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Strain Mapping of Two-Dimensional Heterostructures with Sub-Picometer Precision Yimo Han, Kayla X Nguyen, Michael Cao, Paul D Cueva, Saien Xie, Mark W Tate, Prafull Purohit, Sol M. Gruner, Jiwoong Park, and David A. Muller Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b00952 • Publication Date (Web): 18 May 2018 Downloaded from http://pubs.acs.org on May 18, 2018

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Strain Mapping of Two-Dimensional Heterostructures with Sub-Picometer Precision Yimo Han1, Kayla Nguyen1,3, Michael Cao1, Paul Cueva1, Saien Xie1,2, Mark W. Tate4, Prafull Purohit4, Sol M. Gruner4,5,6,7, Jiwoong Park3, David A. Muller1,6* 1.

School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853,

USA 2.

Department of Chemistry, Institute for Molecular Engineering, and James Franck

Institute, University of Chicago, Chicago, IL 60637, USA 3.

Chemistry and Chemical Biology Department, Cornell University, Ithaca, NY 14853,

USA 4.

Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853,

USA 5.

Physics Department, Cornell University, Ithaca, NY 14853, USA

6.

Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY 14853, USA

7.

Cornell High Energy Synchrotron Source, Cornell University, Ithaca, NY 14853, USA

*Correspondence to: [email protected] Abstract Next-generation, atomically thin devices require in-plane, one-dimensional heterojunctions to electrically connect different two-dimensional (2D) materials. However, the lattice mismatch between most 2D materials leads to unavoidable strain, dislocations, or ripples, which can strongly affect their mechanical, optical, and electronic properties. We have developed an approach to map 2D heterojunction lattice and strain profiles with sub-picometer precision and the ability to identify dislocations and out-of-plane ripples. We collected diffraction patterns from a focused electron beam for each real-space scan position with a highspeed, high dynamic range, momentum-resolved detector – the electron microscope pixel array detector (EMPAD). The resulting four-dimensional (4D) phase space

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datasets contain the full spatially-resolved lattice information of the sample. By using this technique on tungsten disulfide (WS2) and tungsten diselenide (WSe2) lateral heterostructures, we have mapped lattice distortions with 0.3 pm precision across multi-micron fields of view and simultaneously observed the dislocations and ripples responsible for strain relaxation in 2D laterally-epitaxial structures. Strain fields and dislocations play an important role in determining the mechanical and electronic properties of crystalline materials. When forming epitaxial heterojunctions between thick films and a substrate, the primary strain relaxation mechanism is through the formation of misfit dislocations. However, for lateral epitaxial heterojunctions in 2D films, an additional and competing strain relaxation pathway – that of forming out-ofplane ripples – becomes available as well1,2. Understanding the balance between the two strain-relaxation mechanisms will be important for optimizing the properties of 2D planar junctions and their strain engineering. Here we describe a method for simultaneously mapping both the strain fields and the ripples in 2D lateral heterojunctions, and 2D structures more generally. Conventional transmission electron microscopy (TEM) can identify strain fields and dislocations in bulk materials using the diffraction contrast from two-beam analysis3 or weak-beam dark field imaging4. However, given the rod-like nature of diffraction peaks normal to the film, these methods are very difficult to implement in 2D materials, which are confined to atomic dimensions in the direction of the beam propagation. While geometric phase analysis (GPA)5-8 on atomic-resolution images can provide strain maps for 2D materials, the field-of-view is limited to a few tens of nanometers (as every atom needs to be resolved). When grains or heterostructures of 2D materials9-12 laterally reach the more typical micron scales, measuring strain and dislocations at atomic resolution using GPA becomes impractical. Conversely, nanobeam diffraction (NBD) combined with scanning TEM (STEM)13-17 effectively decouples the spatial resolution from the strain mapping precision, allowing for high-precision strain measurements across a larger sample area. However, this approach on 2D materials has historically been limited by the

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speed and dynamic range of the existing detectors, as 2D materials are sensitive to the electron beam and weak scatterers. To overcome these issues, we developed a method to map the strain and identify dislocations in 2D crystals using an electron microscope pixel array detector (EMPAD)18 designed at Cornell. As a result of its high-speed, high dynamic range, and high sensitivity, scanning NBD can be achieved within minutes with no noticeable damage to 2D samples, ultimately providing sub-picometer precision strain mapping over length scales that range from angstroms to many micrometers. The EMPAD operates at a range of accelerating voltages from 20 kV to 300 kV (The work presented here was performed at 80 kV. See SI #1 for experimental conditions). Its single-electron sensitivity allows for quantitative analysis of diffraction from a single atom19,20, which is highly advantageous for studying 2D materials that are only one- to three-atoms thick. Moreover, the EMPAD’s high dynamic range enables collection of all transmitted electrons at small convergence angles with the primary beam unsaturated and diffracted beams clearly resolved (Fig. 1b), as demonstrated by integrating the central beam (one diffracted beam) to plot the virtual bright field (dark field) images, as shown in Fig. 1c and 1d. The samples we examined were laterally-stitched epitaxial monolayer transition metal dichalcogenide (TMD) heterojunctions, which are synthesized through metal-organic chemical vapor deposition (MOCVD)2,21. From the EMPAD’s 4D dataset of a sample on 20 nm SiO2 TEM grids, we extracted the ADF-STEM signal (Fig. 2a) by integrating the diffraction patterns masked by a virtual ADF detector with an inner angle of 25 mrad. The ADF-STEM image provides little contrast difference between WS2 and WSe2, as the heavy tungsten atoms dominate the contrast. In comparison, the lattice constant map (Fig. 2b) calculated by measuring shifts in the reciprocal lattice vectors clearly distinguishes the two materials, which contain nanometer-sharp interfaces (inset of Fig. 2b) (see SI sections #2 and #3 for calculation details). From a histogram of lattice constant measurement (Fig. 2c), we extracted the mean values as the statistically averaged lattice constant for WS2 (3.182 ± 0.0005 Å) and WSe2 (3.282 ± 0.001 Å), indicating a 3.1% lattice mismatch (fully relaxed films have 4.5% lattice mismatch22). The histogram (inset

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of Fig. 2c) from a flat region (gray box in Fig. 2b) indicates this method has a precision higher than 0.3 pm, with local sample distortions placing an upper limit on the spread. The sub-picometer precision of the lattice constant mapping relies on high angular resolution when we measure the centers of the diffraction spots. For 2D materials, the center of mass (CoM) is an efficient approach to achieve a high angular resolution in the diffraction space for strain mapping. The accuracy of the method, and the percentage error in the measurement of a lattice spacing, 𝜎, depends on whether the probe is sourcesize limited as is typical at large beam currents, or diffraction limited as is typical at low beam currents when a coherent probe is desired. If the probe is diffraction-limited the accuracy scales as 𝜎 ∝ 1/&𝑑( × √𝐼, where 𝑑( is the probe size and 𝐼 is the beam current, thus allowing for tradeoffs between dose and accuracy at a fixed spatial resolution. If the probe is source-size limited then probe size and beam current are coupled, and 𝜎 ∝ 1/&𝑑( × -𝛽 , where 𝛽 is the source brightness. In both cases, accuracy and spatial resolution are inversely coupled. The cross-over between the 2 regimes occurs around 30-60 pA for current Schottky-like field emission sources, where a current smaller than 30 pA lies in the diffraction-limited regime. Here we used a ~20 pA beam current, a 1.6 mrad convergence angle, resulting in a ~3 nm spot size. More experimental details are provided in SI #1. The CoM calculation, optimization of pixel sampling, and error analysis are provided in SI #2. From the CoMs of all diffraction spots, we extract the diffraction vectors gi (i=1,2) (Fig. S4), i.e. the reciprocal lattice vectors, to generate strain maps across the heterostructure (see details in SI #4). These strain maps contain the uniaxial strain (ε00 and ε11 ), shear strain (ε01 ), and rotation (ε234 ) maps (Fig. S5). The x-direction uniaxial strain (ε00 ) map (Fig. 3a) shows clear differences between the WS2 and WSe2 as well as small local variations, indicating the film is largely relaxed, but not completely. This is expected since the width of the WS2 is far beyond the critical thickness for strain relaxation by misfit dislocations (~100 nm for this set of materials2). Narrow heterojunctions below the critical thickness remain coherent and exhibit uniaxial strain parallel to the interface (Fig. S6). To see the strain details, we plot the histograms of the x-direction strain map, where

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the WS2 peak in Fig. 3b fits two Gaussian peaks, corresponding to the unstrained (outer edges) and strained (interfaces) parts of the WS2 lattice in Fig. 3a. From a relatively flat WS2 region (gray box in Fig. 3a), we determined that the precision of our technique is 0.18% or better, as given by the spread of the histogram in the insert of Fig. 3b. The contrast of the uniaxial strain maps is dominated by the lattice mismatch between WS2 and WSe2, however the strain fields from interfacial misfit dislocations can be revealed using a different color scale for the ε00 and ε11 maps (Fig. S5c and S5d). The interfacial misfit dislocations are more easily seen in the rotation map (Fig. 3c) as the lattice orientation is the same on both sides of the interface, with their dipole fields located at the interface between WS2 and WSe2. The misfit dislocations along the interface contribute to releasing the lattice strain. However, the observed misfit dislocation spacing (more than 100 nm) is much larger than the spacing required to fully relax the lattice strain caused by the 3.1% lattice mismatch between WS2 and WSe2 (~10 nm). Although some of the dislocations show stronger dipoles (i.e. wider, more intense features) in the rotational strain map (shown by arrows in Fig. 3c), indicating their Burgers vectors are larger than one, the dislocation density still cannot account for the measured strain relaxation across the micrometer-scale junction. We note an internal (i.e. away from the interfaces) periodic rotational strain field in the outer WS2 region in the rotation map (Fig. 3c). Analogous to bulk epitaxy, which forms periodic ripples within the top layers of the thin films23, the periodic strain fields lower the elastic strain energy in 2D heterojunctions. However, the long wavelength of the rotational strain field (in microns) implies that it plays a minor role in releasing the strain. Moreover, the rotational strain is partially released by intrinsic dislocations inside WS2, as depicted in the magnified rotation map (circles in Fig. 3d). Compared to the misfit dislocations at the interface, these intrinsic dislocations have weaker dipolar strain fields (Fig. 3d), indicating that the intrinsic dislocations play a minor role in releasing the lattice strain.

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Since the observed density of both interfacial dislocations and rotation strain fields is an order of magnitude too low to account for the measured lattice relaxation across the junction, an additional strain relaxation method is required. In contrast to traditional 3D bulk crystals, 2D films can buckle up and form out-of-plane ripples without introducing in-plane lattice distortions. We observed ripples in WSe2 (larger lattice constant) rather than WS2 (smaller lattice constant), consistent with the out-of-plane ripples contributing to relaxing the original compressive strain in WSe2 caused by the lattice mismatch at the lateral heterojunctions1,2. To accurately identify the out-of-plane ripples and quantitatively map their orientations and spatial relation to the dislocations, we developed a novel approach, using the EMPAD 4D datasets. Thermal and static fluctuations in 2D materials smear the diffraction rods into cones24 (Fig. 4a). The diffraction pattern is formed where the Ewald sphere intersects the cone, and consequently the measured diffraction spot becomes broader as the macroscopic sample tilt is increased, as illustrated schematically in Fig. 4b. For tilt angles up to about 30°, this is a linear relationship24. The diffraction spots have a roughly Gaussian intensity profile, so we measure their widths from their second moments – i.e. the mean square angular width. Here, we mapped the tilted regions (i.e. the macroscopic ripples) by measuring the relative broadening of the diffraction spots compared to flat regions. We defined the complex ripple measure as 𝑅 = 𝐴 + 𝐵𝑒 ; + 𝐶𝑒 ;@=/> , where A, B, and C are the characteristic widths (as measured by second moments) of the corresponding diffraction spots in Fig. 4a and 4b. The phase of R gives the orientation of the ripples (Fig. 4c and 4d), while the amplitude captures the magnitude of the local tilt in the ripple (Fig. 4e). Additional details on the calculation of the ripple measure can be found in SI #5. Using this approach, the phase plot of the R map (Fig. 4c) illustrates that the ripples form along different orientations, and only appear inside WSe2. As shown in the magnified image (Fig. 4d), these ripples have a tendency to form perpendicular to the interface between WS2 and WSe2 on the WSe2 side, thus releasing the lattice strain. In addition, we can simultaneously map the ripples and dislocations by extracting both maps from the

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same EMPAD 4D dataset. The overlay of the ripple amplitude map and the dislocation map (Fig. 4e) elucidates the strain relaxation mechanism of the 2D lateral heterojunctions. The area (box 1, Fig. 4e) where there are no dislocations exhibits a high density of periodic ripples with an 8-degree maximum tilt (see more details in SI #5, Fig. S7 for angular calibrations), indicating the ripples can relax the strain without causing dislocations. In contrast, the region that is rich with interfacial dislocations (indicated by the arrows in box 2, Fig. 4e) displays fewer ripples, as shown by the lower density and lower intensity of the ripples in box 2 (in Fig. 4e), implying that the strain in this region is predominantly relaxed by the interfacial dislocations. Dislocations with larger Burgers vectors (box 3, Fig. 4e, highlighted in magenta) noticeably interrupt ripple formation, as shown by the discontinuity of the ripples in box 3, Fig. 4e. We now can also understand why some the dislocation strain fields in Fig. 3c,d are present only on the WS2 side – those are relaxed by ripples on the WSe2 side. To conclude, the two above-mentioned strain relaxation approaches – misfit dislocations and out-of-plane ripples – appear to compete against each other. The low density of misfit dislocations (~ 10% of that needed for full relaxation by misfits alone) suggests the ripples play a significant role in relaxing the interfacial strain. So far, we mapped the lattice constant, strain, rotation, and ripples in the lateral heterostructure and identified uniaxial strain, dislocations, and ripples. All the lattice information is recorded within a single EMPAD 4D dataset. In electron microscopy, principal component analysis (PCA) has been widely used for multi-dimensional datasets, such as electron energy loss spectra (EELS)25,26. In EMPAD 4D datasets, PCA as a screening tool provides a statistical approach to immediately obtain a hierarchy of information by extracting the linearly uncorrelated patterns that contain the majority of the variance in the data (SI #6). For our 4D data of the WS2-WSe2 multi-junctions, we blocked the center beam for PCA to avoid any dominating features inside the center beam. The principal components of the diffraction patterns (Fig. 5c-h) and their corresponding weighting maps (Fig. 5i-l) capture the highest variance features in the 4D dataset (more maps in Fig. S8). By comparing the maps generated using the former method (Fig. 5a-d), we can relate the second to fifth principal components to the filtered

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dark field (DF) of the multi-junction (Fig. 5e, i), the rotation of the lattice (Fig. 5f, j), the lattice constant difference (Fig. 5g, k), and the local ripples in WSe2 region (Fig. 5h, l), respectively. PCA offers a swift and facile method to analyze the 4D EMPAD data and quickly highlights the largest changes for our future studies. In conclusion, we developed an approach to simultaneously map lattice constant, strain, dislocations, and out-of-plane ripples with high precision on all relevant length scales. All lattice information can be extracted from the 4D data which requires only a single fast scan, effectively reducing the electron dose in 2D materials. Moreover, the accuracy of CoM measurements allows us to map the lattice constant and strain with precisions greater than 0.3 pm and 0.18% respectively at WS2-WSe2 lateral heterojunctions. In addition, we observed that the lattice strain is released partly by misfit dislocations but mainly by out-of-plane ripples, which act as two competing mechanisms, both of which play an important role in the mechanical and electrical properties of 2D materials. This method will be valuable for studying the lattice distortions in 2D materials and their atomically thin circuitry by identifying the lattice strain and dislocations and offering essential feedback for material synthesis.

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Figure 1 | EMPAD imaging. a, Schematic of the EMPAD operation, where a full diffraction pattern, including the unsaturated primary beam, is recorded at each scan position. b, Diffraction images taken by EMPAD. The top panel shows the diffraction image of a 5 nm SiNx film, while the bottom panel displays the diffraction pattern of a WSe2 monolayer located on the 5 nm SiNx film. c and d show the virtual bright field and filtered dark field images obtained by integrating the central and the labeled diffracted beam, respectively, as indicated on their top left sections.

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Figure 2 | Lattice constant map. a, Annular dark field (ADF) image extracted from the EMPAD 4D data on a wide WS2-WSe2 lateral heterojunction. The inner detector angle is 50 mrad. b, Lattice constant map of micron-sized triangles. The inset displays a line profile across the interface between WSe2 and WS2. c, Lattice constant histogram from b. The inset is the histogram from a flat region (gray box in b), indicating a precision of at least ~0.3 pm.

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Figure 3 | Strain maps. a, Uniaxial strain map showing most of the strain has been released. b, Strain histogram from a. The WS2 peak fits two Gaussians that correspond to unstrained and strained regions. The inset shows the histogram from a flat region (gray box in a) indicating a precision better than ~ 0.18%. c,d, The rotation map displaying misfit dislocations that contribute to relaxing the lattice strain at the WS2-WSe2 junction. The dislocations indicated by arrows possess larger Burgers vectors. The internal strain in WS2 results in a few dislocations inside WS2, which are indicated by the white circles.

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Figure 4 | Map of out-of-plane ripples. a,b, Schematics showing that a local sample tilt causes a broadening of the diffraction spots due to the intersection of the Ewald sphere with the cone-shaped diffraction rods resulting from thermal fluctuations in 2D materials. The broadening of the measured diffraction spots was quantified from the second moment (i.e. mean squared width). c, Map of the orientation of ripples calculated from the phase of the ripple measure, R. The map shows the WSe2 film forms out-of-plane ripples to release the strain, while WS2 is flat. d, Magnified ripple map showing a nanoscale ripple array along the junction. e, Amplitude plot of R, whose intensity reflects the out-of-plane tilt angle with a largest tilt of ~8° (see Fig. S7 for angular calibrations), overlaid with the dislocation map (magenta) that highlights the dislocation positions. (The dislocation map was generated by taking the absolute values of Fig. 3d and then applying a high pass filter to remove the background.)

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Figure 5 | Extracted data vs PCA on EMPAD 4D data. a Filtered DF, b rotation map, c lattice constant map, and d ripple map. The ripple map is the component of R projected along the arrow shown in d. The intensity of the maximum projected ripple measure, 3.5, corresponds to a tilt of ~8 degrees (calibration from Fig. S8). Negative numbers represent the tilt axis perpendicular to the projection direction. e-h, The PCA scores of the second to fifth principal components of the EMPAD 4D dataset and i-l their corresponding PCA loads. e,i show the crystalline structure, f,j depict the lattice rotation, g,k represent the lattice constant difference, and h,l display the local ripples.

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Corresponding Author *David A. Muller ([email protected]) Acknowledgements This work was primarily supported by the Cornell Center for Materials Research with funding from the NSF MRSEC program (DMR-1719875). MC was supported by DOD-MURI (Grant No. FA9550-16-1-0031). Detector development at Cornell was supported by DOE award DESC0017631 to SMG. We thank Mervin Zhao, Megan Holtz, Zhen Chen, Mengnan Zhao, Gabriela Correa, Lei Wang for helpful discussions. We thank Mariena Ramos and Lena Kourkoutis for help with electron microscopes. Author contributions The project was conceived and designed by Y.H. under the supervision of D.A.M.. The experimental results and data analysis were obtained by Y.H., with help from K.N., M.C., and P.C.. The samples were grown by S.X. under the supervision of J.P.. The EMPAD was developed by M.W.T., P.P., K.N., and M.C. under the supervision of S.M.G. and D.A.M.. Supporting Information The Supporting Information is available free of charge on the ACS Publications website providing more experimental details.

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