Non‐destructive and deep learning‐enhanced characterization of 4H‐SiC material

The silicon carbide (SiC) crystal growth is a multiple‐phase aggregation process of Si and C atoms. With the development of the clean energy industry, the 4H‐SiC has gained increasing attention as it is an ideal material for new energy automobiles and optoelectronic devices. The aggregation process is normally complex and dynamic due to its distinctive formation energy, and it is hard to study and trace back in a non‐destructive and comprehensive way. Here, this work developed a non‐destructive and deep learning‐enhanced characterization method of 4H‐SiC material, which was based on micro‐CT scanning, the verification of various optical measurements, and the convolutional neural network (ResNet‐50 architecture). Harmful defects at the micro‐level, polytypes, micropipes, and carbon inclusions could be identified and orientated with more than 96% high performance on both accuracy and precision. The three‐dimensional visual reconstruction with quantitative analyses provided a vivid tracing back of the SiC aggregation process. This work demonstrated a useful tool to understand and optimize the SiC growth technology and further enhance productivity.


INTRODUCTION
The silicon carbide (SiC) is a wide-bandgap semiconductor material, and is able to operate at high current, voltage, power density, and switching frequencies. [1]Currently, the 4H-SiC has gained increasing attention because it is an ideal material for power devices in new energy automobiles and optoelectronic devices in solar-blind light detection. [2,3]The crystal growth of SiC is a multiple-phase aggregation process of Si and C atoms, which is generally conducted by the physical vapor transport (PVT) method. [4]In the PVT growth, the SiC material goes through sublimation from powders to form various gaseous components (growth monomers) such as Si or C atoms, SiC molecules, or Si m C n clusters [5] in vacuum and high temperature (≥2300 K) condition (Figure 1A).These gaseous components are subsequently crystallized on the surface of the SiC seed, but there are subtle differences in formation enthalpy between different stacking positions of SiC atomic attachment. [2]These subtle differences mean that the SiC is prone to face a "structural mutation", especially in the PVT growth conditions (i.e., high temperature and everchanging stoichiometric ratios of the gas atmosphere). [1,6]he structural mutation elicits different defects in the SiC crystal, such as basal plane dislocation (BPD) and threading edge dislocation (TED) at the nanoscale or micropipe and carbon inclusion at the micron scale. [7]These defects negatively influence the further application of SiC materials (e.g., leakage current in the devices), [8] and therefore the aggregation process of SiC is vital and requires monitoring and precise control.However, the conventional SiC PVT growth can be considered as a "blind box", the detailed information within the growing process and the related quality of as-grown crystal need to be detected only after the growth by different destructive measurement ways.For instance, horizontal or vertical cleavages together with the wet etching [9] are normally required to locate the distribution of defects and trace back the evolution of SiC aggregation.The destructive methods are raw material-, time-, and labor-consuming, and usually hard to provide the traceback of SiC aggregation in a multidimensional and intuitive way.Hence, a non-destructive, fast, and multidimensional-reconstruction manner is an urgent need.
The x-ray computed tomography (CT) is a mature technology that can reveal the internal details of objects in three dimensions, [10] and this non-destructive method has been used to profile a wide range of materials. [11]The CT technology has been used for the defect detection of semiconductor wafers, [12] but is less utilized for large-size semiconductor crystals (boule/bulk).This is because the x-rays attenuate quickly (according to Beer-Lambert's Law) when penetrating most single crystals of semiconductor, and thus hard to obtain high-resolution imaging of large-size crystal boule. [13]he first attempt involving x-ray imaging on the SiC crystal was conducted by the research group of P. J. Wellmann, who had developed an in situ way to monitor the growth speed and interface shape of SiC at the millimeter scale within PVT. [14] Current CT technology has evolved to provide fine observations at the micron or nano scales, and the size of observed objects can range from granular materials, [15] synthetic film with microfibers, [16] and to natural mineral. [17]Therefore, as long as the difficulty from x-ray attenuation is solved, the CT technology has the capacity to provide microscopic characterization without any damages (cleavage or etching) to investigate the defects or growth evolution of SiC crystals.Specifically, the gas atmosphere of the SiC PVT growth is dynamically changing, [18] different growth monomers are dominated in the Si-rich or C-rich conditions, [19] and meanwhile, carbon particles might also be released from the crucible graphite material thanks to the high temperature. [20]his could result in the Si or C massively and respectively aggregating in a certain area or the lattice deformations of materials, and the imperfections differed to the long-range ordered crystal structure can be theoretically determined by the x-ray imaging (Figure 1B).Furthermore, abundant and intricate imaging processing needs to be developed to identify and quantify the different characteristics within SiC material, especially the mainstream production size of SiC now, is greater than or equal to 6 inches in boule shape.
The complicated image processing is assisted by using artificial intelligence (AI), which has been rapidly developing recently and is becoming more and more important in various fields (such as medical, [21] material, [22] and physical [23] ).As one of the AI branches, computer vision (CV) encompasses the scientific study of how machines interpret and derive meaning from images and videos.The CV algorithms analyze certain criteria within visual data, enabling them to make predictions or inform decision-making processes. [24]Modern CV is mainly based on deep learning, especially the most utilized deep learning algorithm called convolutional neural network (CNN). [25]The CNNs draw inspiration from the neural structures found in human and animal brains, employing a multilayered architecture to progressively reduce data and computations to the most pertinent subset.This set is subsequently compared against known data for identification or classification purposes. [26]Obviously, CNNs excel in tasks where human capabilities are limited, such as extracting features, analyzing patterns, gaining insights, and enhancing the efficiency of complicated tasks.Their advantages extend automation, modeling, optimization, and controlling of complex systems. [27]The crucial advantages of CNNs have been identified by Goodfellow et al. as equivalent representations, sparse interactions, and parameter sharing. [28]he performance and efficiency of a CNN is determined by its architecture, and many architecture designs have been created, such as LeNet model in 1995, AlexNet in 2012, ZefNet in 2013, VGGNet and GoogleNet in 2014, Residual neural networks (ResNet) in 2015, ResNext in 2017, and high-resolution network (HRNet) in 2020. [25]Therefore, the CT and deep learning technologies can conjointly light up a new characterization method to identify the microscopic defects in 4H-SiC material and trace back the evolution of the SiC aggregation process in a non-destructive, rapid, but precise way.
In this work, a 6-inch boule of 4H-SiC material was grown by PVT.This boule and its cleavages were measured by micro-CT scanning, respectively.The obtained visual data were analyzed, identified, and confirmed by several optical identification methods (such as Raman scattering spectrum, photoluminescence [PL] spectra, differential interference contrast [DIC] optical microscopy, and 3D laser scanning microscope).Meanwhile, the deep learning ResNet-50 was used to assist the visual data processing.Last but not the least, the reconstruction was conducted to investigate the evolution of the SiC aggregation process, and statistical analyses and COMSOL stress distribution simulation were provided.

Non-destructive characterization by micro-CT scanning
The 4H-SiC material was grown intentionally in an optimal condition of temperature and pressure to gain as many different growth products as possible within the 6-inch boule.This boule and its cleavages were conducted for observations by micro-CT scanning in a common transmission mode, but using a tungsten-target reflection for the high yield of x-rays.The detailed operational parameters of micro-CT scanning are shown in Section 4.2 (Experimental section) based on our preliminary text to solve the difficulty of x-ray attenuation for obtaining high-resolution imaging.A monochromatic x-ray was emitted and irradiated on the samples, and the projected light signals were collected by a 2048 × 2048 pixels active-matrix detector (Figure 2A).By the horizontal and vertical movements and the rotation of the sample stage, a comprehensive and multidimensional scanning was obtained.The tomographs (light signals) were subsequently reconstructed and transferred to digital data, and thus, different horizontal/cross-sectional imaging could be gained (Figure 2B and Video S1).Homogeneous responsive background signals would show on the images for long-range ordered SiC crystal structure, but those imperfections (such as lattice deformations, strains, or different particles) could diversify the scattering of the transmitted x-rays, and thus gain different features on images. [29]Among obtained sectional images in this work, obvious features were observed on the gray value (16-bit was involved in this work), which indicated the discrepancy in SiC crystal quality.These features could be categorized into three representative types according to their gray values and sizes (Figure 2C-F).The type i was in a contiguous area, and the gray values ranged from 3.2 × 10 4 to 6.5 × 10 4 .Type ii and iii presented as small spots, and their gray values were 2.9-3.2 × 10 4 and 0-2.3 × 10 4 , respectively.The brighter color within imaging (i.e., higher gray values) means the stronger scattering of the SiC material.In terms of type i, the relatively large-area and brighter-color features on images indicated that it could be the polytypes of SiC.The boundary between areas was clear, which might be due to the severe atomic disorder at the interfaces between polytypes and 4H-SiC.For the type ii, it presented a mass of white spots on the sectional image, and more importantly, these spots continuously existed at the same locations of different horizontal sections.This indicated that type ii was a penetrated defect along the growth direction (i.e., the Z axis), and it might be the type of micropipes.The micropipe could cause a massed accumulation of lattice distortion locally near the core of the micropipe, and thus enhance the scattering of the x-ray, resulting in brighter color on the topography.Besides, type iii was in dispersed distribution and non-penetrated, and the darker color on topography might be due to the lower atomic number of carbon elements.This might infer a hypothesis that type iii was the defect of carbon inclusions.

Different optical identifications
The obtained visual data of micro-CT were further identified and verified by different optical methods.The grown SiC boule was first placed under ultraviolet light (UV), and the UV photo had areas with three different colors (Figure 3A).The shapes of these colored areas were similar to that of the x-ray tomograph.The colored areas could preliminarily confirm that type i was the polytype of SiC, because different polytypes have different electronic band gaps (where the E g is 3.23, 3.98, and 2.96 eV, respectively, for the 4H-, 6H-, and 15R-SiC). [30]Hence, these areas showed different colors under the UV light.Meanwhile, the Raman spectra were used to double-confirm the hypothesis of type i, and specific SiC polytypes were further identified (Figure 3B).The areas shown green, brown, and orange colors under UV were the 4H-, 6H-, and 15R-SiC, respectively, according to the standard aligning peak positions and shapes. [31]Then, the two-dimensional distribution of SiC polytypes was measured by the Raman mapping and plotted with the matching degrees (Figure 3C).Based on these identifications, the type i characteristic of micro-CT was confirmed to be the polytypes of SiC.Subsequently, those types ii and iii that existed on the surface of SiC crystal were located and labeled, and then went through optical identification by different methods.The type ii (Figure 4A) was first conducted at room-temperature PL intensity mapping at wavelength 405 nm, and the obvious nonradiative recombination center was observed.This indicated that the area of type ii was not the 4H-SiC single crystal.Meanwhile, the morphology of type ii was measured by the DIC optical microscopy and 3D laser scanning microscope, and a pear-shaped pit was found (approximately 97.1 µm in length, 72.8 µm in width, and 7.3 µm in depth, with plentiful and clear surface steps).The observed pit and spiral-down steps (a 3D illustration shown in Video S2) strongly indicated that type ii was a micropipe according to Frank's theory. [32]he micropipe model was therefore established to demonstrate the structure of the micropipe, which presented as a pit from the top view but as a penetrating pipe perpendicular to the basal facet of SiC boules from the side view.This structure model was further confirmed by the confocal laser scanning, where penetrating pipe was observed from the side view.There was a discrepancy between the widths of the same micropipe measured by the micro-CT and confocal laser scanning, and this is due to a stronger response from the x-ray scattering caused by severe atomic disorder.Hence, the hypothesis for type ii was accepted, which was the micropipe of SiC.In terms of type iii (Figure 4B), the morphology showed irregular patterns, with sizes ranging from 100 to 350 µm, and it was in light with the observations of carbon inclusions from published works of Xie et al. [33] and Hirose et al. [34] Meanwhile, an elemental analysis was conducted by comparing micro-Raman spectra between the suspected carbon inclusion and SiC material.The obtained D-and G-peaks could be also found in the amorphous carbon or graphite whiskers, [35] and this also means that type iii was carbon inclusions.The identifications for types ii and iii were replicated 300 times from the surface of the 6-inch boule and its cleavages.
As discussed above, the type i, ii, and iii characteristics of micro-CT were polytype, micropipes, and carbon inclusions, respectively.It is worth noting that these CT characteristics were presented in large numbers within a single image, and there were many different sectional images from the CT scanning of the 6-inch SiC boule (thousands of high-resolution raw tomography data in this work).Meanwhile, there was a subtle difference in CT images even with the same type of characteristics.Thus, deep learning was involved to process the CT images in order to avoid fatigue and error from humans.

Deep learning-enhanced characterization by CNN
The CNN algorithm was used in this work to process the visual data from micro-CT to achieve an efficient and precise performance.The main reason to use CNN was the weightsharing feature, which reduced the number of trainable network parameters. [36]Furthermore, the ResNet architecture was selected to face the potential challenges of vanishing gradients and degradation by introducing a "residual block". [36]his enables a "skip connection" that adds the output from the previous layer to the layer after, and it helps the net-work to enhance generalization and avoid overfitting. [25]In this work, the deep learning-enhanced characterization of SiC materials was developed by using the transfer learning technique to retrain the ResNet-50, including fine-tuning of network parameters and setting hyperparameters for our specific dataset.The ResNet-50-enhanced SiC characterization consists of four parts, including data collection, data preprocess, feature learning, and data classification (Figure 5A).The micro-CT images of a 6-inch boule and one of the cleavages (10 × 10 × 13 mm, named as small bulk) were initially collected as two databases, and each database had 1800 images in Bitmap-File (BMP) format.Meanwhile, the conventional manual classification was conducted according to the optical identification, where five categories were set for the 6-inch boule (abbreviation CI for carbon inclusion, MP for micropipe, NO for background, PT for polytype, and SC for single crystal of 4H-SiC), but four categories for the small bulk (because the PT was not detected within the small bulk).Then, the pre-processing was carried out by cropping, resizing, label encoding, normalization, and shuffling of visual data to improve the performance of feature learning.The feature learning had two parts, pre-training on ImageNet and subsequent transfer learning, and then the outcomes were used to automatically classify the SiC materials.
Details of the architecture for the feature learning and data classification are demonstrated in Figure 5B.The pre-training was based on the ImageNet dataset, which has over 14 million images spanning across 1000 categories, and it could avoid any potential quantity shortage of CT images and meanwhile provide much faster and easier learning/training. [37]he weights of pre-training on ImageNet were frozen and transferred to the SiC characterization as a feature extractor, followed by a fully connected layer.Simultaneously, network parameters were fine-tuned and hyperparameters were set, such as batch training size (64), number of categories (5), learning rate (0.001), and optimizer (Adam).The dropout probability was set at 0.3 to reduce overfitting before and after the rectified linear unit (ReLU) activation layer, respectively.Then, the output size was set as 5.The feature extraction for different categories of CT images was visualized to demonstrate different convolution layers (Figures S1 and S2).
Performance metrics of the ResNet-50-enhanced SiC characterization were evaluated (Figure 6), and the values of accuracy, loss, precision, recall/sensitivity, and F1-score were examined, respectively, according to the published literature. [38]The performance metrics for the 6-inch boule are shown in Figure 6A, and it was clear to see that the convergence rate of training accuracy was fast, which tended to be stable after eight epochs.The validation loss gradually became stable after 30 epochs, where a 99.7% validation accuracy was achieved, and the average validating accuracy overall was 99.3%.The loss curves of training and validation were below 0.023 and 0.009, respectively, at the stable stage.The model's generalizability was further assessed using a separate test dataset.In this evaluation, it demonstrated a similar high level of average accuracy, achieving 99.3% for 6-inch boule.Meanwhile, the confusion matrix of the test dataset was plotted to summarize the performance of the classification algorithm (Figure 6B), and those off-diagonal values indicated the error probability of the prediction.The probability of error prediction was all below 3% for all five categories.The obtained values of precision, recall, and F1score were all above 96.7%(Figure 6C), which also indicated good effectiveness in light of other publications in the field of defect detection. [39]In terms of performance evaluation for the small bulk (Figure 6D-F), both correct prediction probability and precision were above 97% for all categories, and the overall accuracy of the model and other classification performance metrics of different defects were above 96.7%.Hence, the ResNet-50-enhanced SiC characterization on the 6-inch boule and small bulk samples performed well with a fast convergence speed and high accuracy and precision of prediction.This means the deep learning-enhanced method developed in this work was not only contributing to the automation, but also to achieve an effective feature extraction and identification of different SiC defects from the complicated CT images, which were difficult for human beings without the assistance of various optical methods.

Reconstruction of the evolution of SiC aggregation
As SiC crystal growth is a complex synthesis process involving the multi-phase aggregation of Si and C atoms, [4] the defects identification and an intuitive visual reconstruction are vital for understanding the evolution process of SiC growth.Therefore, a digital 3D reconstruction was made and optimized on the top of outcomes of the ResNet-50-enhanced SiC characterization (Figure 7A and Video S3).This 3D reconstruction provided more comprehensive information on crystal growth compared to the traditional reconstruction (Figure S3), where different kinds of defects related to spatial inhomogeneity were intuitively shown.For instance, the polytype of 4H-SiC could be identified and visualized rather than the traditional method.The micropipes could be observed and identified, and the example showed two micropipes extending from the seed to the growth surface, and their size in diameter progressively increased along the growth direction.Furthermore, the evolution of 4H-SiC crystal growth was further traced back by the statistics analyses of different defects.It is clear to see that the polytype was originally from the left edge of the seed and expanded with the growth process (Figure 7B), which was also doubleconfirmed by the UV-photo of a cross-sectional cleavage.This phenomenon was most likely related to the atomic steps of seed, where a 4 • off-angle seed was used in this work and the upper atomic step was on the left side.The restriction effect on polytype growth is relatively lower on the upper atomic step, and thus the polytypes are prone to occur and then extend from here. [40]n addition, statistics analyses of micropipe and carbon inclusion were conducted along the axial and radial directions, respectively.The axial direction indicated the growth situations of SiC PVT at different periods.As shown in Figure 7C, the density of the micropipe gradually increased with the growth progress and reached the maximum value near the axial center of the crystal, and some micropipes were gradually annihilated in the later period of growth.The evolution of these defects understandably originated from the changes of growth conditions within the crucible, such as the Si/C composition, gas atmosphere, thermal-field, and thermal stress, and so forth.At the initial stage of the PVT growth, the unstable atmosphere would transport more carbon particles from the source material and the graphite parts, which were further incorporated into the aggregation process of SiC. [41]Thus, a high density of carbon inclusion defects has been observed for this 6-inch SiC boule at the initial growth stage, followed by a continuous decrease of the density as the growth proceeds.42 ] As the growth condition stabilized, the stable step flow growth promoted the healing of these micropipe defects.The analyses along the radial direction could demonstrate the growth situation among the growth interface.Figure 7D shows the shape of M font of defects distribution for both micropipe and carbon inclusion, and the density of carbon inclusion was much higher than micropipe.The observed M-shape distribution had a high probability of being due to internal stress, [43] and the asymmetry of the M shape could be elicited by the existence of polytype on the left side of the boule.Therefore, an analysis of stress was conducted by the COMSOL Multiphysics simulation (Figure 7E) and the Raman shift measurement (Figure S4).The stress simulation gave the evidence of source of M-shape distribution, especially the extracted Von Mises stress intensity across the radical direction, which also had the M shape.Simultaneously, the distances of the Raman peak shift compared to the 4H-SiC standard indicated the stress within the boule, [44] and the Raman shift measurement double-confirmed the findings of the COMSOL simulation.Therefore, the internal stress proved to be the cause of the M-shape distribution of micropipe and carbon inclusion along the radial direction.As the thermal stress was an indicator of the dislocation density, the reduction of the radial temperature gradient has been considered as the key issue for the optimization of the thermal field toward the large size of SiC PVT system. [45]Obviously, the 3D reconstruction presented spatial distribution of defects, and their evolution with the growth process provides valuable insights for the tracing back of the growth conditions, as well as the optimization of thermal field.In addition, a quantitative summary of three main defects of 4H-SiC was provided to illustrate the volume proportions within the 6inch boule (Figure 7F).The defects of polytype, micropipe, and carbon inclusion occupied 23.52%, 0.85%, and 0.24% of the total volume, respectively.The different volume sizes of micropipe and carbon inclusion were also counted, and the majority of micropipes and carbon inclusions were not bigger than 40 and 0.1 mm 3 , respectively.The quantitative summary with defects localization could be further used in the future as the basis of digital twin technology of SiC materials as displayed in Figure 7G, enhancing productivity via proactively improving the core and wafer processing through computeraided optimization.For example, using the areas of defects to place the sawing gaps or using scraps of boule to manufacture wafers in smaller sizes.
Overall, the non-destructive and deep learning-enhanced characterization technology developed in this work was able to provide a fast, intuitive, and effective evaluation of 4H-SiC material at the micro-level.Its vivid visual reconstruction was a serviceable tool to trace back the evolution of the SiC aggregation process, and therefore guide the optimization of PVT growth.The identification for crystal boule at the nanolevel would be the next step for this technology targeting those nano-scale defects such as BPD and TED.Nevertheless, BPD and TED now could be limited in the process of expitaxy, [46] and thus are less harmful than polytypes and micropipe focused on this work.Meanwhile, the application of our developed technology might be further extended as an in situ monitor of PVT growth.In addition, the ResNet-50enhanced SiC characterization could provisionally identify the polytypes of 4H-SiC as a whole, the specific type (6H or 15R) was not yet well identified, and thus required more refined recognition in the future.Last but not least, the non-destructive and deep learning-enhanced characterization technology developed in this work would be not only useful for the SiC but also for AlN, Ga 2 O 3 , and other high-cost third-generation semiconductor single crystals.[49] This broad applicability highlights the versatility and importance of our approach in the semiconductor industry.

CONCLUSION
This work developed a non-destructive and deep learningenhanced characterization method of 4H-SiC material, which was based on micro-CT scanning, the verification of various optical measurements, and the ResNet-50 architecture.
The micro-level and harmful defects (polytypes, micropipes, and carbon inclusions) within the 4H-SiC materials were able to be identified and located in a fast and effective manner.The performance metrics of characterization for both the 6inch boule and the small bulk were satisfactory, where both accuracy and precision were all above 96%.Meanwhile, the visual reconstruction provided a comprehensive evaluation of crystal quality with quantitative analyses, which enabled the tracing back of the SiC aggregation process, and thus was vital for understanding and optimizing the SiC growth and also enhancing productivity.

Materials
The 6-inch 4H-SiC boule (with a thickness of 15.4 mm, and 4 • off-axis orientation) used for the study was grown by the PVT method with a temperature of about 2150 • C near the seed substrate.The growth temperature was monitored by two infrared thermometers targeted at the top and bottom surface of the crucible.At the same time, the crucible pressure was kept at about 10 Torr.Argon gas was used to provide an ambient growth condition, and the growth rate of this boule was around 0.1 mm/h.Notably, the growth temperatures and pressures were changed within the ranges to gain different defects of 4H-SiC.In addition, a diamond wire saw (MTI Cooperation) was used to get the small bulk of the sample (10 × 10 × 13 mm) and other cleavages.

Micro-CT scanning
The micro-CT scanning of the 6-inch boule and the small bulk was performed using the commercial high-resolution industrial micro-CT, the Phoenix v|tome|x m (General Electric Company, Figure S5).During scanning, the sample was

Optical characterization
The ultraviolet (UV) photo for identification of the polytypes SiC was achieved by a 365-nm wavelength light source made by light-emitting diodes.The polytypes were further verified by the Raman scattering spectra via the LabRAMHR800 system (Horiba Jobin Yvon) with 375-and 532-nm laser wavelength, respectively, and the interval of 5 mm was set for Raman mapping.The 3D laser scanning microscope (LSM) measurement for surface characterization was conducted by VK-X1000 (Keyence).The DIC optical microscopy was also used to observe the surface morphology of the (0001) face of SiC samples by DM8000M (Leica).The PL performance for the SiC was determined using a microscope spectrometer (MicOS, HORIBA) using a 369-nm pulsed laser.

ResNet-50 of CNN
The ResNet-50-enhanced SiC characterization was implemented on Python (version 3.7), together with the deep learning platform Tensorflow (version 2.0.0).The program was run on the Intel Core Xeon 3.70 GHz CPU, 128 GB RAM, NVIDIA Quadro P2000 (5G) GPU, and Windows 10 operating system.The CT images (2024 × 2024 pixel) of SiC samples (6-inch boule and the small bulk) were used as databases, and each dataset contained 1800 images.These images were cropped into sizes of 224 × 224 pixels and labeled for subsequent supervised learning.The defects in these labeled images were validated by optical identification methods.In addition, 1200 images of the dataset were used for training, 300 images were used for validating, the remaining 300 images were used as a separate test dataset, and the number of epochs was 50.In our ResNet-50-enhanced SiC characterization, two fully connected layers and two integrated dropout layers, with a random inactivation rate of 0.3, were set.The flowchart of ResNet-50-enhanced characterization of 4H-SiC procedure is illustrated in Figure S6.Details of the code are available in the GitHub repository. [50]

F I G U R E 1
Schematic diagram of SiC aggregation and the x-ray imaging.(A) SiC crystal growth by PVT method, showing the sublimation and crystallization process of SiC from powder to crystal.(B) The fundamental mechanism of the transmitted x-ray imaging.The x-rays are transmitted, absorbed, or scattered when they travel through a matter, and the x-rays could be modulated by different lattice situations.

F I G U R E 2
The micro-CT scanning of 4H-SiC materials.(A) Schematic diagram of the micro-CT equipment used in this work.(B) Different crosssectional imaging after signal reconstruction and transformation, and horizontal or vertical view were obtained.(C-F) Three representative types characterized by the gray values and sizes in micro-CT imaging.The image was the horizontal section 5-mm distance from the SiC seed.

F I G U R E 3
Identification of the type i in the SiC micro-CT scanning.(A) Images of the 6-inch SiC boule under different lights, including natural, x-ray, and ultraviolet (UV) light.Three different regions are labeled according to their color under the UV irradiation.(B) Raman scattering spectrum of three labeled regions.(C) Different polytypes of SiC distribution by Raman mapping.

F I G U R E 4
Identifications of types ii and iii by different optical methods.(A) Observations of type ii with established structural model.(B) Observations of type iii and the elemental analysis of carbon.

F I G U R E 5
Deep learning-enhanced characterization of SiC.(A) Flow chart of ResNet-50-enhanced SiC characterization.(B) Architecture demonstration of feature learning and data classification with the carbon inclusion feature maps of the 2nd, 3rd, and 49th convolution layers.

F I G U R E 6
Performance metrics evaluation of the ResNet-50-enhanced SiC characterization.(A-C) The 6-inch SiC boule.(D-F) The small bulk of SiC sample.The CI, MP, NO, PT, and SC stood for carbon inclusion, micropipe, background, polytype, and single crystal, respectively.The results of the confusion matrix in (B) and (E), as well as the precision, recall, and F1-score for each class label in (C) and (F), were summarized for a separate test dataset, which contained about 300 images.

F I G U R E 7
The 3D reconstruction of the evolution of SiC aggregation with the analyses of statistics and contributed factors.(A) The 3D reconstruction of the grown SiC material.The colors of orange, blue, and green were used to highlight the polytype, micropipes, and carbon inclusions of 4H-SiC, respectively.The subfigure i is the reconstruction of the whole 6-inch boule, and the ii-iv represent 2D CT projection and 3D reconstructions of polytype, micropipe, and carbon inclusion, respectively.(B) Analyses of statistics and contributed factors of the polytype, including distribution along the axial direction, ultraviolet (UV)-photo of a cross-sectional cleavage, and demonstration of atomic steps of seed.(C and D) The distribution of micropipes and carbon inclusions along the axial and radial directions, respectively.(E) Simulation of stress distribution.The white dash line was at 3.45 mm from the seed.(F) Volume proportion of different SiC defects and the proportion of different sizes of micropipe and carbon inclusion.(G) The concept of digital twin technology that could be used in the future.The baby-blue areas represent materials could be further processed as wafers in different sizes, and the purple and red areas represent different defects.
Micro-computed tomography scanning parameters for the 6-inch SiC crystal.on a rotating stage, and the images were taken at 0.3 • per step for the segmentation scanning.The parameters were set as depicted in Table 1, according to our preliminary tests that could obtain high-resolution CT images for SiC materials, and the exposure time was 2400 ms per radiograph.The 3D reconstruction of the evolution of SiC aggregation was assisted by the datos|x (2.0 version), VGStudio Max (3.4 version), and myVGL (2023.1 version).
TA B L E 1placed