building and exploring libraries of atomic defects in graphene: … · building and exploring...

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1Computational Sciences and Engineering Division, Oak Ridge National Laboratory,Oak Ridge, TN 37831, USA. 2Center for Nanophase Materials Sciences, Oak RidgeNational Laboratory, Oak Ridge, TN 37831, USA.*Corresponding author. Email: [email protected] (M.Z.); [email protected] (S.V.K.)

Ziatdinov et al., Sci. Adv. 2019;5 : eaaw8989 27 September 2019

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Building and exploring libraries of atomic defects ingraphene: Scanning transmission electron andscanning tunneling microscopy study
Maxim Ziatdinov1,2*, Ondrej Dyck2, Xin Li2, Bobby G. Sumpter1,2, Stephen Jesse2,Rama K. Vasudevan2, Sergei V. Kalinin2*
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The presence and configurations of defects are primary components determining materials functionality. Theirpopulation and distribution are often nonergodic and dependent on synthesis history, and therefore rarely ame-nable to direct theoretical prediction. Here, dynamic electron beam–induced transformations in Si deposited ona graphene monolayer are used to create libraries of possible Si and carbon vacancy defects. Deep learning networksare developed for automated image analysis and recognition of the defects, creating a library of (meta) stable defectconfigurations. Density functional theory is used to estimate atomically resolved scanning tunneling microscopy(STM) signatures of the classified defects from the created library, allowing identification of several defect typesacross imaging platforms. This approach allows automatic creation of defect libraries in solids, exploring themetastable configurations always present in real materials, and correlative studies with other atomically resolvedtechniques, providing comprehensive insight into defect functionalities.

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INTRODUCTIONMaterials form the basis ofmodern civilization, ranging from structuralmaterials in buildings and machines to semiconductors underpinninginformation technologies to functional materials in batteries, fuel cells,sensors, and other applications. For many materials classes, function-ality is ultimately determined by the presence and configurations ofdefects, ranging from simple substitutional defects in solid solutionsto complex extended defects involved in crystallographic shear phases,dislocations, etc.

In the case of two-dimensional (2D) materials, a growing numberof examples illustrate the possibility of electron beam–induced intro-duction of defects (1–6), some of which offer the possibility of atom-ically precise positioning within the lattice (7–9). These capabilitiesmay open pathways for the atomically precise fabrication of physicallyinteresting and technologically relevant structures such as molecularmagnets (10), quantumdots (11–14), spin diodes (15, 16), and ballistictransport field-effect transistors (17–19). To achieve the level of con-trol necessary to fabricate these structures, a deeper understanding ofbeam-inducedmodifications and a broad grasp of what defect config-urations are experimentally possible must be prioritized.

Clearly, the use of high-throughput computations to create li-braries of materials is not new, as exemplified by Materials GenomeInitiative (20). In this, large databases of first-principles calculationswere created and subsequently mined for materials with interestingproperties or for establishing structure-property relationships. How-ever, while powerful for simple materials, the number of possiblestructures for extended defects makes direct computational searchinfeasible. An alternative approach for materials design is based onartificial intelligence–assisted experimental workflows, where thermo-dynamic databases and density functional theory (DFT) calculationsare integrated to achieve property predictions and establish synthesis-property relationships. The corresponding databases includeMaterials

Data Facility (21), Citrination (22), Dark Reactions (23), andMaterialsInnovation Network (24). However, to date, these efforts use macro-scopic experimental descriptors andmesoscopic structural descriptorsonly. Very recently, Rajan et al. (25) created a theoretical library ofnanosized pore defects in 2Dmaterials and explored their energetics.

Given advances in imaging, it is now possible to image many sys-tems with atomic resolution via electron or scanning probe micros-copy (26–30). The key to understanding and using these data is toextract the different configurations of the atomic species, as their dis-tributions (fluctuations) encode important aspects that govern thesystem’s response to thermodynamic perturbations. However, this re-quires locating and classifying the defects themselves in an automatedmanner because of the numbers required for proper statistics. The taskis evenmore important given the need for complementary data on thesame defect configurations. For instance, imaging of atomic structure ofdefects is relatively straightforward in scanning transmission electronmicroscopy (STEM). However, the finer details of electronic structureat or around the defect necessitate scanning tunneling microscopy(STM)measurements. Because of the differences in imagingmechanismsand limitations of the experimental platforms, correlative atomically re-solved STEM-STM studies are extremely complex. Furthermore, thecontrast in STM and STEM data is completely different, so the com-plementary nature of both techniques cannot always be readily used.STEM measures lattice structure (i.e., the ideal image is the atomicnuclei, and the intensity in the image is roughlyproportional to the squareof the atomic number), while STMmeasures electronic properties [i.e.,the ideal image is the (local) integrated density of states, and the imageintensity reflects spatial distribution of electronic states at the Fermilevel].What is needed, is a combined experimental-theoretical approachto extract defects, classify them, and then perform first-principles cal-culations to explore their electronic structure. The latter can immedi-ately be used to simulate the expected STM images and provides directinsight into the effects of the defect on the material’s properties.

Here, we demonstrate an experimental approach for creatingdefect libraries from STEM data and determine defect statistics inthe Si-graphene system via advanced image recognition tools. Wefurther use these as an input for the DFT calculations to establish

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associated electronic properties and compare these with the STMresults on the same system.

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RESULTS AND DISCUSSIONTo create libraries of defects in graphene, we used active manipula-tion via a 100-kV electron beam to disperse silicon (Si) impuritiesover the graphene lattice (7). This active sputtering approach allowedus to create multiple metastable configurations of Si-C complexes ingraphene. We then acquired images using a 60-kV electron beam,which minimizes damage to the graphene lattice and allows a closerinspectionof the formeddefect structures. Figure 1A shows an exampleof high-angle annular dark field (HAADF) STEM image of a graphenesample with amorphous Si-C regions, which serve as the source of Sidopant atoms. Individual Si impurities embedded in the graphenelattice are seen.

To analyze the created defect structures and to generate a library ofdefects, we have developed a deep learning–based analytical workflowthat searches for and identifies various defect configurations in theavailable “raw” experimental data and categorizes them on the basisof the number of Si atoms in each configuration. As a first step, weused two deep fully convolutional neural networks (see Materials


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andMethods for details). The goal of the first neural network, a “defectsniffer,” is to identify anomalies and irregularities (that is, defects) inthe periodic structure of a crystalline material (in this case, graphene).The second neural network, an “atom finder,” identifies the elementalspecies and positions of atoms in a localized region (typically 2 nm by2 nm) around the detected defect. This two-stage deep learning ap-proach resembles the logic of a human operator who first identifiespoints of interest (irregularities and “anomalies”) in a larger-scale ex-perimental image and subsequently examines specific features (e.g.,details of atomic structure surrounding the detected irregularity) inmore detail. Thus, it can also potentially be applied in the future fora realization of an intelligent (“self-driving”) microscope. Notably,while this two-stage approach can be, in principle, replaced by just asingle deep learning model, the classical generalization versus accura-cy trade-off will likely increase the error of finding positions of atomsand atomic defects. We therefore believe that the current approach(with two specialized models rather than one very general model) isan optimal solution for this type of problem.

The defect sniffer neural network was trained using several weak-ly labeled experimental images [that is, a structure is either a defect(vacancy or impurity) or not, without classifying defects into specificsubcategories at this stage], using the fact that each defect is asso-ciated with violation of ideal periodicity of the lattice. The detailsof the procedure for constructing a training set for this type of prob-lem can be found elsewhere (31). It was trained to find point defectsonly (vacancies and Si dopants), while avoiding areas with extendeddefects (such as larger holes and amorphous Si-C regions). Density-based spatial clustering analysis (32) was applied to the output of aneural network to groupmultiple detected point defects located closeto each other (maximum radius e set to 0.5 nm). The regions of in-terest (in terms of the presence of Si point defects) identified by thisapproach for data from Fig. 1A are shown in Fig. 1B.

The atom finder neural networkwas trained using simulated STEMimages. Recently, several studies (33–35) have demonstrated that deepneural networks trainedusing simulated data can successfully generalizeto real experimental atom-resolved and molecule-resolved STM andSTEM data. The theoretical data were produced by either using aMultiSlice algorithm (36) for STEM image simulations or represent-ing atoms as Gaussian blobs. Both approaches for model traininggave similar results in terms of defect finding and identification forthe current 2D system. Each theoretical image was augmented to ac-count for model uncertainties such as local distortions (±15% displace-ments in atomic positions) and instrumental factors such as globalimage or scan distortion and different levels of noise.

The output of the second neural network was mapped onto thegraph structure representing the classical chemical bonding picture(35). Specifically, we first identified the centers of the mass for each“blob” (atom) in the pixel-wise maps from the output(s) of a neuralnetwork and then used the information about the type and position ofeach atom to construct the graph nodes. The nodeswere then connectedby the graph edges that represent bonds. To construct the bonds, weused chemistry-based hard constraints on the maximum possiblecoordination number of each type of atom, as well asmaximumormin-imum allowed length of atomic bond between corresponding pairs ofatoms.We note that this analysis assumes that a sample has a quasi-2Dconfiguration. If there is no information (e.g., from image “tags”) avail-able on the scan size, then it is possible switch to a calibration based onthe peak in the distribution of nearest-neighbor distances, which arepredominantly C—C bonds.

Fig. 1. STEM data: Original and processed by neural networks. (A) STEMoverview image. Brighter areas typically correspond to amorphous Si-C regions,from which Si atoms can be dispersed into clean graphene lattice, leading to var-ious Si defect structures (in terms of number of Si atoms and their bonding toeach other and to nearby lattice atoms). (B) Results of applying a defect sniffer(deep neural network followed by density-based spatial clustering) to data in (A).White markers show regions of interest as identified by a defect sniffer. Noticethat it ignores amorphous Si-C regions and returns information on the locationof point Si defects, only (C) 2 nm by 2 nm area cropped around one of the iden-tified defects [white box in (B)]. This cropped image serves as an input to atomfinder model. (D) The output of an atom finder network for the image in (C),where red blobs correspond to C lattice atoms and a green blob is associatedwith Si impurity.

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Here, it was crucial to identify accurately the environment of eachSi impurity, which included the information on the lengths and anglesof bonds with the neighboring carbon atoms in the host graphenelattice. To the best of our knowledge, the current methods for atomfinding based on 2D Gaussian fitting in atomically resolved data donot allow a reliable extraction of atomic positions for images whereatoms do not appear as local maxima (such as in Fig. 1C). As a result,there is no ground truth for the experimental data against which ourdeep learning–based atom-finding approach can be tested. Hence, weused images of graphene lattice simulated with theMultiSlice algorithmthat were not part of the model training or testing and therefore canserve as a validation dataset. The number of atoms in the validationimages was comparable to that in the experimental images used in thecurrent study (in the second, “atom finding,” stage). Each image wascorrupted by unique combination of blurring and noise (no twoimages were the same). The average (per each image) deviation ofthe predicted positions from the “ground truth” positions of atomsfor different combinations of noise and blurring is shown in Fig. 2A.We generally found that the trained model can determine robustlyatomic positions until the level of noise becomes so high that thelattice contours become barely distinguishable to the human eye (thiscorresponds to regions with 0′ > 130 and l′ < 110 in Fig. 2A). In Fig. 2(B to D), we show an example of the model output for data where theimage resolution, the number of atoms in an image, and the level


of noise are comparable to those in current experiments. The devi-ation of atomic center positions from “true” positions for these datais mostly below 10 pm, which is within the instrumental error fordetection of atomic position in single-image STEM data with lowsignal-to-noise ratio (37, 38). One of the reasons why a neural net-work shows such a good performancewhen taskedwith finding atomsis because it is “aware” of the system (lattice) under study (i.e., trainedspecifically to look for atoms in this type of lattice, ideal and distorted).We believe that because getting the atomic positions accurately iscrucial for this particular type of pixel-wise classification problem,the approach for testing a network’s accuracy described above is pref-erable to the existing ones from the domain of classical machine ordeep learning.

The total number of analyzed images was approximately 500, witheach image containing either single ormultiple Si impurities. The imagesize varied between 2 and 16 nm, and the image resolution was in therange between 256 pixels by 256 pixels and 2048 pixels by 2048 pixels.Notably, many of the same types of Si defects can exist without 100-kVe-beam “sputtering” but with a much smaller density, which is not suf-ficient for creating a library of defects. The representative examples foreach category were then selected with the assistance of a human expert.Structures that could not be confirmed independently (even on asimple qualitative level) by a human expert eye, either because of veryhigh levels of noise in the image or because of ambiguity associatedwith

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Fig. 2. Evaluation of accuracy in finding the atomic positions via a deep learning model for different levels of noise. (A) The deviation of the predicted positions(average value for all atoms in the image) from the ground truth positions of atoms for different combinations of noise (l′) and blurring (s′). The l′ and s′ are the scaledparameters of Poisson and Gaussian distributions, respectively. See the Supplementary Materials for the details and code of how the noisy data were created andanalyzed. (B) Simulated image of graphene lattice associated with the red cross in (A). (C) Same image overlaid with atomic coordinates. Different colors of circularmarkers show different degrees of atomic positions displacement from ground truth coordinates. (D) The histogram showing atomic displacements for every atomicposition displayed in (C). Most of the deviations are below 10 pm, which is within instrumental uncertainty for atomic position extraction.

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the absence of information in the z direction for certain structures, werenot considered or counted. Last, the input (structural) data for the firstprinciples–based studies of the detected defect were obtained bycropping a square “cell” with ~30 atoms around the defect of interest(for the chosen categories) and embedding them into a larger standardgraphene supercell.

Figures 3 and 4 illustrate a constructed library of Si-containing de-fects in graphene. We define a Si defect as a Si atom and its first co-ordination “sphere” or Si atoms connected either directly or through asingle C atom to each other and their first coordination sphere. Using


this definition for a defect, we began categorizing Si defects on thebasis of the number of Si atoms that each defect contained. The defectscontaining a single Si are shown in Fig. 3, and the defects containingtwo and more Si impurities are shown in Fig. 4. Our approach alsoallowed a further split of these categories into subcategories basedon coordination number, variation in bond lengths in a single defect,proximity to other defects [e.g., multi-atom lattice vacancies locatedwithin a specific radius (one lattice constant, two lattice constants,etc.) from the defect center of mass]. Notably, because our analysiswas performed after the STEM experiments were completed, it does

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Fig. 3. Constructing libraries of defects from STEMdata on graphenewith Si impurities via deep learning–based analysis of raw experimental data. (A and B) Defectscontaining a single three-fold coordinated Si atom (count, 465) (A) and a single four-fold coordinated Si atom (count, 16) (B). (C and D) Histograms of Si—C bondlengths (C) and Si—C bond angles (D) for three-fold Si defect. (E and F) Examples of distorted threefold Si defect located next to a multivacancy (E) and at topologicaldefect (F). The number of distorted (SD s = ( ∑ dx2/n)1/2 in C—Si—C bond angles above 15) and undistorted three-fold Si defects was 231 and 234, respectively.

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not account for the possibility that certain defects appear more fre-quently than others simply because of human operator (confirma-tion) bias and specific interest in certain structures. Hence, thefrequency of different defect occurrences in the analyzed images maynot necessarily reflect the relative frequency of their occurrence in thephysical system. However, automatization of experimental acquisitionwill preclude these problems in the future.

The first category is a defect that has only one Si atom (Fig. 3). Itcontains two subcategories, based on number of bond connectionsto nearby lattice atoms, corresponding to classical three and four-coordinated Si atoms (Fig. 3, A andB, respectively) (39). Ourmodelwasable to identify 465 three-fold coordinated Si atoms and 16 four-foldcoordinated Si atoms. This approach also enables an automated cal-culation of the bond lengths and bond angles in each detected defect.The histograms of bond lengths and angles for all detected three-foldSi defects are shown in Fig. 3 (C and D). We next defined a distortedthree-fold defect as a defect where an SD s = ( ∑ dx2/n)1/2 of three C—Si—C bond angles is larger than 15. This allowed the identification ofadditional subcategories of three-fold defect corresponding to Si im-


purities located adjacent to hole or multivacancies (Fig. 3E) or to atopological defect (Fig. 3F), which are characterized by a substantiallystronger distortion of C—Si—C bond angles (note that both missingatoms in honeycomb lattice and topological reconstructions with anenlarged size of carbon rings are seen as vacancies in our analysis).

We proceed to the discussion of defects containing more than asingle Si atom. Figure 4 shows the identified structures of defect withtwo and more Si atoms. This includes multiple different dimerstructures, in which each Si atom in the dimer has three-fold orfour-fold coordination (Fig. 4, A toD and F) and a two-Si defect whereSi atoms are connected to each other via a C atom (Fig. 4E). As in thecase with a single atom, the two-Si defects located next to the hole ormultivacancy are characterized by a stronger distortion in C—Si—Cbonds compared to when they are observed on a clean lattice (seeFig. 4, A andD). A third category includes Si defects with three or moreSi atoms (Fig. 4, G to I). This category contains trimer (Fig. 4G) andtetramer (Fig. 4H) arrangements of Si impurities and more complexSi-C clusters containing five and more Si that are usually observed atthe edges of graphene vacancies and holes.

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Fig. 4. Atomic defects containing two and more Si atoms. (A to F) Defects with two Si atoms. Si dimer structures with each Si having two C in its first coordinationsphere (count, 6) (A and D); one Si having three C atoms and another one having two C atoms (count, 4) (B); each Si having two C atoms plus one “shared” C atom(count, 3) (C); each Si connected to three C atoms (count, 5) (F); nondimer structure, where two Si atoms are connected via C atom (count, 3) (E). (G to I) Defects withthree and more Si atoms: three Si (count, 50) (G), four Si (count, 6) (H), and five or more Si (count, 56) (I).

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This comprises the library of observed Si atomic defects in mono-layer graphene. We made the images labeled according to the classi-fication scheme described above, available through the Citrinationplatform (40). One immediate application of this library for materialexploration is to compare the experimentally observed structures tostructures calculated with DFT at different levels of strain using theaveraged experimental coordinates as an initial input for geometricrelaxation. By calculating and plotting the strain components, togetherwith translation and rotation transformations, needed for transform-ing the experimental structures into an ideal theoretical structure (seefig. S5) or vice versa, one can estimate a “window of stability” for aparticular defect type.

To demonstrate a further applicability of this library and addi-tional insight into the electronic structure of defects in graphene withSi, we perform DFT-based calculations of electronic structure andexperimental atomic-scale STM measurements on the same sample.The STM images obtained at low-bias voltages reflect spatial distri-bution of electronic states around the Fermi level and can be used toprobe local perturbation in a material’s electronic structure causedby defects. An example of an experimental STM image obtained overa relatively large field of view on the sample from STEM measure-ments is shown in Fig. 5. The STM data typically showed the pres-ence of atomically resolved regions with a lateral size of about 3 to6 nm separated by regions for which no atomic resolution could beachieved. We assigned the latter to amorphous C-Si regions, whichwere commonly seen in the STEM experiment on this and other sam-ples (7). An example of a point defect causing perturbation in theelectronic structure of a nearby graphene region is shown in the mag-nified image in Fig. 5B.

Notably, two important limitations are expected in the interpreta-tion of STM images from a STEM sample. First, because the samplewas transferred through ambient atmosphere, contamination of thesample surface with oxygen functional groups is possible. In addition,in the STM setup used for this study, it was not possible explore theexact same region that was examined in the STEM experiment.

Despite these limitations, we were able to capture a number ofatomic-scale STM images with characteristic point defects and com-pare them to the structures derived from the analysis of the STEMdata. Note that a proper interpretation of STM data requires compar-ison with theoretical calculations of local density of states at the Fermilevel for the structures of interest. For this purpose, we performedDFTcalculations for the first two categories of defects.We limited ourselves


only to single and dimer Si defects occurring on a clean graphene sur-face. Specifically, we first performed full 3D relaxation of the 2Dprojection of atomic coordinates found in the analysis of the STEMdata. Then, the relaxed coordinates were used to calculate the elec-tronic structure for each type of defect. The STMdata for point defectswere then compared with STM images calculated from DFT datawithin Tersoff-Hamman approach (41, 42).

We compared the experimental STM data with DFT calculationsof integrated local density of states associated with two bands aboveand below the Fermi level (if these bands existed within an energyrange of−0.5 to +0.5 eV).We note that of the structures analyzed, onlythe three-fold Si impurity showed an out-of-the-plane displacement inthe final relaxed geometry, whereas the rest of the structures remainedflat. Comparison of point-like defects obtained in the STM at low-biasvoltage (0.1 to 0.3 V) to simulations of three- and fourfold Si defects(Fig. 6, A and B) suggests that we were able to capture the former inthe STM experiment. We next compared the dimer-like structuresobserved in the STM experiment (Fig. 6, C and D) to the DFT simula-tions of dimer structures observed in Fig. 4. We found that the closestmatch is the Si2C6 (Fig. 4F) structure that is characterized by two well-defined bright spots associated with two Si impurities in the relevantenergy range. Either the rest of the tested dimer structures did not pro-duce a well-defined structure with two bright spots or the distance be-tween the spots was smaller than that in the case of STM experimentaldata (see the Supplementary Materials). Last, in fig. S6, we show twoadditional structures that are possible candidate matches with thosedisplayed in Fig. 4 (G to I), containing three and more Si atoms. Theinterpretation of the exact nature of these complex defects will be thesubject of future work.

CONCLUSIONS AND OUTLOOKTo summarize, we combined active electron beam manipulation ofimpurities in graphene and deepmachine learning to construct librariesof Si defect structures. By performing STM experiments on the samesample, supplemented by first-principles calculations, we were able tolink together experimental results that characterize a material’s struc-ture (STEM) and functionalities (STM). Our work shows a pathwaytoward the creation of comprehensive libraries of atomic defects andtheir functionalities based on experimental observations from multipleatomically resolved probes generating synergistic information and per-forming correlative analysis of structure-property relationships on thelevel of single atomic defects.

We propose that an important part of both theoretically and ex-perimentally driven materials prediction will be libraries of atomicdefects. For the theoretical effort, these libraries can significantlyconfine the region of the chemical space to explore by focusingthe effort on the experimentally observed defect classes, as opposedto all those theoretically possible. For experiment, the defect popu-lations and correlations can be used as direct input to machinelearning schemes. Last, this information can shed light on defectequilibria, solid-state reaction pathways, and other fundamentalparameters of materials.

MATERIALS AND METHODSSample preparationGraphene was grown via atmospheric pressure chemical vapordeposition on a Cu foil. (43) The Cu foil was then spin-coated with

Fig. 5. STM experiment on the same sample. (A) Large-scale STM image of arelatively large area of the graphene sample from the STEM experiment. (B) Mag-nified view of an atomic defect highlighted by the white rectangle in (A).Tunneling conditions Vbias = 0.1 V and Isetpoint = 55 pA.

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poly(methyl-methacrylate) (PMMA) as a mechanical stabilizer.The Cu foil was dissolved in a bath of ammonium persulfate–deionized (DI) water (0.05 g/ml). The graphene/PMMA filmwas transferred to hydrogen chloride diluted in DI water bathto remove the ammonium persulfate, followed by a DI water rinse.The graphene/PMMA film was placed on a transmission electronmicroscopy grid and annealed on a hot plate at 150°C for ~20 minto adhere the grid to the graphene. The PMMA was subsequentlydissolved away in an acetone bath, followed by an isopropyl alco-hol rinse. Last, the grid was annealed in an Ar-O2 [450 standardcubic centimeters per minute (SCCM)/45 SCCM] environment at500°C for 1.5 hours to prevent e-beam–induced hydrocarbondeposition in the STEM (44, 45).

STEM experimentSTEM imaging was performed at room temperature using a NionUltraSTEM U100 microscope operated at 60 kV. The images wereacquired in HAADF imaging mode and were introduced to the deeplearning network without any postprocessing.

STM experimentThe STM experiments were performed at room temperature using anOmicron VT-STMmicroscope equipped with a Nanonis controller inan operating pressure of 2 × 10−10 Torr. The STM images were ob-tained with mechanically cut Pt/Ir alloy tips.


DFT calculationsThe DFT calculations were carried out using the VASP (Vienna AbInitio SimulationPackage; 5.4.1) (46, 47) using the projector-augmentedwave (PAW) method (48, 49). The electron-ion interactions were de-scribed using standard PAW potentials, with valence electron config-urations. A kinetic energy cutoff on the plane waves was set to 400 eV,and the “accurate” precision setting was adopted. A G-centered k-pointmesh of 9 by 9 by 1 was used for the Brillouin zone integrations. Theconvergence criteria for the electronic self-consistent loop were setto 10−4 eV.

Data analysisThe deep neural networks were implemented using the Keras deeplearning library (https://keras.io/). The neural networks had anencoder-decoder structure [SegNet-like architecture (50)] that alloweda pixel-level classification of input images. For the atom finder network,the encoder part consisted of six convolutional layers, all activated by arectified linear unit function. The convolutional filters (kernels) in allthe layers were of the size 3 by 3 and stride 1. The first convolutionallayer had 64 filters, the second and third layers had 128 filters each,and the fourth to sixth layers had 256 filters each. The max poolinglayers were placed after the first, third and sixth layers. The decoder partcontained the same blocks of convolutional layers in reversed orderwith a bilinear interpolated upsampling instead of the max poolingunits. The Adam optimizer (51) was used with categorical cross-entropy as the loss function. For the “defect sniffer” network, theencoder part consisted of three convolutional layers with 64, 128,and 256 filters of the size 3 by 3 and stride 1, activated by a rectifiedlinear unit function. The max pooling layers were placed in betweenthe layers. The decoder part contained the same blocks of convolu-tional layers in reversed order with the nearest-neighbor upsamplingbetween them. The focal loss (52) was used for improving identifica-tion of the defect structures. To optimize this loss, the Adam optimizerwas used. The accuracy scores on a test set for atom finder and defectsniffer were ≈96 and ≈99%, respectively. The graph structures wereconstructed using NetworkX library (https://networkx.github.io/). Thelatest versionof aworkflow for creating and exploring the defect librariesis available at https://github.com/pycroscopy/AICrystallographer/tree/master/LibraryNet.

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/9/eaaw8989/DC1Fig. S1. DFT-simulated distribution of electronic charge density for Si1C4 defect.Fig. S2. DFT-simulated distribution of electronic charge density for Si2C4 defect.Fig. S3. DFT-simulated distribution of electronic charge density for Si2C5 (type 1) defect.Fig. S4. DFT-simulated distribution of electronic charge density for Si2C5 (type 2) defect.Fig. S5. Strain analysis for S1C3 defect.Fig. S6. More complex defect structures observed in the STM experiment on STEM sample ofgraphene.Jupyter notebook (atom-finding accuracy versus noise)

REFERENCES AND NOTES1. N. Jiang, E. Zarkadoula, P. Narang, A. Maksov, I. Kravchenko, A. Borisevich, S. Jesse,

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Fig. 6. Comparison of STM data on point impurities with DFT calculations.(A) Experimental STM data on a single impurity obtained under tunnelingconditions Vbias = 0.1 V and Isetpoint = 55 pA. (B) DFT-simulated STM images ofSi1C3 defect for two bands below (E1V and E2V ) and above (E1C and E1C ) the Fermilevel. (C) Experimental STM data on a dimer-like impurity obtained undertunneling conditions Vbias = 0.3 V and Isetpoint = 55 pA. Inset shows a line profilealong the A and B points. (D) DFT-simulated STM images of Si2C6 defect for twobands below (E1V and E2V ) and above (E1C and E1C ) the Fermi level.

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AcknowledgmentsFunding: This research was sponsored by the Division of Materials Sciences and Engineering,Office of Science, Basic Energy Sciences, U.S. Department of Energy (to R.K.V. and S.V.K.).Research was conducted at the Center for Nanophase Materials Sciences, which is a DOEOffice of Science User Facility. STEM experiments (to O.D. and S.J.) and data analysis (to M.Z.)were supported by the Laboratory Directed Research and Development Program of Oak RidgeNational Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy.

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https://doi.org/10.25920/0xv3-8459

https://arxiv.org/abs/1412.6980



Author contributions: S.V.K. and M.Z. conceived the project. O.D. performed the STEMmeasurements. M.Z. performed the STM measurements and the data analysis. B.G.S.performed the DFT calculations. R.K.V. and S.J. aided in the interpretation of results. X.L. aidedin data analysis. S.V.K., M.Z., and R.K.V. wrote the paper with inputs from all the coauthors.Competing interests: All authors declare that they have no competing interests. Data andmaterials availability: All data needed to evaluate the conclusions in the paper are present inthe paper and/or the Supplementary Materials. Additional data related to this paper maybe requested from the authors.


Submitted 4 February 2019Accepted 4 September 2019Published 27 September 201910.1126/sciadv.aaw8989

Citation: M. Ziatdinov, O. Dyck, X. Li, B. G. Sumpter, S. Jesse, R. K. Vasudevan, S. V. Kalinin,Building and exploring libraries of atomic defects in graphene: Scanning transmissionelectron and scanning tunneling microscopy study. Sci. Adv. 5, eaaw8989 (2019).

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electron and scanning tunneling microscopy studyBuilding and exploring libraries of atomic defects in graphene: Scanning transmission

Maxim Ziatdinov, Ondrej Dyck, Xin Li, Bobby G. Sumpter, Stephen Jesse, Rama K. Vasudevan and Sergei V. Kalinin

DOI: 10.1126/sciadv.aaw8989 (9), eaaw8989.5Sci Adv

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