heat Transfer in a Czochralski Melt with a Model Phase Boundary of Two Different Shapes

Convective Interactions and Heat Transfer in a Czochralski Melt with a Model Phase Boundary of Two Different Shapes

Synthesis, crystal growth and mechanical properties of Bismuth Silicon Oxide (BSO) single crystal

Bismuth Silicon Oxide (BSO) is an efficient material for piezo-electric and electro-optic applications. In this article, growth of BSO single crystal by high temperature Czochralski melt growth technique and its detailed mechanical characterization by Vickers microhardness, fracture toughness, crack propagation, brittleness index and yield strength have been reported. The raw material was synthesized by solid state reaction using the stoichiometric ratio of high purity bismuth tri-oxide and silicon di-oxide. The synthesized material was charged in the platinum crucible and then melted. The required rotation and pulling rate was optimized for BSO single crystal growth and good quality single crystal has been harvested after a time span of 5days. Powder X-ray diffraction analysis confirms the parent crystallization phase of BSO. The experimentally studied mechanical behavior of the crystal is explained using various theoretical models. The anisotropic nature of the crystals is studied using Knoop indentation technique.

Experimental Modelling of Czochralski Melt Flow with a Slow Crystal Dummy Rotation

This study examines the e ect of slow crystal dummy rotation on three-dimensional oscillatory instability and time-dependent supercritical ow states in a Czochralski melt ow experimental model. To enable further comparison with numerical modelling, the experiments are carried out using a 20 cSt silicone oil as an experimental liquid and in a large diameter crucible, which allows one to work in a narrow temperature interval, so that temperature dependence of all the thermophysical properties of the experimental liquid can be neglected. The measurements con rm, partially qualitatively and partially quantitatively, earlier numerical predictions on destabilization ofthe Czochralski convective ow by a slow rotation. A simple power dependence of ow oscillations frequency on the Grashof and rotational Reynolds numbers that ts all the experimental runs was found.

On experimental and numerical prediction of instabilities in Czochralski melt flow configuration

A new experimental facility for experimental validation of numerical codes calculating Czochralski melt flow is described. The setup is built to make all the boundary conditions reproducible in a mathematical model. Measurements are focused on the steady-oscillatory flow transition, which is defined by appearance of temperature oscillations measured independently by thermocouples and interferometer. Location of thermocouples is defined according to numerical predictions, which ensures measurements at locations where oscillations amplitude is large. Current state of comparison of experimental and numerical results is discussed.

Calibration of the Enthalpy-Porosity Based Method for CZ Silicon Growth

A global transport model for industrial Czochralski (CZ) silicon growth is reported in the paper. The model quantifies the temperature fields in all components of the growth system. The heat transport by the conduction, convection (melt and argon flows) and radiation are treated along with the momentum balance in the presence of the static magnetic fields. The crystallization process is modeled by an enthalpy-porosity method in which, the phase change occurs across a finite region defined by volumetric sink/source of heat (enthalpy) and momentum. The momentum sink/source is formulated based on the Darcy's law for porous medium, which is simply a numerical treatment for the isothermal solidification. The flow field in the Czochralski melt predicted by the global enthalpy-porosity based model is compared with that predicted by a more accurate simplified local model. Our studies indicate that the intensity of the flow induced by the presence of the crystal/melt interface is underestimated by the enthalpy-porosity based formulation.

An application of proper orthogonal decomposition to the stability analysis of Czochralski melt flows

In Czochralski (Cz) crystal growth, the observed complicated melt flows are caused by different types of instability such as buoyancy-induced instability, Marangoni instability or baroclinic instability. In order to grow single crystals of large size and high quality, it is very important to strictly control these melt flows, and in particular to know which instability is dominant in such flows. Proper orthogonal decomposition (POD) is a powerful method to disclose the basic structures of complicated flows. It was traditionally used to analyze flow structures and, more recently, to construct low-order dynamic models able to reproduce complicated flows. An attempt to apply POD to analyze the flow instabilities was conducted in the case of the oscillatory melt flows occurring in an axisymmetric Cz configuration and caused by both buoyancy-induced and surface tension-induced instabilities. Direct numerical simulation was used to obtain the flow fields driven by both buoyancy and surface tension and also the flow fields driven by one of these forces alone. POD was then employed to extract the basic modes from the flow fields. By comparing the basic modes between these situations, the dominant instability involved in such complicated flows has been revealed. In addition, it was found that the basic modes corresponding to buoyancy-induced instability are global and rotating and those to Marangoni-induced instability are local and traveling. All these indicate that the POD could be a powerful method in instability analysis.

The effect of crystal rotation direction on the thermal and velocity fields of a Czochralski system with a low Prandtl number melt

The purpose of this study is to understand the effect of crystal co- and counter-rotation on the thermal and velocity fields of a Czochralski (Cz) melt in a large crucible. The physical modeling of the Cz system was performed using Wood's metal, which has a similar Prandtl ( Pr) number (=0.019) with Si melt and a low melting temperature (70 °C). The velocities and temperatures in a large crucible with 800 mm diameter were measured using an incorporated magnetic probe and thermocouples, respectively. The rate of crystal rotation affects the temperature and velocity fields. Without crystal rotation, the maximum thermal fluctuation region is located under the crystal due to buoyancy convection. With increasing crystal rotations rate, however, the maximum thermal fluctuation region migrates toward the crucible sidewall. When the rate of crystal counter-rotation is increased, the azimuthal velocities decrease and the thermal fluctuations are reduced at the edge of the crystal. With increasing crystal co-rotation rate, however, the azimuthal velocities increase considerably and the temperature fluctuations remain strongly at the edge of the crystal. The results of 3-D numerical simulations using the k– ε turbulent model are well in agreement with the experimental results.

411 Cz法流動における非導電性流体の磁化力対流(GS 熱工学I)

411 Cz法流動における非導電性流体の磁化力対流(GS 熱工学I)

Characteristics of thermal fluctuation in a low Pr number melt at a large crucible for Czochralski crystal growth method

The purpose of this study is to understand the characteristics of thermal fluctuation in the Czochralski (Cz) melt of a large crucible. The physical modelling of Cz system used Wood's metal that has a similar Pr number with Si melt and a low melting temperature (70 °C). The thermal fluctuations in a large crucible with 800 mm diameter, corresponding Grashof number ( Gr) ∼10 10 and Rayleigh number ( Ra) ∼5×10 6 are analyzed. Crucible and crystal rotation rates affect the main frequencies and amplitude of fluctuations at various positions. The crystal rotation is a dominant factor at the center of the crystal. Both crystal and crucible rotation affect the temperature fluctuation near the edge crystal region when the crystal rotation rate is low.

Numerical study of three-dimensional instabilities in a hydrodynamic model of Czochralski growth

A computational approach to the study of three-dimensional instabilities of flows in a Czochralski crucible is proposed. The flow is driven by buoyancy, thermocapillarity and rotation of the crystal and the crucible. The thermal boundary conditions account for the prescribed temperatures or heat flux, as well as convective and radiative heating or cooling of the boundaries. The numerical approach is based on finite volume discretization and consists of a Newton-type solver for the calculation of the steady flow states and an Arnoldi solver for the solution of the eigenvalue problems associated with the linear stability of the flow. Preliminary test calculations and examples of stability studies for the Czochralski melt flow are reported.

Experimental investigation of the temperature disturbances in the azimuthal cross-section of the Czochralski melt model

Experimental investigation of the temperature disturbances in the azimuthal cross-section of the Czochralski melt model

Growth and optical activity of strontium tantalum gallium silicon oxide (Sr3TaGa3Si2O14, STGS)

Single crystals of strontium tantalum gallium silicon oxide were grown with high perfection along the Cartesian Y-axis [12.0] by conventional Czochralski melt pulling technique. The crystals grew with an atomically smooth phase boundary as confirmed by straight growth striations along the entire length of the crystal. The optical transmission in the c-(Z)direction (optical axis) was determined as a function of the wavelength f(λ) between 350 nm and 850 nm. From the extrema of the periodic optical transmission curve between crossed polarisers a specific rotation of 175°/mm at a wavelength of 300 nm was obtained. This values is lower than that of SNGS with 230°/mm.