A crystal growth monitoring system and method
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- FUZHOU GUANGCHEN OPTOELECTRONICS TECHNOLOGY CO LTD
- Filing Date
- 2026-05-26
- Publication Date
- 2026-06-26
AI Technical Summary
Existing crystal growth monitoring methods have limited monitoring dimensions and cannot simultaneously perceive crystal morphology, temperature distribution, mass changes, and environmental parameters. They are also susceptible to radiation interference, resulting in low image analysis accuracy, insufficient real-time performance, and inadequate precision. Furthermore, the control system relies on open-loop adjustment based on human experience, leading to lag and poor consistency in regulation.
By employing multimodal sensors to synchronously acquire crystal growth information, and combining deep learning fusion networks with physical simulation comparisons, multi-dimensional data fusion and intelligent decision-making are achieved, automatically optimizing growth parameters and constructing a closed-loop control system for the entire chain.
It enables comprehensive and accurate monitoring and real-time control of the crystal growth process, significantly improving the dimensionality and accuracy of monitoring parameters, and providing the ability to intuitively compare growth simulation with actual results, thereby improving the uniformity, consistency and yield of crystal growth.
Smart Images
Figure CN122279732A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of crystal growth monitoring and control technology, and in particular to a crystal growth monitoring system and method. Background Technology
[0002] Crystal growth is a non-equilibrium physicochemical process that is extremely sensitive to thermal, flow, and concentration fields. Even minor process fluctuations can lead to defects such as dislocations, inclusions, and cracks in the crystal. To obtain high-quality crystals, precise monitoring and real-time control of the growth process are necessary.
[0003] Existing crystal growth monitoring methods, including diameter measurement using a single industrial camera, diameter estimation using weighing signals, and infrared thermometry, generally suffer from the following limitations: They lack a single monitoring dimension, failing to simultaneously perceive crystal morphology, temperature distribution, mass changes, and environmental parameters; images from high-temperature furnaces are affected by radiation interference and thermal convection disturbances, resulting in low clarity and signal-to-noise ratio, leading to insufficient accuracy in subsequent image analysis; there is a lack of means to intuitively compare actual growth with theoretical models, making it difficult to detect early signs of deviation from the ideal morphology; important process parameters such as growth rate and crystal volume can often only be obtained through indirect calculation or offline measurement, resulting in poor real-time performance and low accuracy; control systems mostly rely on open-loop adjustments based on human experience, failing to achieve an automated closed-loop of "perception-analysis-decision-execution," leading to lagging control and poor consistency. Summary of the Invention
[0004] In view of this, the purpose of this invention is to provide a crystal growth monitoring system that can comprehensively and accurately perceive the crystal growth state, has the ability to perform physical simulation comparison and extract key parameters online, and can automatically optimize growth parameters.
[0005] A crystal growth monitoring system includes: a multimodal sensing and acquisition module, an image preprocessing and enhancement module, a multimodal data fusion and analysis module, a growth state prediction and trend analysis module, and an intelligent decision-making and control module.
[0006] A multimodal sensing and acquisition module is used to simultaneously acquire multidimensional physical information during crystal growth. This module includes at least an optical imaging unit, an infrared thermal imaging unit, a weighing sensing unit, and an environmental parameter sensing unit. The optical imaging unit contains at least two high-resolution industrial cameras mounted at the observation window of the growth furnace. The cameras are equipped with a filter-neutralizing glass assembly to effectively suppress high-temperature radiation from the melt and acquire high-contrast visible light images of the crystal growth interface. The infrared thermal imaging unit is used to acquire the temperature field distribution near the solid-liquid interface, achieving non-contact, full-field temperature measurement. The weighing sensing unit records real-time changes in crystal weight, providing a high-precision data source for monitoring mass growth. The environmental parameter sensing unit may include temperature sensors, concentration sensors, or particulate matter sensors to sense the temperature gradient, solution supersaturation, or impurity particle concentration in the crystal growth environment online. This organic combination of multiple sensors overcomes the limitations of single-sensor information, which is often incomplete and fails to reflect the full picture of the growth process, laying a rich data foundation for subsequent fusion analysis.
[0007] The image preprocessing and enhancement module is connected to the multimodal sensing acquisition module to perform adaptive contrast enhancement, deep learning-based super-resolution reconstruction, and multi-frame noise reduction on visible light and infrared thermal imaging images. This processing effectively overcomes the problems of blurred imaging and low signal-to-noise ratio under high-temperature conditions, significantly improves image resolution and edge sharpness, and makes the detection of crystal contours and minute defects more accurate and reliable.
[0008] The multimodal data fusion and analysis module receives enhanced images and other sensor data, and achieves deep integration and analysis of multimodal information through a deep learning fusion network. This fusion network includes: a multi-branch feature extraction network, which extracts features from visible light images, infrared thermal imaging, weight time-series signals, and environmental parameter time-series signals respectively; a cross-attention fusion layer, which calculates the correlation weights between different modal features and performs weighted fusion to generate a multimodal fusion feature vector with high representational capability; and multiple task heads, which output crystal geometric parameters (such as crystal contour coordinates, diameter, and cross-sectional area), solid-liquid interface concavity / concavity, defect type and location, and growth uniformity thermograms in parallel based on this fusion feature vector. Specifically, the solid-liquid interface concavity / concavity is determined by comparing the actual growth rate calculated from weighing data with the theoretical flat interface growth rate derived from the pulling speed and diameter, and combining this with the infrared temperature field. This allows for real-time identification of the interface's flatness, convexity, and concavity, providing a direct basis for optimizing interface morphology. This module transforms previously isolated heterogeneous information into unified and interpretable growth state parameters, significantly improving the comprehensiveness and accuracy of monitoring.
[0009] The growth status prediction and trend analysis module is the core of realizing intelligent early warning and predictive control. It includes a growth simulation and image comparison unit, a growth rate calculation unit, a real-time volume monitoring unit, and a time-series prediction model.
[0010] The growth simulation and image comparison unit incorporates a physical model-based simulation engine. This engine uses real-time acquired heating power, pulling speed, crystal and crucible rotation speed, and interface temperature gradient derived from infrared thermography to numerically solve a simplified diameter evolution equation, obtaining the axial distribution of the crystal radius. This is then projected and rendered to generate a simulated image matching the optical imaging perspective. This simulated image is registered and compared with an enhanced actual visible light image, calculating the structural similarity index and local deviation map to obtain a weighted quantized growth deviation index. This comparison mechanism directly maps abstract process parameters to a visualized ideal crystal morphology, making the deviation between actual growth and the theoretical model readily apparent. This not only provides operators with an intuitive basis for judgment but, more importantly, inputs physical consistency constraints into the prediction model and control algorithm, facilitating early detection of growth anomalies.
[0011] The growth rate calculation unit obtains a robust comprehensive growth rate by weighted fusion of multi-source data: axial and radial geometric growth rates are calculated based on the displacement of the crystal profile in consecutive frames; mass growth rate is calculated based on the mass increment of the weighing sensor; and interface migration rate is calculated based on the displacement of feature points in infrared thermal imaging. These three rate sources complement each other: the geometric profile rate directly reflects shape changes, the mass rate is stable and reliable, and the thermal imaging rate responds quickly to local interfaces. The fused comprehensive growth rate eliminates measurement noise and hysteresis from individual methods, providing a key process parameter with high dynamic response and low latency for fine-tuning.
[0012] The real-time volume monitoring unit directly obtains the image volume for solid-of-rotation crystals by integrating the single-view profile around the rotational symmetry axis; for non-solid-of-rotation crystals, it calculates the volume by reconstructing the three-dimensional profile through multi-view stereo vision. Simultaneously, the reference volume obtained by dividing the weighed mass by the theoretical density is fused with the image volume using Kalman filtering to output a high-precision, continuous real-time crystal volume. This method overcomes the errors caused by occlusion or viewpoint limitations in pure image methods and by density fluctuations and buoyancy interference in pure weighing methods. It achieves accurate online sensing of crystal volume, which is of great value for maintaining constant-diameter growth and evaluating growth quality.
[0013] The time-series prediction model employs a Long Short-Term Memory (LSTM) network or Transformer architecture. Its input layer concatenates multimodal fusion feature vectors, deviation feature vectors between simulated and actual images, normalized integrated growth rate sequences, and volume change sequences. This allows the model to learn the statistical patterns of historical growth data and perceive the degree to which current growth deviates from the physical ideal state. The model outputs predictions of crystal size, defect evolution trends, and volume changes within a preset future time period. Because it integrates physical simulation deviations and key rate and volume information, the prediction results exhibit higher accuracy and physical consistency, providing reliable support for forward-looking regulation.
[0014] The intelligent decision-making and control module, based on the crystal geometry parameters, concavity / convexity, defect and uniformity assessment results output by the multimodal data fusion and analysis module, and the deviation index, growth rate, volume and trend prediction output by the growth state prediction and trend analysis module, generates a growth parameter control strategy through a multi-objective optimization algorithm and automatically sends it to the crystal growth equipment for execution. Optimization objectives include crystal diameter stability, solid-liquid interface flatness, defect generation index, uniformity index, minimizing the deviation between simulated and actual images, and minimizing volume error. This achieves a closed-loop automation of the entire chain from "perception-analysis-simulation-prediction-decision-control," proactively adjusting parameters such as heating power, pulling speed, and crystal and crucible rotation speed at the initial stage of deviation, keeping the growth process within an ideal window and significantly improving crystal quality stability and batch consistency.
[0015] The system also includes a human-computer interaction and visualization module, which is used to display multimodal monitoring data, simulation and actual comparison images, deviation heat maps, volume and rate dashboards, etc. in real time, and supports operators to set targets and make manual interventions.
[0016] Accordingly, the present invention provides a crystal growth monitoring method, comprising the following steps: S1. Simultaneously acquire visible light images, infrared thermal imaging temperature field, crystal weight, and environmental parameters; S2. Adaptive contrast enhancement, super-resolution reconstruction, and noise reduction are performed on the image to improve image quality; S3. Input the enhanced multimodal data into the deep learning fusion network, and obtain the multimodal fusion feature vector through multi-branch feature extraction and cross-attention fusion; S4. Extract crystal geometric parameters based on fused feature vectors, calculate the concavity and convexity of the solid-liquid interface, and perform defect detection and growth uniformity assessment. S5. Run the growth simulation engine to generate a simulated crystal image and compare it with the actual image to obtain the deviation index; fuse multi-source data to calculate the comprehensive growth rate; obtain the crystal volume in real time; input the current and historical fused features, deviation index, growth rate and volume sequence into the prediction model, and output the growth trend prediction; S6. Based on the analysis results of S4, the deviation index and prediction results of S5, a multi-objective optimization algorithm is used to generate and execute a growth parameter regulation strategy. S7. Repeat steps S1 to S6 until crystal growth is complete.
[0017] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention organically combines multimodal sensing, image enhancement, deep learning fusion, physical simulation comparison, and predictive control through the above-mentioned system and method, realizing a fully intelligent closed loop of the crystal growth process of "perception-analysis-simulation-prediction-decision-regulation"; compared with existing technologies, it significantly improves the dimensionality and accuracy of monitoring parameters, has the ability to intuitively compare growth simulation with actual conditions, can accurately measure growth rate and volume online, and achieves more refined feedback control based on physical deviations, effectively improving the uniformity, consistency, and yield of crystal growth; this method organically unifies multimodal sensing, physical simulation comparison, online extraction of key process parameters, and intelligent predictive control, significantly improving the level of monitoring refinement and control intelligence of the crystal growth process. Attached Figure Description
[0018] Figure 1 This is a block diagram of the overall architecture of the system of the present invention.
[0019] Figure 2 This is a flowchart of the method of the present invention.
[0020] Figure 3 This is a schematic diagram of a deep learning network structure for multimodal data fusion.
[0021] Figure 4 This is a diagram of the internal structure of the growth status prediction and trend analysis module.
[0022] Figure 5 Compare the actual image, simulated image, and deviation image at a certain moment.
[0023] Figure 6 To compare the online monitoring crystal volume with the offline reference volume curve. Detailed Implementation
[0024] Example 1: Monitoring of Czochralski Single Crystal Silicon Growth
[0025] The system of this invention is configured in a Czochralski single crystal furnace. Optical imaging employs two 2448×2048 pixel, 30fps CCD industrial cameras, mounted on symmetrical observation windows within the furnace body and equipped with filter-reduction components; the infrared thermal imager has a temperature measurement range of 600℃–1600℃ with an accuracy of ±1℃; the weighing sensor has an accuracy of 0.1g; and multiple thermocouples are arranged inside the furnace. The system operates continuously according to the growth stages:
[0026] During the seeding stage, the image preprocessing module enhances the image of the contact area between the seed crystal and the melt, and the multimodal data fusion and analysis module identifies the contact state and monitors dislocation growth. Once a grain boundary anomaly is detected, the intelligent decision-making module quickly fine-tunes the heating power and pulling speed to avoid defect propagation.
[0027] During the necking stage, the crystal geometry parameter extraction submodule continuously calculates the neck diameter. Once the diameter reaches the set value of 3–5 mm and stabilizes, the system automatically determines that necking is complete and guides the process to shoulder development.
[0028] During the shoulder formation stage, the optical profile and infrared temperature field are integrated to provide real-time crystal diameter growth rate and solid-liquid interface morphology coefficient. The time-series prediction model in the growth state prediction and trend analysis module predicts the diameter change trend 1–3 minutes in advance, and the intelligent decision-making module smoothly adjusts the lifting speed and power based on the prediction results to ensure a smooth transition of the shoulder angle.
[0029] The constant-diameter growth stage is the core of the control. At this stage, the growth simulation engine takes the current heating power, pulling speed, rotation speed, and interface temperature gradient as inputs, and employs a simplified diameter evolution model based on thermal equilibrium and geometric constraints. This model simplifies heat transfer near the crystal growth interface into a steady-state heat conduction problem, and, combined with the crystal pulling motion, establishes the governing equations for the crystal radius R as a function of the axial coordinate z: ;in, L is the crystal density (2.33 g / cm³ for single-crystal silicon), and L is the latent heat of crystallization (1800 J / g). To increase lifting speed, (22 W / m·K) (64 W / m·K) are the thermal conductivity of the crystal and the melt, respectively. , Let be the temperature fields of the crystal and the melt, respectively, and r be the radial coordinate. The temperature gradient at the interface is estimated using a simplified analytical expression: the temperature gradient on the solid side is approximately ( - ) / The liquid phase temperature gradient is approximately ( - ) / ,in This is the melting point temperature of silicon (1685 K). The crystal surface temperature is measured by infrared thermal imaging along the crystal surface. The internal temperature of the melt obtained by an immersion thermocouple. , The thicknesses of the solid and liquid phase temperature boundary layers are 5 mm and 8 mm, respectively (offline calibrated based on the furnace structure and fluid state). The engine receives the current process parameters and temperature field in real time, and uses the fourth-order Runge-Kutta method to solve the ordinary differential equation along the z-axis in a stepwise manner with a step size of 0.1 mm. The initial radius at the current moment is provided by the crystal profile diameter output by the multimodal data fusion and analysis module, thereby generating a crystal shape prediction curve for a future period of time.
[0030] The process of generating the simulated image is as follows: Based on the assumption of a crystal body of revolution, the radius distribution curve obtained from the above solution along the axial direction is combined with the projection geometry obtained from camera calibration (focal length and object distance are known) to render a crystal contour mask image on the two-dimensional image plane that is consistent with the viewpoint of the camera on the right, thus forming a simulated optical image.
[0031] simulated image Compared with the enhanced actual visible light image After registration, the Structural Similarity Index (SSIM) and Local Deviation Map are calculated. The SSIM is calculated within a rectangular window encompassing the crystal region and is used to assess overall morphological similarity. The Local Deviation Map is calculated pixel-by-pixel. - | And generated using Gaussian smoothing, defining a quantitative index for growth deviation. It is the weighted sum of the percentage of pixel area exceeding the threshold (20% of the maximum gradient of the image) in the deviation map and the average deviation value.
[0032] The growth rate calculation unit integrates the axial and radial variations of the crystal profile in consecutive frames, the mass growth rate of the weighing sensor, and the displacement rate of feature points in infrared thermal imaging, and obtains the comprehensive growth rate through weighted fusion. The real-time volume monitoring unit obtains the image volume by integrating the single-view profile around the rotational symmetry axis, and then performs Kalman filtering fusion with the reference volume obtained by dividing the weighed mass by the theoretical density to output the real-time crystal volume.
[0033] A continuous 60-minute constant-diameter growth experiment was conducted on a 6-inch single-crystal silicon growth platform. Samples were taken every 30 seconds, resulting in 120 comparative samples for quantitative validation of the simulation engine and comparison method.
[0034] Similarity between simulated and actual images: The mean SSIM value for all samples is 0.962, and the standard deviation is 0.011. At a certain point, the comparison between the simulated and actual images shows that the deviation is mainly concentrated near the crystal edges, with a maximum deviation of no more than 2.1 pixels, corresponding to an actual size of approximately 0.8 mm. This indicates that the simulation engine can highly reproduce the real crystal outline.
[0035] Growth rate verification: The diameter change rate predicted along the axis by the simulation engine was converted into an axial growth rate and compared with the comprehensive growth rate benchmark obtained by the growth rate calculation unit through weight data fusion. The root mean square error (RMSE) of both was 0.12 mm / min, and the coefficient of determination R² = 0.987. The table below lists the comparison data for five representative time points:
[0036]
[0037] Volume monitoring accuracy: The volume of the crystal monitored online was compared with the actual volume measured offline by the high-precision drainage method after growth. The relative error of the volume monitored online within a 60-minute interval was less than 0.8%, and the volume curves matched well.
[0038] Deviation-driven control effect: In another set of experiments, when the deviation index between the simulated image and the actual image... When the threshold value exceeds 0.05, the intelligent decision-making module is triggered to fine-tune the heating power through a multi-objective optimization algorithm. Statistical results show that after enabling deviation-driven control, the standard deviation of the diameter in the constant diameter stage decreased from ±0.9 mm to ±0.4 mm, a reduction of 55.6%, and the volume fluctuation rate also decreased significantly.
[0039] This embodiment demonstrates that the system of the present invention can accurately simulate ideal growth morphology, monitor key parameters in real time, and significantly improve crystal quality through closed-loop control.
[0040] Example 2: Monitoring of KDP Crystal Growth Using Solution Method
[0041] In the solution-based KDP crystal growth apparatus, a high-resolution camera and an infrared thermal imager are positioned outside a transparent observation window. Multiple temperature and concentration sensors are installed within the solution, and a weighing sensor is mounted on the crystal support. A multimodal data fusion and analysis module continuously calculates the growth rates of cone and cylindrical crystals, and estimates supersaturation based on concentration and temperature fields. The growth simulation unit generates theoretical crystal form simulation images based on solution hydrodynamics and crystal facet growth kinetics. By comparing these images with actual acquired images, anomalies such as solvent inclusion and uneven growth on facets can be identified. When the growth rate of a particular crystal facet deviates from its target, an intelligent decision-making module comprehensively optimizes the temperature gradient distribution or crystal rotation mode to restore balanced growth across all crystal faces, achieving stable growth of high-optical-quality KDP crystals.
Claims
1. A crystal growth monitoring system, characterized in that, include: The system includes a multimodal sensing and acquisition module for simultaneously acquiring visible light images, infrared thermal imaging temperature field data, crystal weight data, and environmental parameter data during crystal growth; an image preprocessing and enhancement module for adaptive contrast enhancement, super-resolution reconstruction, and noise reduction of the visible light and infrared thermal imaging images; a multimodal data fusion and analysis module for inputting the preprocessed multimodal data into a deep learning fusion network and outputting crystal geometric parameters, solid-liquid interface roughness, defect detection results, and growth uniformity evaluation results; and a growth state prediction and trend analysis module, including a growth simulation and image comparison unit for generating data based on current process parameters. The system simulates crystal growth images and compares them with enhanced actual visible light images to obtain indicators characterizing growth deviations; a growth rate calculation unit is used to calculate the comprehensive growth rate of the crystal by fusing multi-source sensor data; a real-time volume monitoring unit is used to acquire the crystal volume in real time; a time-series prediction model is used to receive multi-modal fusion features, the deviation indicators, the comprehensive growth rate, and the crystal volume sequence, and predict the growth trend in future periods; an intelligent decision-making and control module is used to generate growth parameter control strategies through multi-objective optimization based on the outputs of the multi-modal data fusion and analysis module and the growth state prediction and trend analysis module, and send control commands.
2. The crystal growth monitoring system according to claim 1, characterized in that, The optical imaging unit in the multimodal sensing and acquisition module includes at least two high-resolution industrial cameras installed at the observation window of the crystal growth furnace. The front end of the camera is equipped with a filter-light reduction glass assembly to suppress high-temperature radiation interference. The environmental parameter sensing unit includes at least one of a temperature sensor, a concentration sensor, and a particulate matter sensor.
3. The crystal growth monitoring system according to claim 1, characterized in that, The deep learning fusion network in the multimodal data fusion and analysis module includes: a multi-branch feature extraction network, used to extract visible light image features, infrared thermal imaging features, weight time-series features, and environmental parameter time-series features respectively; a cross-attention fusion layer, used to calculate the correlation weights between each modal feature and perform weighted fusion to obtain a multimodal fusion feature vector; and multiple task heads, used for crystal contour extraction and diameter calculation, solid-liquid interface concavity and convexity determination, defect type identification and location, and uniformity thermal map generation respectively.
4. The crystal growth monitoring system according to claim 1, characterized in that, The growth simulation and image comparison unit has a built-in physical model-based simulation engine. The simulation engine uses the diameter evolution equation to numerically solve the distribution of the crystal radius along the axis based on the real-time collected heating power, pulling speed, crystal rotation speed, crucible rotation speed and solid-liquid interface temperature field, and generates a simulated image that matches the optical imaging perspective through projection rendering. The growth deviation index includes a weighted measure of structural similarity index and local deviation map.
5. The crystal growth monitoring system according to claim 1, characterized in that, The growth rate calculation unit obtains the comprehensive growth rate by weighted fusion of the following rates: axial and radial geometric growth rate based on continuous frame crystal profile changes, mass growth rate based on weighing sensor mass changes, and interface migration rate based on infrared thermal imaging feature point displacement.
6. The crystal growth monitoring system according to claim 1, characterized in that, When the crystal is a body of revolution, the real-time volume monitoring unit obtains the image volume by integrating the single-view profile around the rotational symmetry axis; otherwise, it calculates the image volume by reconstructing the three-dimensional profile through multi-view stereo vision. The image volume is then fused with the reference volume obtained by dividing the weighed mass by the theoretical density using Kalman filtering to output the real-time crystal volume.
7. The crystal growth monitoring system according to claim 1, characterized in that, The time-series prediction model is a long short-term memory network or a Transformer. Its input layer is composed of multimodal fusion feature vectors, bias feature vectors, normalized comprehensive growth rate sequences, and volume change sequences.
8. A method for monitoring crystal growth, characterized in that, Includes the following steps: S1. Simultaneously acquire visible light images, infrared thermal imaging temperature field data, crystal weight data, and environmental parameter data; S2. Perform adaptive contrast enhancement, super-resolution reconstruction, and noise reduction on the visible light image and infrared thermal imaging image; S3. Input the enhanced multimodal data into the deep learning fusion network, and obtain the multimodal fusion feature vector through multi-branch feature extraction and cross-attention fusion; S4. Extract crystal geometric parameters based on the fused feature vector, calculate the solid-liquid interface roughness, and perform defect detection and growth uniformity assessment. S5. Run the growth simulation engine to generate a simulated crystal image and compare it with the enhanced actual image to obtain the deviation index; fuse multi-source data to calculate the comprehensive growth rate; obtain the crystal volume in real time; input the fused feature vector, deviation index, comprehensive growth rate and volume sequence of the current time and historical time into the prediction model, and output the growth trend prediction. S6. Based on the analysis results of S4, the deviation index and prediction results of S5, a multi-objective optimization algorithm is used to generate a growth parameter control strategy and send it to the crystal growth equipment for execution. S7. Repeat steps S1 to S6 until crystal growth is complete.
9. The crystal growth monitoring method according to claim 8, characterized in that, In step S5, the growth simulation engine takes the current process parameters and the interface temperature gradient derived from infrared thermal imaging as input, solves the diameter evolution ordinary differential equation to obtain the axial distribution of the crystal radius, and generates a simulated image based on camera projection geometry rendering; the deviation index is obtained by calculating the structural similarity index between the simulated image and the actual image and the weighted sum of the local deviation map.
10. The crystal growth monitoring method according to claim 8, characterized in that, The optimization objectives of the multi-objective optimization algorithm in step S6 include: crystal diameter stability, solid-liquid interface flatness, defect generation index, growth uniformity index, as well as minimizing the deviation between the simulation and the actual image and minimizing the volume error.