Crucible Rotation Rate 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.

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.

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.

Effects of different cusp magnetic ratios and crucible rotation conditions on oxygen transport and point defect formation during Cz silicon crystal growth

The effects of different crucible counter- and iso-rotation rates and cusp magnetic ratios (MRs) on the melt flow, temperature, oxygen content, and point defect formation during the growth of a 5-inch diameter silicon crystal are discussed numerically. In cases without a cusp magnetic field (CMF), the oxygen content gets smaller at a low crucible rotation speed than at a high one, for both counter- and iso-rotation conditions. This trend is reversed under a CMF. The flow field is controlled by the crucible rotation rate, the rotation direction between the crucible and the crystal, and the MR. Since the melt flow motion is retarded by the Lorentz force at a high MR, diffusion has a greater effect on oxygen transport in the bulk melt. It promotes the transport of oxygen atoms from the crucible wall towards the melt surface and the growth interface. The point defect density is quite dependent on the thermal field arising from changes in the growth interface shape. Microdefects in the silicon crystal can be reduced in density and enhanced in the radial uniformity using a high crucible iso-rotation rate and high unbalanced MR. A flatter shape of growth interface can be obtained under these growth conditions.

Effect of the pulling, crystal and crucible rotation rate on the thermal stress and the melt–crystal interface in the Czochralski growth of germanium crystals

The effect of the pulling rate on the melt–crystal interface shape and melt streamline is investigated.

Optimization of the melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process using an artificial neural network and a genetic algorithm

The melt/crystal interface shape and oxygen concentration during the Czochralski silicon crystal growth process significantly influence the crystal quality. In this paper, an optimization system with the combination of an artificial neural network and a genetic algorithm is proposed to optimize the growth parameters during the growth process. Flattening the melt/crystal interface and reducing the oxygen concentration along the interface were chosen as the optimization targets. Two important growth parameters, the crystal rotation rate and crucible rotation rate, were chosen as optimization variables. First, a global heat and mass transfer model was developed to simulate the crystal growth process and then tested with experimental data. The verified heat and mass transfer model was then used to train an artificial neural network with the aim of rapidly assessing the complex nonlinear dependence of the interface shape and oxygen concentration on the growth parameters. The trained neural network combined with a genetic algorithm was then used to obtain the optimal growth parameters. Both deflection of the melt/crystal interface and the oxygen concentration along the interface decreased after optimization. Finally, the optimal growth parameters were checked in the heat and mass transfer model to evaluate the performance of the optimization system. The proposed method will also be useful for optimization of other crystal growth processes.

Eddy-resolving numerical simulation of silicon melt convection in a Czochralski crucible: effects of radiation from the free surface at various crucible rotation rates

The contribution covers results of numerical study based on conjugate heat transfer formulation of turbulent silicon melt convection in an industrial system for CZ Si-crystal growth of 100 mm diameter crystals. The computations have been performed using an eddy-resolving method treated as Implicit LES for two values of the emissivity from the melt free surface (0.25 and 0.3) and the crucible rotation rate of 2 and 5 rpm. The effects of these parameters on melt convection and characteristics of heat transfer are analyzed.

Melt surface change measurement under different crucible rotations in Czochralski furnace using an image-processing method

Effect of different crucible rotations on the silicon melt surface in Czochralski furnace is studied using an image-based measurement system. The mathematical model on the relationship between the target feature in the image and the melt level is discussed. A new improved approach based on Otsu method is applied to segment the feature area from the imperfect image due to uneven illumination. The calibration experiment indicates that the measurement system has resolution of 0.00371 mm. The effectiveness experiment shows that system measurements are very accurate. The surfaces of silicon melt with different crucible rotation rates are measured and analyzed. The result reveals that the melt surface becomes a paraboloid shape with crucible rotation. Moreover, crucible rotations cause more fluctuation on the melt surface under less silicon melt mass. This work may provide us with an effective method to monitor the melt surface change during crystal growth.

Numerical Simulation of Thermal-Solutal Capillary-Buoyancy Flow of Ge1–xSix Single Crystals Driven by Surface-Tension and Rotation in a Czochralski Configuration

A series of three-dimensional numerical simulations were performed to understand the thermal-solutal capillary-buoyancy flow of Ge1-xSix melts during Czochralski crystal growth with a rotating crystal or crucible. The crystal and crucible rotation Reynolds numbers in this work are 0∼3.5 × 103 (0∼4.4 rpm) and 0∼−2.4 × 103 (0∼−1.5 rpm), respectively. Simulation results show that if the thermal capillary Reynolds number is relatively low, the flow will be steady and axisymmetric, even though the crystal or crucible rotates at a constant rate. The critical thermal capillary Reynolds number for the initiation of the three-dimensional oscillatory flow is larger than that of pure fluids. As the crystal or crucible rotation rate increases, the critical thermal capillary Reynolds number first increases and then decreases. The dominant flow pattern after the flow destabilization is azimuthal traveling waves. Furthermore, a reversed evolution from the oscillatory spoke pattern to traveling waves appears in the melt. Once the crystal or crucible rotation rate is relatively large, the traveling waves respectively evolve to rotating waves at the crystal rotation and a spindle-like pattern at the crucible rotation. In addition, the maximum amplitude of solute concentration oscillation on the free surface initially decreases, but finally rises with the crystal or crucible rotation rate increasing.

Effect of the crucible/crystal rotation on thermocapillary instability in a shallow Czochralski configuration

To understand the effects of crucible/crystal rotation on the instability of thermocapillary flow in a shallow Czochralski configuration, a series of linear stability analysis were performed by using Legendre spectral element method, and the energy analysis was applied to explore the instability mechanism. The results indicate that there are two types of instabilities with the increase of dimensionless crucible rotation rate ωc. Thermocapillary force and crucible rotation are the main causes of flow instability for low and high crucible rotation rate, respectively. In the interval 1627<ωc < 1822, with the increase of Marangoni number, three turning points were observed, indicating three transitions between two-dimensional axisymmetric steady flow and three-dimensional oscillatory flow due to the interaction between thermocapillary force and crucible rotation. For crystal rotation, two oscillatory modes for flow instability were observed. When the dimensionless crystal rotation rate is small (ωs < 3600), the oscillatory flow rotates in the opposite direction of the crystal rotation, but in the same direction in the case of large crystal rotation rate (ωs > 3600), and the thermocapillary force is the primary inducement of flow instability.

Effect of crucible and crystal rotations on the solute distribution in large size sapphire crystals during Czochralski growth

In this study, the flow, temperature and solute concentration fields in the melt during the CZ growth process are numerically investigated. The results show that the magnitude and distribution of the solute concentration in the melt is strongly affected by the convective flow and thermal distribution. The maximum solute concentration always occurs at the crucible sidewall where the maximum temperature in the melt is found and the solute concentration at the crystal-melt interface increases from the triple point to the centerline. Heat transport from the side crucible wall towards the crystal-melt interface is enhanced by the crucible rotation. The level of the solute concentration inside the melt is reduced due to the lowering of the maximum temperature at the crucible wall. As a consequence, the distribution of the solute concentration along the crystal-melt interface becomes smaller and more uniform as the crucible rotation rate increases. However, after the crucible rotation rate becomes large enough, the maximum solute concentration and the solute concentration along the crystal-melt interface start to increase. Heat transport inside the melt is also affected by the crystal rotation. The centrifugal force induced by the crystal rotation generates a vortex below the crystal-melt interface. This vortex gets larger and stronger as the crystal rotation rate increases. In the smaller crystal rotation rate regime, this vortex is very small, suppressing the solute concentration at the crystal-melt interface. Therefore, the solute concentration along the crystal-melt interface becomes less when the crystal rotation rate is higher, although there is an increase in the maximum solute concentration in the melt due to the higher maximum temperature. In the higher crystal rotation rate regime, there is a reduction in the convexity of the crystal-melt interface due to enhancement of heat transport from the bottom wall of the crucible by vortex motion under the crystal-melt interface. Therefore, there is a switch to an increase in the transport of solute impurities into the crystal-melt interface. Hence, the solute concentration along the crystal-melt interface increases as the crystal rotation rate increases. However, with a further increase in the crystal rotation rate, as the shape of the crystal-melt interface changes becoming concave towards the melt, the solute concentration along the crystal-melt interface decreases because the maximum temperature is significantly reduced. In this study, both counter- and iso-rotations are considered. The results of a comparison of the cases of iso- and counter- crystal rotation show that the lowest and most uniform solute distribution along the crystal-melt interface is achieved when there is no crystal rotation and the crucible rotation rate is fixed at 1 rpm. In other words, the lowest and most uniform solute concentration can be achieved with the only crucible rotation.

Modification of growth interface of CdZnTe crystals in THM process by ACRT

The accelerated crucible rotation technique (ACRT) was introduced in the traveling heater method (THM) growth process of detector-grade CdZnTe (CZT) crystals to regulate the convection in the melt and to modify the growth interface morphology. Several ingots with the diameter of 53 mm were grown by THM with/without ACRT. The ingots were quenched during the growth to show both macroscopic and microscopic morphologies of the growth interfaces. The results show that by using ACRT the growth interface can be changed from a concave one to the flat or even convex one depending on the ACRT parameters, which is favorable for reducing nucleation in the melt to get larger CZT grains. Meanwhile, by using ACRT in THM process, the microscopic interface was changed from a diffused one to cellular or even planar one (at suitable ACRT parameters), through which the trapped Te inclusions was decreased for one order. An ingot grown by THM with constant rotation rate of 40 rpm was also grown, which have also reduced the interface curvature in macro-scale and Te inclusions to some extent, but the effects are not as significant as ACRT with high crucible rotation rate.

Experimental study on complex flow of a binary mixture in Czochralski configurations with different aspect ratios and rotation rates

This paper reported the experimental study on complex flow stability of a binary mixture in the Czochralski configurations subjected to a radial temperature gradient. The working fluid was the n-decane/n-hexane mixture with an initial mass fraction of 50%. Results show that the rotation of crucible and crystal can promote the flow destabilization at a small aspect ratio. However, the crucible rotation can suppress the flow instability at a large aspect ratio. When the thermocapillary Reynolds number exceeds a certain threshold value, the hydrothermal waves, the bud shaped and fringes spokes appear in proper order with the increase of the aspect ratio. Furthermore, the flow patterns are also dependent on the crystal and crucible rotation rates. When the crystal and crucible rotate synchronously, the temperature fluctuation frequency in the binary mixture is nearly the same with that in the pure fluid at a small aspect ratio; however, there is a large difference at a large aspect ratio. Moreover, the temperature fluctuation amplitude in the binary mixture is greater than that in the pure fluid at a small aspect ratio, but it is contrary at a large aspect ratio.

Experimental study on the flow instability of a binary mixture driven by rotation and surface-tension gradient in a shallow Czochralski configuration

A series of experiments have been conducted on the flow instability of a binary mixture driven by the combined surface-tension gradient and rotations of the crystal and crucible in a shallow Czochralski configuration with the aspect ratio and radius ratio of 0.043 and 0.5 respectively. The working fluid was the n-decane/n-hexane mixture with an initial mass fraction of 50%. The results indicate that the hydrothermal waves (HTWs) instability appears when the thermal capillary Reynolds number exceeds a critical value. Furthermore, the critical thermal capillary Reynolds number increases at first, then decreases with the increase of the crystal or crucible rotation rate. At the combined crystal and crucible rotation, it decreases first, and then almost maintains a constant value with the increase of the crystal rotation rate. The Soret effect in the binary mixture makes the flow more unstable than that in the pure fluid. The propagating direction of the HTWs is the same as the crucible rotation direction at the beginning, and then influenced by the crystal rotation with the increase of the crystal rotation rate at a small thermal capillary Reynolds number. In addition, the propagation angle of the HTWs is greatly affected by rotations.

Numerical analysis of solid–liquid interface shape during large-size single crystalline silicon with Czochralski method

Numerical analysis is an effective tool to research the industrial Czochralski (CZ) crystal growth aiming to improve crystal quality and reduce manufacturing costs. In this study, a set of global simulations were carried out to investigate the effect of crystal-crucible rotation and pulling rate on melt convection and solid–liquid (SL) interface shape. Through analyses of the simulation data, it is found that the interface deformation and inherent stress increase during the crystal growth process. The interface deflection increases from 7.4 to 51.3 mm with an increase in crystal size from 150 to 400 mm. In addition, the SL interface shape and flow pattern are sensitive to pulling rate and rotation rate. Reducing pulling rate can flat SL interface shape and add energy-consuming. Interface with low deflection can be achieved by adopting certain combination of crystal and crucible rotation rates. The effect of crystal rotation on SL interface shape is less significant at higher crucible rotation rates.

Effect of crucible and crystal rotations on the convexity and the thermal stress in large size sapphire crystals during Czochralski growth

In this study, the effect of the temperature and flow fields generated by the rotation of the crucible and the crystal on the convexity of a c-axis, large-diameter sapphire crystal during the Czochralski growth process is investigated numerically. The thermal stress distributions in different sizes of crystal are also considered. The computational results show that the convexity and the thermal stress of the crystal are strongly dependent on the crucible and crystal rotation rates. The counter rotation between the crucible and the crystal results in a flatter crystal-melt interface, compared to the case of no crucible rotation or crystal rotation. Maximum thermal stress occurs at the highest curvature of the crystal-melt interface which appears near the center of the growing crystal, and the value is directly proportional to the crystal's size. Moreover, there is a significant decrease in the von Mises stress for the crystal-melt interface with lower convexity due to a reduction in the temperature gradient in the radial direction along the interface. As the crystal length gets larger, the maximum von Mises stress rapidly reduces.

Simulation analysis on impurity distribution in mc-Si grown by directional solidification for solar cell applications

Abstract We carried out global transient simulation of impurity distribution in multi-crystalline silicon grown by directional solidification using appropriate software. Non-metallic impurities such as carbon, nitrogen and oxygen originate from the furnace parts and each impurity atom was segregated into the mc-Si ingot based on their solubility in the crystal. During the solidification process the temperature distribution causes melt fluctuation in the Si melt, which is controlled by applying an external body force that leads to a uniform distribution of impurity atoms. Here the uniform distribution of impurity atoms was obtained by rotating the crucible at 10 rpm and the investigations were also carried out without crucible rotation and with a crucible rotation rate of 3 rpm. In this paper we have analyzed the segregation of non-metallic impurity atoms and chemical reactions between the impurity atoms, wherein three types of simulations were carried out and their results analyzed.

Numerical simulation of the oxygen concentration distribution in silicon melt for different crystal lengths during Czochralski growth with a transverse magnetic field

A three-dimensional simulation model is used to study the oxygen concentration distribution in silicon crystal during the Czochralski growth process under a transverse uniform magnetic field. The flow, temperature, and oxygen concentration distributions inside the furnace are calculated for different crystal lengths. There is significant variation in the flow structure in the melt with the growth length. The results show that in the initial stages, there is a decrease in the oxygen concentration at the crystal-melt interface as the length of the growing crystal increases. As the crystal lengthens further, a minimum value is reached after which the oxygen concentration increases continuously. This trend is consistent with that shown in the experimental results. The variation of the oxygen concentration with the growth length is strongly related to the depth of the melt in the crucible and the flow structure inside the melt. Better uniformity of the axial oxygen concentration can be achieved by proper adjustment of the crucible rotation rate during the growth process.

Simulation ofV/GDuring Φ450 mm Czochralski Grown Silicon Single Crystal Growth Under the Different Crystal and Crucible Rotation Rates

For discovering the principle of processing parameter combination for the stable growth and better wafer quality of Φ450 mm Czochralski grown silicon single crystal (shortly called Cz silicon crystal), the effects of crystal rotation rate and crucible one on the V/G ratio were simulated by using CGSim software. The results show that their effect laws on the V/G ratio for Φ450 mm Cz silicon crystal growth are some different from that for Φ200 mm Cz silicon one, and the effects of crucible rotation rate are relatively smaller than that of crystal one and its increasing only makes the demarcation point between two regions with different V/G ratio variations outward move along radial direction, and it promotes the wafer quality to weaken crystal rotation rate and strengthen crucible one.