Crucible Rotation Research Articles

Rapid prediction of interface morphology and oxygen transportation in crystal growth based on the response surface method

In this paper, a two-dimensional (2D) axisymmetric model subjected to the gas shear effect and thermal Marangoni effect is developed. It is highlighted that the growth conditions of pulling rate, gas flow rate, crucible, and crystal rotation rates play important roles in determining the crystal behaviors of interface morphology and oxygen transportation during the crystal growth process. A Kriging-based response surface method (RSM) is proposed to rapidly predict the crystal growth behaviors, indicating that the outputs of interface morphology and oxygen concentration can be predicted by the corresponding input growth conditions. By global sensitivity analysis, the pulling rate is identified as the key factor in determining the interface morphology, while gas flow rate and crucible rotation rate have a greater effect on oxygen transportation. Furthermore, these two inputs with the highest sensitivities are used to construct the response surface and predict unknown oxygen transportation. When compared with the numerical simulations, the presented model proves to be an effective tool for reducing measurement time and improving accuracy in predicting crystal behaviors. Our findings provide important insights into understanding the crystal growth process under different growth conditions and inspire a data-driven method for crystal growth prediction.

Decision Tree-Supported Analysis of Gallium Arsenide Growth Using the LEC Method

In this study, an axisymmetric Czochralski furnace model for the LEC growth of gallium arsenide is presented. We produced 88 datasets through computational fluid dynamics simulations. Among the many parameters that affect crystal growth, a total of 13 input parameters were selected, including the geometry and material parameters of the hot zone (crucible, heaters, radiation shield, and crystal), as well as the process parameters (such as pulling and rotation rates, heating power, etc.). Voronkov criteria (v/Gn), interface deflection, and the average interface temperature gradient were selected as the output parameters. We carried out a correlation analysis between the variables and used decision trees to study the impact of the 13 input variables on the output variables. The results indicated that in the growth of gallium arsenide, the main factor affecting interface deflection and the average interface thermal gradients is the crucible rotation rate. For v/Gn, it is the pulling rate.

Design of follow-up superconducting Cusp magnetic field and system performance analysis of Czochralski single crystal furnace

This paper proposes a magnetic system structure for a single crystal furnace that addresses the issue of unreasonable distribution of magnetic field lines on the free surface caused by DHL (Distance between the lower edge of the heat shield and the liquid surface) fluctuation during early stages of crystal growth. The proposed structure adjusts with the fluctuation of the free surface during the crystal pulling process, enabling the magnetic system to positively impact the thermal system. The thermo-magnetic coupling in a 160-type single crystal furnace before and after magnetic system optimization was simulated using the finite element method. Numerical simulation was employed to compare the temperature gradient, S-L (solid–liquid) boundary temperature distribution, and radial oxygen content in the single crystal furnace before and after magnetic system optimization under the conditions of Cr (crystal rotation) and Gr (graphite crucible rotation). The results reveal that the optimized magnetic system helps adjust the shape of the S-L boundary, decrease the temperature gradient, and lower the oxygen levels at the S-L boundary. However, when the Gr is rotated at high speed, although the S-L interface becomes flatter, the temperature gradient and oxygen concentration at the boundary increase. On the other hand, When Cr is at high speed, the S-L boundary tends to become flatter and the temperature gradient at this boundary decreases, but the oxygen concentration at the S-L boundary increases. Compared to the original single crystal furnace with a fixed magnetic system, the single crystal furnace with a lifting magnetic system experiences a 6.34% reduction in radial temperature gradient and a 3.02% reduction in axial temperature gradient during the actual crystal pulling process parameters. The temperature gradient at the S-L boundary decreases by 36.50%, and the radial average oxygen concentration decreases by 26.58%. Furthermore, the temperature distribution of the crystal and melt becomes more uniform, the oxygen content at the S-L boundary is effectively controlled, and the overall crystal quality improves. These findings can serve as a reference for designing a new magnetic system for a single crystal furnace.

Growth and characterization of Fe2+:ZnSe single crystals for tunable mid-infrared lasers

Iron-doped ZnSe (Fe:ZnSe) single crystals were grown by the traveling heater method with the accelerated crucible rotation technique (ACRT) using SnSe as a solvent. The as-grown Fe:ZnSe single crystals were characterized by XRD, Raman, XPS, IR transmission imaging microscope, and the X-ray rocking curve. The results show two kinds of inclusions existing in Fe:ZnSe crystals, i.e. solvent SnSe inclusions, and hexagonal ZnSe inclusions with a wurtzite structure. The inclusions with sizes ranging from 30 to 150 μm were homogeneous distributed with a total concentration of only 2.68 × 102 cm−2. The full width at half-maximum (FWHM) of X-ray rocking curve on (220) diffraction planes was 38 arcsec and the average infrared transmittance exceeded 70%. Furthermore, it was confirmed that the iron ions were successfully incorporated into ZnSe lattice without degrading the crystalline quality, and the bivalence was dominant for iron atoms in Fe:ZnSe crystals, meaning that they are suitable for developing mid-infrared (3–5 μm) gain medium applications.

Effects of melt depth on oxygen transport in silicon crystal growth by continuous-feeding Czochralski method

The continuous-feeding Czochralski method (CCz) is an effective and promising way for the high-quality and large-weight monocrystalline silicon growth. In the CCz technology, the inner crucible is employed to prevent unmelted silicon granules from being transported to the melt-crystal interface, which introduces a new source of oxygen impurities and makes the temperature and flow distribution in the melt complicated. So it is challenging to regulate the oxygen impurities at the m-c interface in the CCz process. The melt depth stays constant during the CCz process, and it determines the crucible area where oxygen impurities are dissolved. Therefore, in order to manage and minimize the oxygen impurities at the m-c interface, controlling the melt depth may be a good way. In the study, the influence of melt depth on oxygen impurity distribution at the melt-crystal interface is investigated using a series of global simulations coupled with the transport of oxygen and carbon impurities. The findings indicate that as melt depth increases, the temperature of the crucible wall inside the inner crucible drops, and oxygen impurities transported from the melt between the inner and outer crucibles to the interior of the inner crucible likewise decrease in content. However, the rate of SiO evaporation at the free melt surface inside the inner crucible essentially stays the same. Therefore, the oxygen impurity content at the melt-crystal (m-c) interface decreases with the increase of melt depth. The paper also suggests that while constructing the scheme for lowering oxygen content, it is necessary to take into account the position relation between the heater and the crucible, the height of the crucible above the free melt surface, and the rotation of the inner crucible.

Particularities of the thermal and oxygen concentration instabilities in a Czochralski process for solar silicon growth

A previous presented numerical model was used to study the time behavior particularities of temperature and oxygen concentration in a Czochralski (Cz) growth process of 200 mm diameter silicon single crystals for photovoltaic applications. First, some important model issues have been addressed: the dependence of the numerical results on the refinement level of the grid and on the model for oxygen equilibrium concentration at the melt-crucible interface. Then a parametrical study have been performed to study how the pulling rate and the rotation rate of the crucible influence the fluctuations of temperature and oxygen concentration near the crystallization interface. The numerical simulations have revealed that the temperature oscillations are closer to a normal distribution than the oxygen concentration, which is closer to a skewed left distribution.Both the increase of crucible rotation rate and pull speed has an effect of “pushing to the left”: the histogram of temperature fluctuations tends from a skewed right distribution to a normal distribution with the increase of the pull speed and crucible rotation values while the oxygen concentration is more skewed to the left. As a general conclusion, the numerical simulations have shown that the oxygen concentration is more sensitive to the crucible rotation than the temperature field, while the pull speed has a stronger effect on temperature oscillations than on the oxygen concentration oscillations.

Study of Flow Pattern Defects and Oxidation Induced Stacking Faults in Czochralski Single-Crystal Silicon Growth

This paper emphasizes that the furnace pressure, crucible rotation, and pulling rate have important effects on interstitial oxygen (Oi) concentrations and micro-defects during growth in a Czochralski single-crystal silicon (CZ-Si) growth furnace. Since oxygen in a silicon ingot influences minority carrier lifetime, different set-points of furnace pressure and crucible rotation were controlled to achieve different degrees of Oi. The Oi content has a positive correlation with furnace pressure and crucible rotation. Various numbers of micro-defects were generated under the influence of different pulling rates, owing to the transformation from liquid to solid. The sample also underwent Secco etching and a high-temperature wet oxidation to observe defects caused by the Oi concentration and pulling rate, namely, flow pattern defects (FPDs) and oxidation-induced stacking faults (OISFs). Optical microscopy was employed to confirm the surface topography, and for defect number counting, to observe the correlation between the defects and the minority carrier lifetime. The overall results show that the minority carrier lifetime is mainly dominated by OISFs under high Oi content and FPDs under low Oi content. Therefore, growth using a CZ-Si growth furnace should be carried out with low furnace pressure, low crucible rotation, and low pulling rate to reduce micro-defects.

Control of growth interface shape during InGaSb growth by vertical gradient freezing under microgravity, and optimization using machine learning

The growth of high-quality InGaSb crystals by Vertical Gradient Freezing (VGF) under microgravity was numerically simulated. Machine learning tools were used to optimize the growth conditions. The study focuses on controlling growth interface shape which directly affects the quality and homogeneity of the grown crystals. Initially, Bayesian optimization was utilized to search for the most favorable growth conditions that promote a desirable flatter growth interface shape. Afterward, a reinforcement learning model was developed. The system was subjected to a lower temperature gradient near the feed crystal and to crucible rotation with a rate ranging according to the obtained optimal strategy. Results showed that the interface deformation is considerably reduced, and a flatter growth interface could be maintained. The growth rate and solute concentration uniformity were also improved. This adaptive control recipe proves to hold great potential in the continuous and rapid optimization of other crystal growth processes.

Cl-Doped CdTe Crystal Growth for Medical Imaging Applications

CdTe:Cl doped single crystals were grown under conditions of tellurium excess by using an accelerated crucible rotation technique, modified vertical Bridgman (ACRT-MVB) method. Chlorine dopant levels were kept at 4.4 × 1019 at·cm−3, for all growths, while the Te excess level varied from 3.5 to 15% by weight. The relationship between the detector performance, Te inclusions, and resistivity was investigated in detail. Tellurium excess caused additional nucleation which decreased the average single crystal grain size. At the same time, the increasing Te excess level improved the electrical transport properties. In the three Cl-doped, and one In-doped CdTe crystals, detectors from Cl-doped CdTe grown under 15% Te excess showed better response to gammas and alphas, and high µτ for electrons (1.8 × 10−3 cm2/V), as well as for holes (5.1 × 10−4 cm2/V). The full-width half maximum for the Cl-doped CdTe were very large, as the peaks were broadened, especially at high bias. This could be due to hole trapping in a Cl-related A-center (VCd-ClTe)−, and in Cd- vacancies (VCd)−, and electron trapping in Te-antisites (TeCd)+.

Impact of dopant-induced band tails on optical spectra, charge carrier transport, and dynamics in single-crystal CdTe

Cadmium telluride (CdTe) semiconductors are used in thin-film photovoltaics, detectors, and other optoelectronic applications. For all technologies, higher efficiency and sensitivity are achieved with reduced charge carrier recombination. In this study, we use state-of-the-art CdTe single crystals and electro-optical measurements to develop a detailed understanding of recombination rate dependence on excitation and temperature in CdTe. We study recombination and carrier dynamics in high-resistivity (undoped) and arsenic (As)-doped CdTe by employing absorption, the Hall effect, time-resolved photoluminescence, and pump-probe in the 80–600 K temperature range. We report extraordinarily long lifetimes (30 µs) at low temperatures in bulk undoped CdTe. Temperature dependencies of carrier density and mobility reveal ionization of the main acceptors and donors as well as dominant scattering by ionized impurities. We also distinguish different recombination defects. In particular, shallow AsTe and deep VCd−AsCd acceptors were responsible for p-type conductivity. AX donors were responsible for electron capture, while nonradiative recombination centers (VCd−AsTe, As2 precipitates), and native defects (VCd−TeCd) were found to be dominant in p-type and n-type CdTe, respectively. Bimolecular and surface recombination rate temperature dependencies were also revealed, with bimolecular coefficient T−3/2 temperature dependence and 170 meV effective surface barrier, leading to an increase in surface recombination velocity at high temperatures and excitations. The results of this study allowed us to conclude that enhanced crucible rotation growth of As-doped CdTe is advantageous to As activation, leading to longer lifetimes and larger mobilities and open-circuit voltages due to lower absorption and trapping.

Mechanism to form ring-like distributed oxidation-induced stacking fault bands through relaxing thermal stress during stopping the growth in CZ silicon crystals

This paper aims to study the mechanism to form ring-like distributed oxidation-induced stacking fault (R-OSF) bands in CZ silicon. In this experiment, pulling crystals was stopped during the growth, and the crystals were held for predetermined periods contacting the melt while the seed rotation and converse crucible rotation were maintained. Then, the crystals were detached from the melt and cooled rapidly to freeze the defect distribution. In CZ crystals during the growth, high-temperature mass (crystalized silicon) is transferred upward from the growth interface with the crystal pulling. The top of the crystals is directly cooled by the cooling water chamber, while the peripheral part is heated by the radiation from the heater through the gap under the heat shield and the radiation from the melt surface. Thus, the temperature of the upper center part becomes lower than that of the peripheral part, and isotherms in the crystal form U-shape. When the growth is stopped, the crystals also stop raising the “high-temperature mass” from the growth interface. Thus, cooling rapidly proceeds from the center upper part to the growth interface, and the U-shape isotherms fall downward. When the temperature of a region along a U-shaped isotherm decreases to around 1000 ℃, and a temperature gradient exceeding a certain threshold also forms vertically to the U-shaped isotherm, a thermal stress (expansion stress) is applied from the high-temperature side part to the low-temperature center part. At this time, oxygen precipitates, the nuclei of the R-OSFs, are presumably generated there to relax the thermal stress. Although some researchers have presumed that the R-OSF band is a vacancies (Vs)/interstitials (Is) boundary formed at a temperature near the melting point, the results of this study contradict their presumption.

The crystal growth of ZnSe by the traveling heater method with the accelerated crucible rotation technique

The accelerated crucible rotation technique (ACRT) was employed in the traveling heater method (THM) growth of ZnSe crystals to manage the convection in the melt. Considering the large solubility, the PbCl2 was chosen as a solvent. During the growth, the growth interface changed from concave to slightly convex depending on the ACRT parameters. The ZnSe single crystals were obtained, when the ACRT with the maximum rotation of 15 rpm at the suitable growth rate (2.4 mm/day) was used. Furthermore, the chemical mappings of the energy-dispersive X-ray spectroscopy (EDS) show that there are two kinds of the solvent inclusions existed in the grown ZnSe crystals, i.e. PbCl2 and ZnCl2. And the PbCl2 inclusions are homogeneous with a total concentration of 7.03 × 102 cm−2. In addition, the FWHM on X-ray rocking curve of the (220) diffraction planes is 22 arcsec. The chemical etch pit density on the (110) cleavage plane is (1–2) × 105 cm−2 and the average infrared transmittance is over 68% in the range from 650 cm−1 to 4000 cm−1. All of these indicate that the grown ZnSe single crystals have good crystalline quality.

Virtual experiments of Czochralski growth of silicon using machine learning: Influence of processing parameters on interstitial oxygen concentration

For a process development, it is crucial to know the influence of each process parameter on the process result. However, it is difficult to gauge the influence by experimentally changing only one parameter value owing to constraints of the combination of the parameter values and experimental costs. Machine learning models can predict results that will be obtained under conditions that have not been considered for the experiment. Utilizing a virtual experiment based on a machine learning model, we evaluated the influence of process parameters on the interstitial oxygen (Oi) concentration in Czochralski-grown Si crystals. A dataset for the parameter analysis was constructed, wherein the crucible rotation rate and/or Ar flow rate were systematically changed while maintaining the other parameters at the reference value of an experimental datum. Thereafter, the dataset was input into a neural network model that had been trained with 450 ingot data; consequently, the corresponding Oi concentration was obtained. The evaluated results were consistent with the scientific knowledge previously studied: Oi concentration increases with increasing crucible rotation rate and decreasing Ar flow rate. Furthermore, the two-parameter analysis illustrated a nonlinear relationship between the parameters quantitatively. These approaches demonstrating the Czochralski growth of Si in this study are useful in other crystal growth processes as well.

Three-dimensional characteristics of turbulent flow and heat transfer in Czochralski silicon melt with different cusp magnetic field configurations

Three-dimensional unsteady simulations are performed for the turbulent flow and heat transfer in a Czochralski silicon melt for 300 mm crystal growth. The influence of the horizontal symmetry plane in the cusp magnetic field on the melt flow, temperature field, and crystal/melt interface is systematically analyzed. The numerical results show that the melt velocity and its fluctuation near the interface decrease, while the temperature and its fluctuation increase gradually with the downward horizontal symmetry plane position. For each horizontal symmetry plane position, the oscillation frequencies of melt temperature and velocity consist of a basic frequency and its integer multiple frequencies. Thermal waves with a regular shape rotate on the melt-free surface, and the rotational direction is consistent with the crucible rotation. The interface shape is strongly associated with the heat transfer near the interface, which depends on the melt flow direction and velocity magnitude as well as the temperature gradient below the crystal. In addition, the oscillation of interface temperature is affected by the melt flow below the crystal, changing from high-frequency small fluctuation to low-frequency large fluctuation with the horizontal symmetry plane moving down.

Granulated Expanded Glass Manufacturing Method Using Electromagnetic Waves

The paper presents experimental results obtained in the process of experimental manufacture in a microwave oven of lightweight granulated glass aggregates. The process was conducted to obtain the highest dimensional class (between 18-23 mm), the almost spherical shape of the aggregates being facilitated by cold processing of raw spherical pellets (between 11-15 mm) containing the powder mixture formed by glass waste, borax. calcium carbonate, aqueous sodium silicate solution and water addition and then rotation of the high electromagnetic wave susceptible ceramic crucible containing raw pellets during the heat treatment at temperatures between 822-835 ºC. In terms of quality, the expanded glass aggregate granules are almost similar to those manufactured in conventional rotary kilns heated by burning fuel, having the following characteristics: bulk density of 0.17 g/cm3, compressive strength of 2.2 MPa, thermal conductivity of 0.047 W/m·K, water absorption of 1 vol. % and pore size between 0.3-0.6 mm. The experimental product has not yet been tested as a raw material in the manufacture of some light weight concretes, but the use of similar granulated glass aggregates manufactured in the world confirms the ability of this aggregate type to produce light weight and energy efficient concretes for building construction. 

Granulated Expanded Glass Manufacturing Method Using Electromagnetic Waves

The paper presents experimental results obtained in the process of experimental manufacture in a microwave oven of lightweight granulated glass aggregates. The process was conducted to obtain the highest dimensional class (between 18-23 mm), the almost spherical shape of the aggregates being facilitated by cold processing of raw spherical pellets (between 11-15 mm) containing the powder mixture formed by glass waste, borax. calcium carbonate, aqueous sodium silicate solution and water addition and then rotation of the high electromagnetic wave susceptible ceramic crucible containing raw pellets during the heat treatment at temperatures between 822-835 ºC. In terms of quality, the expanded glass aggregate granules are almost similar to those manufactured in conventional rotary kilns heated by burning fuel, having the following characteristics: bulk density of 0.17 g/cm3, compressive strength of 2.2 MPa, thermal conductivity of 0.047 W/m·K, water absorption of 1 vol. % and pore size between 0.3-0.6 mm. The experimental product has not yet been tested as a raw material in the manufacture of some light weight concretes, but the use of similar granulated glass aggregates manufactured in the world confirms the ability of this aggregate type to produce light weight and energy efficient concretes for building construction.

Stability-based optimization of ACRT for the growth of CZT by the traveling heater method

Numerical modeling is employed to study the effects of several accelerated crucible rotation technique (ACRT) rotation schedules on the growth of cadmium zinc telluride (CZT) by the traveling heater method (THM). In conjunction with these analyses, a measure is developed to estimate the amplitude of disturbances associated with cellular interface growth morphologies that develop over time and across the melt-solid interface. This disturbance amplitude measure is used to assess the ability of ACRT to stabilize the growth interface and thereby minimize inclusion formation processes. Notably, our analyses reveal that interfacial instability is not well correlated with melt undercooling, explaining why classical ACRT approaches to reduce undercooling by mixing may not stabilize growth. Computations show that interface stability is best achieved via rotation schedules that accentuate outward Ekman flows during spin-up and, during spin-down, eliminate Taylor-Görtler flows and minimize inward Ekman flows.

The effects of ACRT on melt undercooling during the growth of CZT via the traveling heater method: Ekman versus Taylor-Görtler flows

For the first time, a comprehensive model for the traveling heater method, including detailed species transport and phase-change thermodynamics, is applied to understand the effects of accelerated crucible rotation (ACRT) on the growth of cadmium zinc telluride. A rotation schedule that is designed from classical considerations does not completely mix the melt, rather undercooled regions of localized melt are swept periodically across the growth interface. Even without melt homogenization, these ACRT-driven flows disrupt the persistent undercooling that occurs during THM growth without rotation. An ACRT schedule designed to promote Ekman flows results in lower levels of melt undercooling than a schedule designed to promote Taylor-Görtler flows and greater mixing.

Optimizing ACRT to reduce inclusion formation during the VGF growth of cadmium zinc telluride: II. Application to experiments

Two different accelerated crucible rotation technique (ACRT) rotation schedules are assessed, via theoretical computations and growth experiments, according to their ability to reduce tellurium-rich inclusions during the vertical gradient freeze (VGF) of cadmium zinc telluride (CZT). A vigorous rotation schedule based on classical ACRT guidelines produces a well-mixed melt that is expected to reduce tellurium inclusions compared to growth without crucible rotation. In contrast, a new ACRT schedule, derived from model-based optimization for interface stability, employs slower rotation with longer periods and is predicted to further reduce inclusions. Growth experiments corroborate these expectations. Namely, both ACRT schedules result in crystals with inclusion size and volume significantly decreased from levels found in material grown with no rotation, and material grown using the computationally optimized ACRT parameters exhibits a median inclusion size that is smaller and with a sharper distribution than in material grown via classical ACRT.

Optimizing ACRT to reduce inclusion formation during the VGF growth of cadmium zinc telluride: I. Computational approach

Theoretical computations reveal insight into parameters that govern the accelerated crucible rotation technique (ACRT) applied to the gradient freeze (VGF) growth of cadmium zinc telluride (CZT). A metric based on the classic Mullins and Sekerka instability criterion is put forth that provides a quantitative means of assessing the impact of different ACRT rotation schedules on morphological stability and inclusion formation during CZT growth. This metric is employed in a 2-k factorial design of experiments that identifies the maximum rotation rate as the most important ACRT parameter, followed by the acceleration period and the rest period. Subsequent optimization of rotation schedule is performed for a specific VGF growth system, and mechanistic explanations are provided for the preferred ACRT schedule, which improves interface stability via slower rotation rates and longer acceleration periods than would be applied using classical ACRT schedules.