Gap States at Low-Angle Grain Boundaries in Monolayer Tungsten

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Gap States at Low-Angle Grain Boundaries in Monolayer Tungsten Diselenide Yuli Huang, Zijing Ding, Wenjing Zhang, Yung-Huang Chang, Yumeng Shi, Lain-Jong Li, Zhibo Song, Yu Jie Zheng, Dongzhi Chi, Su Ying Quek, and Andrew Thye Shen Wee Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00888 • Publication Date (Web): 03 May 2016 Downloaded from http://pubs.acs.org on May 4, 2016

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Gap States at Low-Angle Grain Boundaries in Monolayer Tungsten Diselenide Yu Li Huang,*,†,§, ¶ Zijing Ding,‡,§, ¶ Wenjing Zhang‡, Yung-Huang Chang,∥ Yumeng Shi, ⊥ LainJong Li, ⊥ Zhibo Song,†, § Yu Jie Zheng, § Dongzhi Chi†, Su Ying Quek, *,§,#, Andrew T. S. Wee*,§,# †

Institute of Materials Research & Engineering (IMRE), A*STAR (Agency for Science,

Technology and Research), 2 Fusionopolis Way, Innovis, Singapore 138634, Singapore ‡

SZU-NUS Collaborative Innovation Center for Optoelectronic Science & Technology, Key

Laboratory of Optoelectronic Devices and Systems of Ministry of Education and Guangdong Province, Shenzhen University, Shenzhen 518060, China §

Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117551,

Singapore ∥Department

⊥Physical

of Electrophysics, National Chiao Tung University, Hsinchu 300, Taiwan

Sciences and Engineering, King Abdullah University of Science and Technology,

Thuwal, 23955-6900, Saudi Arabia #

Centre for Advanced 2D Materials, National University of Singapore, Block S14, Level 6, 6

Science Drive 2, Singapore 117546, Singapore

ACS Paragon Plus Environment

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KEYWORDS: STM/STS, monolayer WSe2, low-angle grain boundaries, dislocation core, gap states, first principles calculations

ABSTRACT: Two-dimensional (2D) transition metal dichalcogenides (TMDs) have revealed many novel properties of interest to future device applications. In particular, the presence of grain boundaries (GBs) can significantly influence the material properties of 2D TMDs. However, direct characterization of the electronic properties of the GB defects at the atomic scale remains extremely challenging. In this study, we employ scanning tunneling microscopy and spectroscopy to investigate the atomic and electronic structure of low-angle GBs of monolayer tungsten diselenide (WSe2) with misorientation angles of 3°-6°. Butterfly features are observed along the GBs, with the periodicity depending on the misorientation angle. Density functional theory calculations show that these butterfly features arise from gap states in tetragonal dislocation cores, and extend to distorted six-membered rings around the dislocation core. Understanding the nature of GB defects and their influence on transport and other device properties highlights the importance of defect engineering in future 2D device fabrication.


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Since the emergence of two-dimensional (2D) materials, there has been intensive interest in intrinsic and extrinsic point and line defects1-7 as they strongly influence the material properties. As a prototypical line defect, grain boundaries (GBs) are particularly common in 2D crystals grown by bottom-up approaches such as chemical vapour deposition (CVD)3-6 and other methods2, 8, 9. A rich variety of GBs has been observed in graphene2, 8-10, hexagonal boron nitride (h-BN)11, as well as transitional metal dichalcogenides (TMDs)3,4,12. GB defects can modify the properties of TMDs, including mechanical plasticity13,14, electron transport properties15, optical properties16,17, magnetic properties18,19 and chemical reactivity20,21, and can significantly influence the performance of electronic devices built on 2D crystal sheets. Depending on the origin of the GB, different phenomena could be induced. For instance, a periodic GB arising from a parallel translation of two graphene domains acts as a metallic wire2; while a GB formed by an orientational tilt exhibits strong valley polarization9. Therefore, it would be possible to engineer the material properties of 2D crystals if we can control the formation of GB defects. Characterizing the atomic and electronic structures of the GB defects is of profound importance for applications. Using high-resolution scanning transmission electron microscopy (STEM), the atomic structures of various intrinsic point/line defects in TMD materials have been well resolved at the atomic scale4,

12, 14, 22, 23

. As predicted by theoretical computations,

remarkable changes to the electronic structure, such as mid-gap states, can be introduced by various defects12,24,25. From experimental measurements including photoluminescence (PL)16,17, conductivity4 and bandgap26 characterizations, it has been verified that the GBs can dramatically change the optical and electrical properties of the 2D TMD materials. Mid-gap states induced by point defects have also been detected by direct27 and indirect28 techniques. As a powerful characterization tool capable of determining atomic structures and electronic properties with


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atomic precision, scanning tunneling microscopy (STM) has been widely applied to studies of graphene8,9,29. For 2D semiconductors (e.g. MoS2 et al) and insulators (e.g. BN), the lack of conductivity requires STM measurements to be performed in combination with selected conducting top27 or bottom electrodes, e.g. using graphite/graphene or metals as conductive substrates11,30,31. Furthermore, the sandwich structure of the individual TMD layers make it more complicated to characterize the atomic arrangements from STM images. It is therefore still a challenge to determine the defect structures and the electronic properties of 2D TMDs at the atomic scale. In this article, we present a comprehensive study of the GB defects in CVD-grown monolayer tungsten diselenide (WSe2) using low-temperature STM measurements combined with first principles calculations. Low-angle GBs, typically with misorientation angles of 3°-6°, are found in the WSe2 sample. Butterfly patterns periodically spaced along the GBs are observed in STM images. The interspacing between butterflies increases as the misorientation angle decreases, in accordance with Burgers model. Together with density functional theory (DFT) calculations, these butterfly features are attributed to tetragonal dislocation cores, which give rise to multiple deep gap states. The gap states are located closer to the conduction band and extend over the tetragonal dislocation cores to the surrounding distorted WSe2 lattices, consistent with STM images and STS spectra. The energies of the gap states have a small variation for all the lowangle GBs studied here, which are suggested to be sensitive to local strains. Our results suggest that precisely determining the atomic structures and the local environments (e.g. strain) are critical in evaluating the electronic properties of GB defects, and emphasize the importance of controlling defect formation in order to engineer the device performance based on 2D crystals.


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Figure 1a shows a typical STM image of a WSe2 monolayer film transferred onto a graphite substrate32, where the WSe2 flakes are easily distinguishable by the irregular island edges with bright contrast26. A schematic structure of the WSe2/graphite heterostructure is illustrated in Fig. 1d. The step edge profile in Fig. 1e corresponding to the blue line in Fig. 1a reveals a height of 7 Å, consistent with the height of monolayer WSe2. Although unknown contaminations are observed at the edges, the surface is atomically clean within the WSe2 domains as shown in the atomically-resolved STM images in Fig. 1b and 1c. Moiré patterns are formed due to the lattice and/or orientation mismatch between the top WSe2 layer and the underlying graphite substrate. In Fig. 1b, the lattice parameters of the moiré superstructure highlighted by the blue parallelogram are |c| = |d| = 9.9 ± 0.2 Å with an intersection angle of 60° ± 2°. The unit cell of the hexagonal WSe2 lattices is denoted by a black parallelogram in Fig. 1c, with a lattice constant of 3.3 ± 0.1 Å 33. The orientations of the WSe2 atomic lattices and the moiré pattern, as denoted by the blue and black arrows respectively in Fig. 1b, are not aligned well; the angle between them is φ(WSe2,

Moiré)

= 8˚±1°. As the WSe2 monolayer (a continuous film) and the graphite

substrate (highly oriented pyrolytic graphite, HOPG) are both polycrystalline, a variety of moiré superstructures with different dimensions and φ(WSe2,

Moiré)

are observed over the whole

transferred sample, depending on their relative stacking orientations. The moiré superstructures can be used as fingerprints to identify different grain domains26,34, as discussed below. The cleanliness and uniformity of the WSe2 sample can be further verified by the electronic structures deduced from STS spectra. Fig. 1f shows a typical dI/dV spectrum of the monolayer WSe2 (averaged over 100 spectra taken randomly over the sample). The conduction band minimum (CBM) is located at (tip biases of) -1.09 ± 0.04 V and the valence band maximum (VBM) at 0.89 ± 0.03 V relative to the Fermi level (0 V). The deduced quasi-particle band gap


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Eg of 1.98 ± 0.06 eV for the WSe2 monolayer with slightly p-doped characteristic on graphite, is very close to the values previously reported35, 36. One-dimensional (1D) GBs, forming the lateral interfaces between two single-crystalline grains, can be observed at the monolayer WSe2 film. Figure 2 demonstrates typical GBs with misorientation angles (θ) (highlighted in Fig. 2c) of (a) 6°, (b) 3°, (c) 4.5°, and (d) 3.5°. More images of GBs can be found in Figure S1 in the Supplementary Information (SI). Different moiré patterns are observed in each domain due to the different orientations34. For instance, the moiré patterns highlighted in insets (i) and (ii) of Fig. 2a corresponding to the left and right domains respectively are different. It is worth noting that only low-angle GBs, namely with misorientation angles θ smaller than 10°, are found in this sample (Fig. S1). A possible reason is that the GBs of large misorientation angles are less stable24, and do not survive after high-temperature annealing (the highest temperature is 900°C during CVD-growth). In Fig. 2, all the GBs marked with dotted lines have discrete bright protrusions under negative tip bias (e.g. Vtip = -1 V). The GBs are usually meandering and aperiodic at the large-scale, as shown in Fig. 2a (100×100 nm2) and 2b (60×60 nm2), but more regular periodicity can be found in smaller areas (see also Fig. S1). As highlighted in Fig. 2c (16×16 nm2) and 2d (13×13 nm2), the bright protrusions, which most likely correspond to dislocation cores, are approximately evenly spaced under local thermodynamic equilibrium due to long range elastic interactions. In the following discussion, we will focus our attention on these intrinsic periodic GBs. The atomically-resolved STM images in Fig. 2c and 2d reveal that the discrete bright protrusions along the periodic GBs display butterfly patterns that look similar for both misorientation angles for the chosen bias voltages. Such butterfly patterns are also frequently


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observed in the aperiodic regions (Fig. S1). The butterfly protrusions are of 2-fold symmetry with the symmetric axes parallel to the GBs and appear as darker lines along the symmetry axis. Standing-wave patterns around the “butterflies” are produced by scattering of the free electrons off the dislocation cores, similar to that previously observed at the GB defects of graphene9, 10. The distance between dislocation cores is 42±2 Å for the 4.5°(±0.5°) GB in Fig. 2c, increasing to 50±2 Å for the 3.5°(±0.5°) GB in Fig. 2d. As summarized in Table 1, the distance between dislocation cores increases with decreasing misorientation angles. In order to understand the formation of the periodic low-angle GBs, we need to elucidate their atomic structures and electronic properties. Figure 3a-d are bias-dependent STM images of a dislocation core at the 3.5° GB (Fig. 2d), recorded at Vtip of -1.0 V, -0.8 V, -0.5 V and 0.6 V. The defect displays similar butterfly patterns at the three negative tip biases (Fig. 3a-c), which disappear at positive bias (Fig. 3d). The dimensions of the butterfly denoted by a trapezoid in Fig. 3c are around 2.5 nm (midline) by 1.8 nm (the height along the symmetric axis). Height profiles across the defect reveal a height of over 3 Å at negative tip biases, but almost zero at positive bias (Figure S2). Therefore, this suggests that the butterfly superstructures are mainly caused by changes in the electronic structure, i.e. redistributions of the local density of states (LDOS) at the defects, rather than outof-plane lattice deformations. This deduction is consistent with previous theoretical studies, which have predicted that gap states could arise at the dislocation cores at GBs of 2D TMD materials4,12. Further details of the gap states are revealed by STS spectra in Figure 4. Fig. 4a shows a series of dI/dV curves obtained at different positions over the periodic 3.5˚ GB. The electronic structure changes dramatically at the GBs, and multiple deep gap states are observed close to the


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dislocation cores (e.g. points 4 and 5). The gap states are located above the Fermi level (closer to the CBM) and are unoccupied, corresponding to the bright butterfly protrusions recorded at negative tip biases. The signals of the gap states decay fast as the STM tip moves away from the dislocation core, e.g. points 3 and 7. In addition, the VBM shifts slightly away from the Fermi level as highlighted by the short black lines, e.g. ~ 0.25 eV at point 4 in Fig. 4a. The shift of the VBM decreases gradually as the tip moves away from the GBs. When the distance is 3 nm further away from the GB, e.g. at the positions 1 and 9 inside the WSe2 domain, the electronic bandgap reverts to the intrinsic one (Fig. 1f). Similar bending at the valence and conduction band edges has been previously reported for monolayer MoS2 GBs, which is possibly a result of lattice strain combined with defect-/substrate- induced charge transfer26. The screening distance of several nm is also consistent with the values reported for MoS2 GBs26 and edges31. The dI/dV spectra in Fig. 4b reveal that the changes observed at the 4.5° GB are very similar to the 3.5° case (Fig. 4a): multiple gap states arise at similar energies and the VBM shifts further away from the Fermi level at the dislocation cores (e.g. points 12 and 13). Between the dislocation cores (e.g. points 10 and 15) along the GB, the gap states decay significantly, and the band structures (spectra 10 and 15) are very similar to that of pristine WSe2 (e.g. spectrum 16). The small difference between spectra 10/15 and spectrum 16 is likely to be caused by unrelaxed strain in the limited space (~4 nm) between the dislocation cores. More atomically-resolved STM images and dI/dV spectra of the 4.5° GB are shown in Figure S3 (SI). Similar changes to the electronic structure observed at the 3.5° and 4.5° GBs (Fig. 4), together with their similar STM images (Fig. 2), strongly suggest that the dislocation defects in these different low-angle GBs have very similar atomic structures. STEM studies on GBs in 2D TMDs have found that a variety of non-6-membered rings (4-, 5-, 7- and 8- membered rings) together


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with strained 6-membered rings are present at GBs with relatively large misorientation angles (>10°)3,4,12,14,22,23. DFT calculations have shown that all these non-6-membered dislocation cores can induce deep gap states4,12,14,22-25. In order to determine the atomic structure of the dislocation cores observed here, we have proposed different structures including 4|6 (tetragonal), 5|8|5, 6|8 and 5|7 dislocation cores (Fig. S4 and S5), and simulated their projected density of states (PDOS) with DFT. Preliminary calculations were performed on flake models (flake size: ~35 Å × 40 Å) with a dislocation core at the centre and four edges that are fully relaxed (Fig. S4). We find that dislocation cores consisting of 4-membered tetragons match best with the experimental information. Not only do their atomic structures match well with the STM images (Fig. 3f and Fig. S3b), but they also give rise to multiple gap states that are closer to the conduction band edge. The other proposed structures all give rise to gap states that are closer to the valence band edge (Fig. S6). Furthermore, the simulated STM image at the energy corresponding to the lowest unoccupied defect orbital (LUDO) of the tetragonal dislocation core also shows the distinctive butterfly shape (Fig. S4). Based on the tetragonal atomic structure, we construct a periodic arrangement of the dislocation cores with interspacing D for a low-angle GB as illustrated in Fig. 3e. This structure is in fact consistent with the application of Burgers model to the low-angle GBs, with WSe2 lattice arrays being added into or removed from the GB (along armchair direction) between two tilting domains (Fig. S7a)37. As explained by the Burgers model, the distance D between the dislocation cores is determined by the misorientation angle θ and Burgers vector b of the dislocation: = b/ ≈ a/ ≡ 10,37. Here, b is the length of the Burgers vector b, and is equal to a, the WSe2 lattice parameter (3.28 Å).


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Further DFT calculations were performed on WSe2 ribbon models with about 35 Å (10 to 11 unit cells) width, with tetragonal dislocation cores placed periodically along the GB direction (WSe2 armchair direction) with interspacing D (Fig. S9). In Fig. 3e, one can also see that

≈ + √3a, where n is the integer number of W atoms or Se columns between two

adjacent dislocation cores (Fig. S7). By choosing different values of n, GBs with different values of θ can be modelled ( ≈

). In order to relax the strain between dislocation cores, the

√(/)

distance D between cores is varied slightly from the initial value of + √3a, so that

= + √3a + ∆. When the ribbon system has zero strain, ∆ = ∆ is in the range of 0.20 Å to 0.27 Å for 4 ≤ n ≤ 9 (Fig. S10), and the corresponding value of ≡ is shown in Table 1. The relaxed atomic structure of the 6.0° GB, with D5 = 31.49 Å is shown in Fig. S9, and the calculated electronic structure is given in Figure 5a and 5b. In Fig. 5a, the black plot corresponds to the PDOS of the intrinsic monolayer WSe2 and the red one corresponds to that of the atoms in the tetragonal dislocation core and the surrounding strained hexagonal rings. The Fermi level is given by the graphite substrate, set to 0.0 eV (see Methods). Similar to the STS spectra shown in Fig. 4, significant changes on the electronic structure are brought about by the dislocation cores. The VBM is ~ 0.2 eV lower than that for intrinsic monolayer WSe2, agreeing well with the experimental result. It is also found that three gap states with pronounced intensities arise above the Fermi level, similar to the STM/STS observations. The lowest unoccupied defect state, corresponding to P1 in the STS images, is at ~0.4 eV, relatively deep in the intrinsic WSe2 bandgap and in good agreement with the STS results.


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The simulated STM image in Fig. 5b was calculated at the energy corresponding to the LUDO, and the distinctive butterfly-shaped feature is clearly seen, consistent with the experimental image in Fig. 5c, obtained at the energy corresponding to P1. The two-fold symmetric axis of the butterfly corresponds to the dark line, while the bright wings of the butterfly are located at the strained hexagonal rings surrounding the dislocation core. The slight differences between the simulated and experimental STM images may be due to edge-induced defect states in our ribbon models (see SI), and/or the limit of the STM tip resolution which may smear out the fine features of the image. We further simulated STM images corresponding to different tip biases for the 3.5° GB (D9 = 54.27 Å), revealing similar butterfly image features for the chosen unoccupied energy levels and featureless images for the occupied one (Fig. S11). These phenomena agree with the experimental observations in Fig. 3. We further evaluate the possible factors that could influence the energy levels of the gap states, such as the GB misorientation angle and associated interspacing distance D, and applied strain. Calculations based on the ribbon model with different D values were performed. As plotted in Fig. 5d, the black squares represent the LUDO energy positions for D in the range from 25.77 Å to 54.27Å with 4 ≤ n ≤ 9 and 7.4° ≥ θ ≥ 3.5° (Table 1). The theoretical simulations reveal that the LUDO energy ranges from 0.33-0.39 eV for all D considered here, indicating that the local atomic structure of the dislocation core (i.e. lattice distortions) is very similar in all cases and that the interaction between dislocation cores is weak, which is reasonable for the large values of D. Calculations performed on the flake models with different D values (flake lengths along the WSe2 armchair direction) show a constant energy of 0.35 eV for the LUDOs, as highlighted by the red dashed line in Fig. 5d. This result could be attributed to a more complete relaxation of the strains through the four unfixed edges in the flake models.


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In the STS results, P1 (corresponding to LUDO) is centred at tip biases of -0.52 V for the 3.5° GB, and at -0.34 V for the 4.5° case as denoted by the red dashed lines in each panel of Fig. 4. The slightly larger variation in energies seen in experiment may be due to unrelaxed strain fields in the experiment. Indeed, we find that applying strain in the direction along the GB can cause the LUDO energy to change by tenths of eV. Fig. 5e plots the change in LUDO energy as a function of percentage strain along the GB. It is found that for the cases considered here, n = 5, 7 and 9, the plots are parallel to each other with approximately the same slope, indicating that the strain-induced change in the LUDO energy is independent of the distance Dn in the ribbon model. For every 1% change in strain, the energy of LUDO changes by about 50 meV in all the cases. These straininduced changes suggest that strains can potentially engineer the levels of the gap states in these low-angle GBs. By combining high-resolution STM/STS measurements with first principles calculations, we observe that GB defects at monolayer WSe2 can significantly change the electronic properties of the 2D TMD semiconductor. Under local thermodynamic equilibrium, GBs, typically with low misorientation angles in the range of 3˚ to 6˚, can form ordered arrangements of discrete dislocation cores. The distance between dislocation cores decreases as the misorientation angle increases, which can be explained by the Burgers model. Multiple deep gap states displaying butterfly patterns are centered at the tetragonal dislocation cores and extend to the surrounding distorted hexagonal rings over several unit cells. The spatial patterns of these states, as well as their energies, are very similar for the low-angle GBs with different misorientation angles studied here. Furthermore, application of small external strains along the GB can change the energy levels of the gap states and can potentially be used as a means to engineer defect levels in


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GBs. Our systematic study of the atomic and electronic structure of low-angle GBs are important for a comprehensive understanding of GB defects, which can help improve the device performance of 2D TMDs grown by scalable bottom-up approaches.

Experimental Methods. The monolayer WSe2 sample was synthesized by a modified CVD method on sapphire and then transferred onto highly oriented pyrolytic graphite (HOPG) substrate. More details about the sample preparations can be found in previous reports32,33. The WSe2/graphite sample was degassed overnight at 350°C in an ultra-high vacuum (UHV) chamber before STM/STS measurements. STM and STS measurements were carried out in a UHV system (10-10 mbar) housing an Omicron LT-STM interfaced to a Nanonis controller at 77 K. A chemically etched tungsten tip was used. The STM images were recorded in constantcurrent mode with tunneling current in the range of 50–100 pA. For dI/dV spectra, the tunneling current was obtained by a lock-in amplifier, with a modulation of 625 Hz and 40 mV. Note that the bias voltage (Vtip) is applied to the STM tip, hence negative values correspond to the conduction band and positive values correspond to the valence band. Theoretical Calculations. The first principles calculations were carried out within the framework

of

density

functional

theory,

employing

projector

augmented

wave

pseudopotentials38,39 and the Perdew-Burke-Ernzerholf form40 of the exchange-correlation functional, as implemented in the Vienna ab initio simulation package code41. The experimental WSe2 lattice constant of 3.28 Å is used42. Models including WSe2 ribbons composed of periodic arrangements of dislocation cores with different periodicities, and flakes with one dislocation core are constructed (SI). We employ an energy cutoff of 250 eV for plane waves, and the


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criterion for total energy convergence is set to 10-4 eV. All atoms of the WSe2 flake are relaxed during geometry optimization until the magnitude of forces is less than 0.04eV/Å. The Fermi level is obtained from a calculation of pristine WSe2 on graphite (Fig. S12), while the levels of the dislocation core in WSe2 are aligned relative to the levels of pristine WSe2 (by aligning the vacuum levels in calculations of isolated pristine and defective WSe2 monolayers). This procedure assumes that the charge transfer between the graphite substrate and the experimental WSe2 sample is similar to that between graphite and pristine WSe2 in our calculations. This assumption is approximately true for a sample with a low density of defects. Furthermore, DFT cannot give quantitatively accurate energy level alignments, and we expect some quantitative deviations between theory and experiment for the actual energies of the defect states. Calculations of a WSe2 ribbon with a GB defect, with and without a single-layer graphene substrate were performed. The results are shown in Figure S13, which suggest that the substrate does not have a significant influence on the electronic properties of the GB defects. The theoretical STM images were simulated based on the Tersoff-Hamann approximation43 (at the energy 0.5 eV corresponding to the LUDO energy for Fig. 5c).


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FIGURES

Figure 1. Atomic and electronic structures of WSe2. (a) A typical large-scale STM image of the transferred WSe2 sample on graphite surface (100×100 nm2; Vtip = -1.2 V). (b) STM image (15×15 nm2; Vtip = -1.2 V) showing a moiré pattern highlighted by the blue parallelogram. The angle between the moiré pattern and WSe2 lattice is φ(WSe2,

Moiré)

= 8˚±1°. (c) An atomically-

resolved STM image reveals the WSe2 lattice constant of 3.3 Å (6×6 nm2; Vtip = 0.9 V). (d) A schematic image shows the single-layer WSe2 adsorbed on the graphite substrate (side view). Gray, green and brown spheres denote W, Se and C atoms, respectively. (e) Lateral profile corresponds to the blue line in panel a, revealing a height of 7 Å for monolayer WSe2. (f) STS spectrum reveals a 1.98 eV bandgap for the single-layer WSe2 (set point: Vtip = -1.0 V, Itip = 70 pA). Scale bar, 2 nm.


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Figure 2. Small-angle GBs in monolayer WSe2. (a) In the large-scale STM image, the 6˚ GB is meandering and aperiodic (100×100 nm2; scale bar, 10 nm; Vtip = -1.2 V), where the insets (i) and (ii) reveal the different lattice orientations for the corresponding domains (each inset: 3×3 nm2; scale bar, 1 nm; Vtip = 0.6 V). (b) Another aperiodic GB with a misorientation angle of 3˚ (60×60 nm2; scale bar, 10 nm; Vtip = -1.0 V). (c) and (d) are periodic GBs of 4.5˚ and 3.5˚ misorientations, respectively, where the dislocation cores appear as butterfly features (c, 16×16 nm2; Vtip = -1.0 V; d, 13×13 nm2; Vtip = -0.9 V; scale bar, 2 nm).


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Figure 3. Atomic structure of the small-angle GB. (a-d) are bias-dependent STM images of a dislocation core at the 3.5˚ GB, where the butterfly feature disappears at positive tip bias (size: 4×8 nm2; scale bar, 1 nm; a, Vtip = -1V; b, Vtip = -0.8 V; c, Vtip = -0.5 V; d, Vtip = 0.6 V). (e) Top view of the small-angle GB constructed by a periodic arrangement of tetragon dislocation cores, analogous to Burgers model (n=5). Gray and green spheres denote W and Se atoms, respectively. (f) An enlarged image corresponds to the trapezoid region in panel d, where the atomic structure is traced by the overlaid atoms. A similar figure for the 4.5° GB is shown in the SI (Figure S3).


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Figure 4. Electronic structure changes significantly at the GB defects. (a) STM image (top) recorded at the 3.5˚ GB and STS spectra (bottom) taken across the GB, reveal that the electronic structure varies with the perpendicular distance from the GB (STM image: 4×8 nm2, Vtip = -0.8 V; STS set points: Vtip = -1.1 V, Itip = 68 pA). (b) STM image (top) of the 4.5˚ GB and STS spectra (bottom) taken along the GB (STM image: 7×14 nm2, Vtip = -1.0 V; STS set points: Vtip = -1.0 V, Itip = 73 pA). The triangles denote the positions for dI/dV measurements. Scale bar, 1 nm.


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Figure 5. Electronic properties of the dislocation defect. (a) Calculated PDOS of the intrinsic WSe2 single-layer (black) and atoms in the tetragonal dislocation core and the surrounding strained hexagonal rings (red) for a prototype model of 6° misorientation-angle. (b) and (c) are simulated and experimental STM images (with the same size of 23×26 Å2; scale bar, 5 Å) of the dislocation core at the energy corresponding to LUDO, respectively. (d) Calculations based on periodic ribbon models show that the energy levels of the LUDOs for different Dn (4 ≤ n ≤ 9) have very small variations (black line). The dashed red line highlights the energy level of the LUDO obtained from the flake model. (e) The LUDO energy is sensitive to strains. The plots are for n = 5 (black), n = 7 (red), and n = 9 (blue).


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Table 1. Summary of the distances D between the dislocation cores for the GBs with different misorientation angles. D increases as the misorientation angle θ decreases. The experimental value of D is consistent with that obtained from Burgers model

≈ a/ (θ is in radians)

as well as = + √3! + ∆ . θ (exp.)

D (exp.)

DBurgers

n

Dn

θn [

"

]

√#($"/%)

--

--

--

4

25.77 Å

7.4°

6°

28±2 Å

31.32 Å

5

31.49 Å

6.0°

5°

38±2 Å

37.57 Å

6

37.19 Å

5.1°

4.5°

42±2 Å

41.76 Å

7

42.90 Å

4.4°

4°

45±2 Å

46.98 Å

8

48.57 Å

3.9°

3.5°

50±2 Å

53.69 Å

9

54.27 Å

3.5°

3°

67±2 Å

62.64 Å

11

--

2.9°

ASSOCIATED CONTENT Supporting Information. Additional information on other GBs observed in the WSe2 monolayer, height profiles of the GB defect, dislocation core of the 4.5˚ GB, flake models, formation of the periodic low-angle GB, misalignments observed in the real GBs, Ribbon model, Calculations with substrate, and Shift in energy levels with external stains for different Dn. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] (A.T.S.W.).


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*E-mail: [email protected] (S.Y.Q.). *E-mail: [email protected] (Y.L.H.). Author Contributions ¶These authors contributed equally. Notes The authors declare no competing financial interests. ACKNOWLEDGMENT A.T.S.W. acknowledges financial support from MOE AcRF Tier 1 grant number R-144-000321-112 and S.Y.Q. acknowledges support from grant NRF-NRFF2013-07 from the National Research Foundation, Singapore. Computations were performed on the NUS Graphene Research Centre cluster. S.Y.Q. and A.T.S.W. acknowledge support from the Singapore National Research Foundation, Prime Minister’s Office, under its medium-sized centre program. Y.L.H and D.C. acknowledge financial support from IMRE Pharos project IMRE/15-2C0115.

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Gap States at Low-Angle Grain Boundaries in Monolayer Tungsten

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