Deep Learning‐Assisted Quantification of Atomic Dopants and Defects in 2D Materials

Abstract Atomic dopants and defects play a crucial role in creating new functionalities in 2D transition metal dichalcogenides (2D TMDs). Therefore, atomic‐scale identification and their quantification warrant precise engineering that widens their application to many fields, ranging from development of optoelectronic devices to magnetic semiconductors. Scanning transmission electron microscopy with a sub‐Å probe has provided a facile way to observe local dopants and defects in 2D TMDs. However, manual data analytics of experimental images is a time‐consuming task, and often requires subjective decisions to interpret observed signals. Therefore, an approach is required to automate the detection and classification of dopants and defects. In this study, based on a deep learning algorithm, fully convolutional neural network that shows a superior ability of image segmentation, an efficient and automated method for reliable quantification of dopants and defects in TMDs is proposed with single‐atom precision. The approach demonstrates that atomic dopants and defects are precisely mapped with a detection limit of ≈1 × 1012 cm−2, and with a measurement accuracy of ≈98% for most atomic sites. Furthermore, this methodology is applicable to large volume of image data to extract atomic site‐specific information, thus providing insights into the formation mechanisms of various defects under stimuli.

M2. Full-size ADF STEM images and the corresponding atom site maps of V-WSe 2 .
M3. Full-size ADF STEM images and the corresponding atom site maps of MoS 2 .
M4. Full-size ADF STEM images and the corresponding atom site maps of V-MoS 2 .

Note S1. Estimation of measurement precision and minimum detectability
The total number of atoms that can be captured in the image is determined in a fixed fieldof-view (FOV) of ADF STEM imaging. As the imaging FOV is decreased (in other words, as the magnification is increased), the number of atoms captured in an image gets reduced. Therefore, the measurement precision for the point defects could become poor at small FOV.
In contrast, the analysis of atom position becomes difficult in an excessively large FOV owing to insufficient image resolution. Hence, it is important to track how the measurement error can increase with decreasing FOV to define an allowable measurement precision while maintaining atomic resolution. From the results in Figure S1, we see that the measurement error is substantial for the small FOVs of 10 2 nm 2 for both concentration measurements of V dopant and Se vacancies, even though the averaged concentrations obtained from more than 100 selected images show similar values over the entire FOV range. To secure sufficient image resolution for atom feature segmentation, we chose the imaging FOV of the ADF STEM to be 10 2 nm 2 . Under these imaging conditions, the measurement precision and minimum detectability were obtained as ~±0.2% and ~1×10 12 cm -2 , respectively. Figure S1. Measurement error and detection limit for the defect quantification as a function of imaging field-of-view (FOV) via atomic-resolution ADF STEM. Measurement errors (standard deviations, insets) for the contents of a) V dopants and b) Se vacancies in WSe 2 monolayer according to the change in the FOV of STEM imaging. To estimate the measurement error of our method, we used simulated ADF STEM images as test data (100 images for every FOV), which were derived from the V-WSe 2 supercell model with the dimension of 20 x 20 nm 2 . The contents of V dopants and Se vacancies (Vac Se , Vac Se2 ) randomly seeded into the supercell structure were 2.15 and 2.08% (marked by red dotted lines), respectively, which were obtained from the experiments. The test images with different FOVs were arbitrarily selected within the large simulated ADF image for the statistical estimation of the defect concentration. Figure S2. An experimental demonstration of the artificial enhancement of the signal intensity of defects in a low SNR STEM image after the application of fast Fourier transformbased noise filtering process such as Wiener filtering and Bragg pattern filtering. Note that our denoiser model works properly without the false generation of signal intensity and the frame-averaged image with high SNR is provided as a ground truth image for comparison. Note S2. The effect of signal-to-noise ratio (SNR) with respect to restoration accuracy of the denoising algorithm At a too low value of SNR, our denoising model would not work properly and artificially change the relative intensities of atoms and defects. Generally, we would expect that as the SNR is gradually decreased, the measurement error becomes notable below a certain value of SNR, which limits the practical application of our deep learning-assisted denoising algorithm. To find the critical SNR, we evaluated restoration accuracy of the site classification as a function of SNR from a series of simulated images generated with different SNRs. As a result, we can see that the restoration accuracy maintains above 98% for all atomic sites and defects of V-doped WSe 2 when the SNR is larger than 1.1. However, statistical error in restoration accuracy is noticeably increased from the images with the values of SNR below 1.1 (Fig. S2a-c). We see that the classification error arises from the fake features generated after the application of denoising algorithm (Fig. S2d-f). Based on the result, we can define the fastest acquisition rate in STEM imaging for the V-WSe 2 sample, while maintaining a reliable restoration accuracy of above ~98%. To satisfy the condition that the SNR should be higher than 1.1, experimental ADF STEM images of the V-WSe 2 sample were recorded at the high scanning rate of 1 μsec/pix in this study. For V-MoS 2 , we found that the minimum limit of SNR should be ~1.5 to maintain the classification accuracy similar to the case of V-WSe 2 . This is ascribed to the lower scattering contrast of MoS 2 at the same electron probe condition (see Fig. S2g-i). As in the V-WSe 2 , we can see that fake feature contrast appears in the STEM image with the SNR of below 1.5 by the denoising process ( Fig. S2j-l). These results suggest that the fastest allowable scanning rate should be determined after carefully surveying the effect of SNR with respect to the restoration accuracy. Figure S3. The effect of signal-to-noise ratio (SNR) with respect to restoration accuracies. a,g) Plots showing changes in restoration accuracies of our denoising algorithm for atoms and defects in the respective V-WSe 2 and V-MoS 2 as a function of SNR. b,c,h,i) Confusion matrices displaying the classification results below or at the critical value of SNR for the two respective samples. Note that the critical SNRs at which the restoration accuracy for most atomic sites except for Se di-vacancy maintains under 98% were differently estimated to be 1.1 and 1.5 for the two samples, V-WSe 2 and V-MoS 2 , respectively. The diagonal boxes from top-left to bottom-right in the matrices represent the correct matching of site classification to the ground truth. d-f, j-l) Comparison of the ground truth image with the images generated below or at the critical SNR after denoising treatment for the two samples, V-WSe 2 and V-MoS 2 , respectively. Note that fake feature contrast appears in the STEM images with low SNR values below the critical SNR after denoising (see red circles in e and k).  Figure 2a, which was extracted from image data volume collected before the onset of electron beam-induced damage. b) A high SNR STEM image obtained by averaging 10 images in the image data volume. c) Restored ADF STEM image after denoising process of a shown as Figure 2b. Note that the right half parts of b and c are the results of site classification to evaluate the consistency between the ground truth and the denoised images. d) Confusion matrix obtained by matching of the site classification results for the frameaveraged and the denoised ADF STEM images.  . Note that the color-shaded regions in the graph indicate the threshold times (or doses) allowed to capture the intact structures of MoS 2 (blue) and V-MoS 2 (pink) monolayers, respectively, without radiation-induced structural damage. Scale bars in the ADF images are 2 nm. Figure S8. Spatiotemporal trajectory analysis of the V dopants and chalcogen vacancies for a) V-WSe 2 , b) WSe 2 , c) V-MoS 2 , and d) MoS 2 samples, respectively. These 3D trajectory diagrams describe how the defects evolve and transition under electron beam irradiation, which can be readily visualized from the results of stacked site classification maps obtained by the automated quantification algorithm.