Evidence of Local Commensurate State with Lattice Match of Graphene on Hexagonal Boron Nitride Na Yeon Kim,†,⊥ Hu Young Jeong,‡ Jung Hwa Kim,† Gwangwoo Kim,§ Hyeon Suk Shin,§,⊥ and Zonghoon Lee*,†,⊥ †
School of Materials Science and Engineering, ‡UNIST Central Research Facilities, and §Department of Chemistry and Department of Energy Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea ⊥ Center for Multidimensional Carbon Materials, Institute for Basic Science (IBS), Ulsan 44919, Republic of Korea S Supporting Information *
ABSTRACT: Transition to a commensurate state changes the local symmetry periodicity on two-dimensional van der Waals superstructures, evoking distinctive properties far beyond individual layers. We investigate the morphology of moiré superstructures of graphene on hexagonal boron nitride (hBN) with a low twist angle (≈0°) through moiré fringe analyses with dark field transmission electron microscopy. The moiré fringes exhibit local variation, suggesting that the interaction between graphene and hBN depends on the stacking configuration and that local transition to the commensurate state occurs through the reduced crystalline mismatch (that is, by lattice stretching and twisting on the graphene lattices). This moiré superstructure analysis suggests an inventive method for studying the interaction between stacked van der Waals layers and for discerning the altered electronic and optical properties of graphene on hBN superstructures with a low twist angle, even at low magnification. KEYWORDS: moiré, dark field transmission electron microscopy, commensurate, graphene, boron nitride of graphene layer distortion.19,20 The interaction between the layers varies, as the stacking configurations cause inhomogeneous strains and corrugation. The graphene lattice primarily relaxes around the AB-stacked regions, wherein carbon (C) atoms are located above the boron (B) atoms. Lattice relaxation changes the electronic structures by opening a small band gap at the Dirac point of graphene.19,21 Moiré superstructures can be topologically analyzed under a scanning tunneling microscope (STM) and transmission electron microscope (TEM).22,23 Mismatches of crystals with different lattice constants and relative orientations produce periodic moiré superstructures with larger periodicity than the lattice constants themselves.24 The moiré configuration magnifies and emphasizes the local configurational changes induced by defects and strain, although the individual lattice structures cannot be resolved.25−27 Moreover, dark field TEM (DF-TEM) analysis with selected area electron diffraction (SAED) reveals information along a selected orientation with an appropriate objective aperture, so it has been widely applied
T
he production of two-dimensional (2D) materials has advanced in recent years, triggering intensive research on the van der Waals (vdW) heterostructures of 2D materials.1 Replacement of SiO2 substrates with hexagonal boron nitride (hBN) has improved the charge carrier mobility of graphene by more than 2 orders of magnitude.2−5 The commensurate state of vdW heterostructures of 2D materials promises to overcome the inherent drawbacks of graphene on pure 2D crystals such as MoS2 and WSe2.6,7 The crystalline mismatch between the layers changes the periodicity of the superlattice, leading to a spontaneous alternation of the periodicity in each 2D layer. These spontaneous changes, which arise from the van der Waals adhesion potential (according to the Frenkel−Kontorova model8,9), induce interesting characteristics not observed in a multilayer superstructure.10−14 A low twist angle is especially important for graphene on hBN (G/hBN).15−17 When the twist angle of G/ hBN (θG‑BN) is less than 2°, G/hBN exhibits a distinctive Hofstadter’s butterfly structure with additional satellite resistance peaks, and the maximum band gap appears at θG‑BN = 0°.18 As θG‑BN decreases, the in-plane elastic energy weakens and approaches the vdW energy. Under this condition, the graphene lattice can relax toward an hBN lattice at the cost © 2017 American Chemical Society
Received: April 19, 2017 Accepted: June 14, 2017 Published: June 14, 2017 7084
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ACS Nano in analyses of structural defects such as stacking boundaries,28,29 grain boundaries,30 and dislocations of 2D materials.31 In this article, the stacking configurations of G/hBN are identified through DF-TEM with SAED of the moiré superstructures and by imaging of the atomic lattice fringes. Analyses were performed on freestanding specimens, which were free from substrate effects. The distribution of the moiré fringes under DF-TEM immediately provides the interlayer relation through θG‑BN. Furthermore, we suggest that variation of the moiré fringes could reflect local disturbance of the stacking configuration when the crystallographic orientations of the graphene and hBN lattices are almost identical.
RESULTS AND DISCUSSION Figure 1a shows a DF-TEM image of the G/hBN stack. The inset of Figure 1a comprises two overlapped sets of hexagonalshaped diffraction patterns. The dot-shaped and arc-shaped diffraction reflections are sourced from graphene and hBN, respectively. This overlap indicates that graphene and hBN are aligned along the same crystallographic orientation. The parallel lines in the DF-TEM image (Figure 1a) are generated by phase interference of the electron beams diffracted from graphene and hBN (called moiré f ringes in this article). To investigate the interaction between graphene and hBN, θG‑BN was precisely measured from the moiré fringes of G/hBN by two methods (Figure 1b). The first method uses the spacing between the moiré fringes (dgm). The general moiré fringes (ggm) are caused by the difference between the diffraction vectors of graphene (gG) and hBN (gBN). The length of the diffraction vector is reciprocally related to the interplanar spacing of the diffracted reflections and is expressed as dG × dBN dgm = 2 2 1/2 . The interplanar spacing (dG + dBN − 2dG·dBN cos(θG − BN))
of the {101̅0} diffraction reflections (d{1010̅ }) of graphene and hBN is also required. The lattice mismatch has been theoretically computed as 1.6% to 1.8%,17,18 but has not been determined experimentally.32 In the present study, dG and dBN were approximately measured as 2.130 and 2.169 Å, respectively (see Supporting Information 1). Inserting dgm = 6.6 nm (Figure 1b) and the experimentally determined dG and dBN into the above equation, θG‑BN is estimated as 1.56°. The second method applies the sine law to the measured angle between the moiré fringes and gG(α). (See Supporting Information 2.) Substituting the measured α (34°; see Figure 1b) into the equation in Supporting Information 2, θG‑BN was estimated as 1.56°. The angles estimated by the two methods are very similar (approximately 1.5°). The consistency of the calculated θG‑BN with real lattices was checked by nanobeam diffraction (NBD) patterns and atomic resolution (AR-TEM) imaging. The NBD pattern and the digital diffractogram (FFT) corresponding to an AR-TEM image are presented in Figure 1b and c, respectively. The FFT distinguishes two sets of diffracted reflections with a θG‑BN of approximately 1.5°. Moreover, the experimental AR-TEM image is consistent with the schematic atomic model of G/hBN (Figure 1d). Therefore, the moiré fringe analysis with DF-TEM imaging can reliably resolve θG‑BN. When the twist angle between the layers is less than 1°, it is not easily discerned in overlapped electron diffraction patterns and AR-TEM images. However, DF-TEM imaging with SAED can distinguish twist angles of 0.1° from moiré fringes.33 G/ hBN is especially composed of materials with different lattice constants, so it has direction of the moiré fringes (α)
Figure 1. Analysis of the moiré fringe of G/hBN under transmission electron microscopy (TEM) images. (a) Dark field TEM image acquired from the orange-squared (101̅0) diffraction reflection in the inset. The inset is an electron diffraction pattern of G/hBN. The dot-shaped and arc-shaped diffraction reflections are sourced from graphene and hBN, respectively. The reflections are overlapped, meaning that their diffraction vectors lie along similar crystallographic orientations. (b) θG‑BN is computed from dgm and from the angle between gG and the moiré fringes (α). The corresponding electron and nanobeam diffraction patterns reveal the θG‑BN and the orientation of gG (marked by the red line). The orientation of the moiré fringes and distribution of dgm are highlighted by the yellow line and magenta box, respectively. (c) Atomic resolution TEM image of the G/hBN corresponding to (b). The inset shows the corresponding digital diffractogram (FFT). (d) Schematic atomic model of G/hBN.
depending on the θG‑BN (being especially sensitive at low θG‑BN). When graphene and hBN are aligned along the same crystallographic orientation, the dgm is maximum at approximately 12.04 nm and its value decreases with a large change in α with increasing θG‑BN. So the configurational changes in G/ hBN can be analyzed in detail.12 As θG‑BN decreases, the moiré fringes in the DF-TEM images become unevenly distributed and exhibit periodic bending (Figure S3). To investigate this feature in detail, the AR-TEM image was subjected to lattice fringe imaging analysis. For this purpose, we masked selected orientations on the FFT 7085
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Figure 2. Widening and bending of the moiré fringes of G/hBN at low θG‑BN. AR-TEM images of G/hBN and the corresponding selected lattice fringe images, formed by masking diffraction reflections on the FFTs with (a) θG‑BN ≈ 0° and (b) θG‑BN = 3.2°. The bright and dark moiré fringes are caused by constructive and destructive interferences, respectively, between the graphene and hBN lattice fringes.
Figure 3. (a) Lattice fringe image taken by masking all first-order diffraction reflections of an AR-TEM image of G/hBN with large θG‑BN (3.2°). (b) AR-TEM image formed by overlapping the lattice fringe images. The corresponding FFT reveals two sets of hexagonal diffraction reflections twisted by 3.2°. (c) Schematic atomic model of G/hBN and corresponding simulated and real AR-TEM images for θG‑BN = 3.2°. The simulated and real AR-TEM images are consistent and distinguishable in the diffraction reflections of their corresponding FFTs (yellow lines for hBN; green lines for graphene). All scale bars in the AR-TEM images are 1 nm.
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Figure 4. Transition to commensurate state in the AB-stacked regions of G/hBN. (a) Unevenly distributed intensities of the moiré fringes of G/hBN when all first-order diffraction reflections on an AR-TEM image are selected. (b) Colored moiré fringe image superimposed on an AR-TEM image. The widening and zigzagged morphology accord with the stacking configurations. The orientation of the hBN sheet is indicated by the hBN defect (orange triangle). Areas delineated by gray, blue, and red rectangles were selected for FFT analysis. (c) Simulated and experimental AR-TEM images corresponding to the selected areas in (b) and their FFTs. The dark and bright areas are composed of two stacked atoms or vacuum and/or single atoms, respectively. Different stacking configurations yield different twisting and diffracted reflection distances of graphene and hBN. All scale bars are 1 nm. (d) Average lattice mismatch between graphene and hBN versus twist angle (the trend decreases below θG‑BN = 1°).
hexagonal symmetry. Moreover, the dgm of the moiré fringes (Figure 4b and S5a) are nonuniform in different orientations, indicating uneven twist and strain in the G/hBN.29 The width of the moiré fringes also slightly varies. The periodically zigzagged morphology around 25° is related to the AA-stacked regions and reflects local changes in θG‑BN. For comparison, the lattice fringe images obtained by masking the FFTs of monolayer graphene and hBN are deliberately overlaid (see Supporting Information 3). The moiré fringes by deliberate overlay are straight and constant in width. Thus, the morphological change in the moiré fringes arises from the interaction between the artificially stacked graphene and hBN. The moiré fringes are generated by three factors: θG‑BN, dG, and dBN. When θG‑BN is zero for the maximum dgm and dBN is expressed in terms of dG and the lattice mismatch (μ), dgm_max
corresponding to the AR-TEM image (see Supporting Information 3). As shown in Figure 2, the features of the moiré fringes in the AR-TEM image of G/hBN depend on θG‑BN. When graphene and hBN are aligned along the same orientation (θG‑BN ≈ 0°), the moiré fringes are largely corrugated in all orientations, and some dgm exceed 12.04 nm (Figure 2a). At high θG‑BN (θG‑BN = 3.2°), the moiré fringes are evenly distributed at all orientations; that is, the dgm along all three orientations are consistent and equal to 3.66 nm (Figure 2b). At this θG‑BN, the moiré fringes appear quite straight and parallel and are noncorrugated and constant in width. Moreover, the lattice fringes on all first-order diffraction reflections at θG‑BN = 3.2° (Figure 3a) are periodic, being brightest in the AA-stacked regions and darkest in the BA- and AB-stacked regions. This intensity variation is caused by interference of the electron beam (see Supporting Information 3).29 The lattice fringes in the AR-TEM images show nearly parallel moiré fringes with unvarying morphology for each firstorder diffraction reflection. The AR-TEM images are also well matched with the simulated ones and with the distinguishable diffraction reflections in the FFTs. At low θG‑BN (∼0.4°) estimated from the unit size of the hexagonal moiré patterns (∼13 nm) and α (∼65°), the dark area is larger in the AB-stacked regions than in the BA-stacked regions (Figure 4a), which means that AB stacking is an energetically favorable stacking sequence. This uneven contrast distribution indicates that the G/hBN loses its periodic
(
simplifies to dG 1 +
1 μ
). As μ decreased from 1.8% to 1.4%,
dgm_max increased from 12.04 to 15.49 nm (see Supporting Information 1). Changing dgm widened the moiré fringes because this parameter affects the periodicity of the sinusoidal intensity oscillations.34 Therefore, the intensity of the moiré fringes is changed by changing dgm, in other words, by changing μ. For a detailed analysis, a defect on the hBN sheet provides the hBN layer orientation marked by an orange triangle in the AR-TEM image (Figure 4b).35 The directionality of the moiré fringes shows that, relative to graphene, the hBN is twisted by 7087
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Several calculation studies have sought the reason for the transition to a commensurate state. G/hBN has different interaction energy between the layers and the in-plane elastic energy depending on the stacking configurations. These different energies alter the interlayer distances and strain distribution.20,37,38 Moiré fringes in AA-stacked regions are considered as the pivot points of the moiré fringes because Young’s modulus and adhesion energy are highest in these regions. Recently, moiré is twisted on a pivot around the AAstacked regions in an analytical model of bilayer graphene at low twist angles.39 On the other hand, moiré fringes of this model exhibit local variation on their widths and corrugation around the AB-stacked regions with the lowest in-plane elastic energy. The low elastic energy triggers transformation on graphene lattices by stretching and local twisting and provokes the transition to commensurate state. From the local morphology variation of the moiré fringes, we elucidated that transition to the commensurate state occurs by decreasing lattice mismatch and twisting between the graphene and hBN in the AB-stacked regions. The transition loses the hexagonal symmetry of the G/hBN superstructures, generating a graphene band gap.40 Therefore, the moiré fringe TEM imaging analysis immediately reveals the relation between the local structural variation and electronic properties, even under low magnification. This provides an ingenious insight into the inconsistency between the experimental results and the theoretical research, namely, the insufficient band gap opening on the graphene.18,41
approximately 0.4° along the counterclockwise direction. In addition, the configuration of the AB stack relative to that of the BA stack is also distinguished (Figure S4). The stacking configurations are consistent with the local variations in the AR-TEM images and their corresponding FFTs (Figure 4c). In the AA-stacked regions, two sets of diffracted reflections indicate twisting and different lengths along the {112̅0} diffraction reflections. The BA-stacked regions also show two distinguishable sets of diffracted reflections, but with less twisting than in the AA-stacked regions. The simulated images are also consistent with the real images in both AA- and BAstacked regions. In contrast, the AB-stacked region displays a single set of diffracted reflections. A real AR-TEM image shows that intensities of single atoms are much clearer and the areas enlarged where the atoms maintain their hexagonal structure particularly at the AB-stacked region compared to the simulated AR-TEM image. These phenomena denote that the two layers become commensurate states by decreasing their lattice mismatch and locally twisting. In particular, the diffraction patterns of graphene exhibit larger twisting and shrinking behavior than those of hBN; that is, the graphene lattices are transformed to become identical with hBN lattices. This result is in good agreement with the theoretical works about strain concentration on the graphene lattices depending on the stacking configuration of G/hBN with the atomistic model and DFT calculation.21,36,37 To determine whether the moiré fringes were varied by the commensurate state transition, the lattice fringe was imaged by Photoshop (see Supporting Information 3). When the lattice fringes of graphene were locally enlarged in the AB-stacked regions, they became corrugated in the same vicinity, thereby inducing bending and enlargement of the dark regions in the moiré fringes of G/hBN. This simulation is consistent with Figure 4a, which has a larger dark region at the AB-stacked region originated from stretching of the interatomic bond length of graphene. The local commensurate transition in the AB-stacked regions reduces the average μ (Figure 4d). The lowest average μ is 1.58% when θG‑BN approaches 0°, below the minimum μ of 1.62% in monolayer graphene and hBN. As θG‑BN increases from 0° to 1°, the average μ increases but remains below 1.8%. When θG‑BN exceeds 1°, the average μ reaches 1.8%, close to the average μ obtained from pristine monolayer graphene and hBN. In this scenario, the graphene and hBN lattices do not interact. The difference in lattice constants between graphene and hBN is as low as 0.05 Å when μ is 1.8%; in other words, the transition on the graphene lattices is extremely small for decreased lattice mismatch at the AB-stacked regions. Moiré patterns take the role of magnification, which projects the interatomic interaction. Consequently, the image contrast slightly increases in regions of single atoms and decreases in the transition area between the AB- and BA- stacked regions. In other words, the area occupied by distinguishable single atoms increases, which provides evidence of decreased lattice mismatch from image simulations performed by MacTempas software (Figure S6c). As the lattice variation is too small to distinguish in the AR-TEM imaging, the corresponding ARTEM images (Figure 4c) appear similar to the simulated images. However, small changes in μ become large morphological differences in the moiré fringes, which are reciprocally related to μ; thus, dgm and the width of the moiré fringes also become noticeable.
CONCLUSION In summary, the moiré superstructures of G/hBN were comprehensively studied to demonstrate the relation between the stacking configurations and interlayer interactions through DF-TEM with SAED and lattice fringe analysis on the ARTEM images. At low twist angles, uneven intensity between the AB- and BA-stacked regions provides evidence for losing their hexagonal symmetry on the moiré superstructures and moiré fringes depending on the stacking configurations such as widened and zigzagged morphology. These features present local twisting and decreasing of the lattice mismatch as the graphene lattices stretch in the AB-stacked regions; in other words, graphene lattices become similar to hBN lattices, and it indicates local transition from incommensurate to commensurate state at AB-stacked regions. Thus, this work provides insights into the spontaneous interactions between van der Waals 2D materials under free-standing state, even under low magnification. To the best of our knowledge, our TEM work is the most comprehensive report to directly demonstrate the reduced lattice mismatch on G/hBN depending on the stacking configuration under not only microscale with moiré fringes but atomic scale with expansion of AB-stacked area. Furthermore, it can provide an inventive route to study van der Waals 2D structures for understanding the outstanding electronic properties in detail. METHODS Preparation of G/hBN. Graphene film was synthesized by chemical vapor deposition (CVD) on 25-μm-thick copper foil (99.8% Alfa Aesar, Ward Hill, MA, USA). For synthesizing largesized grains of graphene, the vapor pressure of hydrogen and methane was controlled as previously described.42 The working pressure of hydrogen was 1.5 × 10−2 Torr, increasing to 1.3 × 10−1 Torr after inputting methane. The synthesized graphene was transferred to 7088
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ACS Nano Quantifoil TEM grids by the direct transfer method.43 The copper substrate was etched away in Na2S2O8 solution (0.2 mg Na2S2O8/mL water) for 12 h. The average grain size of the graphene exceeded 2 μm; consequently, the grains covered the whole area of a 2-μm-diameter hole in the Quantifoil TEM grid. The synthesis and transfer process of the hBN film are described in a previous paper.44 The hBN films were synthesized under lowpressure CVD on platinum foil of thickness 125 μm (99.95%, Goodfellow) and transferred onto a graphene/Quantifoil TEM grid by the electrochemical bubbling method. Structural Characterization. TEM characterization was conducted in a Cs image aberration-corrected FEI Titan Cube TEM with an electron monochromator operated at 80 kV. The moiré fringes were acquired along the {1010̅ } diffraction reflections of graphene and hBN by DF-TEM imaging. The diameter of the objective aperture was approximately 1.2 nm−1 in electron diffraction mode. The acquisition times of the DF-TEM images and atomic resolution TEM images were 5 and 0.3 s, respectively. Image Simulation. The atomic model simulation images (Figures 1d and 3c) were generated in Photoshop and Jmol, an open-source Java viewer for three-dimensional chemical structures that reads a variety of file types and generates output from quantum chemistry programs. Jmol animates multiframe files and computes the normal modes from the quantum programs. The mainframe of the model was constructed by VESTA. Atomic resolution TEM images were simulated by the multislice method in MacTempas package (Figures 3c and 4c).
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ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b02716. Additional information including supplemental TEM images, image simulations, and schematics for moiré fringes of graphene on hBN (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Na Yeon Kim: 0000-0003-3424-5965 Jung Hwa Kim: 0000-0002-2615-963X Hyeon Suk Shin: 0000-0003-0495-7443 Zonghoon Lee: 0000-0003-3246-4072 Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS This work was supported by the Institute for Basic Science (IBS-R019-D1), a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2015R1A2A2A01006992), and the Nano Material Technology Development Program (2012M3A7B4049807). REFERENCES (1) Geim, A. K.; Grigorieva, I. V. Van Der Waals Heterostructures. Nature 2013, 499, 419−425. (2) Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Boron Nitride Substrates for High-Quality Graphene Electronics. Nat. Nanotechnol. 2010, 5, 722−726. (3) Xue, J.; Sanchez-Yamagishi, J.; Bulmash, D.; Jacquod, P.; Deshpande, A.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; LeRoy, B. J. Scanning Tunnelling Microscopy and Spectroscopy of 7089
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DOI: 10.1021/acsnano.7b02716 ACS Nano 2017, 11, 7084−7090
