Three-dimensional Architecture Enabled by Strained Two-dimensional

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3D Architecture Enabled by Strained 2D Material Heterojunction Shuai Lou, Yin Liu, Fuyi Yang, shuren lin, Ruopeng Zhang, Yang Deng, Michael Wang, Kyle B Tom, Fei Zhou, Hong Ding, Karen C. Bustillo, Xi Wang, Shancheng Yan, Mary Scott, Andrew M. Minor, and Jie Yao Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b05074 • Publication Date (Web): 20 Feb 2018 Downloaded from http://pubs.acs.org on February 21, 2018

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3D Architecture Enabled by Strained 2D Material Heterojunction Shuai Lou†, Yin Liu†, Fuyi Yang†, Shuren Lin†, Ruopeng Zhang†,‡, Yang Deng†, Michael Wang†, Kyle B. Tom†,§, Fei Zhou†, Hong Ding§, Karen C. Bustillo‡, Xi Wang†, Shancheng Yan†, Mary Scott†,‡, Andrew Minor†,‡, Jie Yao†,§* †Department

of Materials Science and Engineering, University of California, Berkeley, California 94720, USA

‡The

National Center for Electron Microscopy, Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

§Materials

Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA *Email: [email protected]

ABSTRACT Engineering the structure of materials endows them with novel physical properties across a wide range of length scales. With high in-plane stiffness and strength, but low flexural rigidity, 2-dimensional (2D) materials are excellent building blocks for nanostructure engineering. They can be easily bent and folded to build 3-dimensional (3D) architectures. Taking advantage of the large lattice mismatch between the constituents, we demonstrate a 3D

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heterogeneous architecture combining a basal Bi2Se3 nanoplate and wavelike Bi2Te3 edges buckling up and down forming periodic ripples. Unlike 2D heterostructures directly grown on substrates, the solution-based synthesis allows the heterostructures to be free from substrate influence during the formation process. The balance between bending and in-plane strain energies gives rise to controllable rippling of the material. Our experimental results show clear evidence that the wavelengths and amplitudes of the ripples are dependent on both the widths and thicknesses of the rippled material, matching well with continuum mechanics analysis. The rippled Bi2Se3/Bi2Te3 heterojunction broadens the horizon for the application of 2D materials heterojunction and the design and fabrication of 3D architectures based on them, which could provide a platform to enable nanoscale structure generation and associated photonic/electronic properties manipulation for optoelectronic and electro-mechanic applications.

KEYWORDS Bi2Se3/Bi2Te3, lateral heterojunction, 3D architecture, ripples, width/thickness dependence Novel material properties and functionalities may originate from not only the utilization of different material components, but also the design of new material structures. In the nano regime, the introduction of different 3D architectures has introduced numerous novel mechanical, optical or electronic functionalities to existing materials. 1 , 2 For example, the Origami technique, originating from the art of paper folding, has been utilized to prepare complex reconfigurable structures of various nanomaterials and has led to applications such as nanoelectromechanical systems and metamaterials.3-6 Recent extensive researches on 2D materials have demonstrated ,

that these materials, capable of withstanding strains much larger than conventional materials, can


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transform into various conformations due to their high strength and flexibility, therefore bringing new opportunities in realizing more functionalities through nanostructure engineering.7,8 The 3D architectures of graphene have been shown to open up the electronic bandgap, induce a pseudo-magnetic field, generate electron-hole ‘puddles’, and tune the optical transparency and surface wettability. 9 , 10 , 11 Similar findings have also been reported for other 2D materials, including h-BN, transition metal dichalcogenides, and black phosphorus. The ripples observed on annealed few layer h-BN are believed to facilitate a significant second harmonic generation response due to symmetry breaking. 12 In a wrinkled MoS2 membrane, it was suggested that excitons exhibit ‘funnel effect’ and become concentrated at the center point of the delaminated region with smaller bandgap.13 A study of rippled multilayer black phosphorus sheets showed that the absorption band-edge exhibits a ~0.7eV shift between the tensile and compressive regions.14 Many methods have been used to prepare 3D architectures based on 2D materials, such as rapid evaporation of aerosol droplets containing precursors and transfer onto pre-patterned substrates.15,16 Periodic ripples can be created in suspended graphene sheets when they are heated up and cooled down on trenched substrates, due to the mismatch of their thermal expansion coefficients.17 The texturing can also be realized via thermally inducing contractile deformation of the underlying polystyrene (PS) substrate by heating above the glass transition temperature.18,19 A more reversible and simpler method is a widely-used pre-stretch and release process of an elastic polymeric substrate with 2D materials on the surface.20 To date, however, the reported approaches are mostly based on manipulation of the substrates, and after generation of 3D architectures, it is difficult to remove the polymeric substrates while preserving the material integrity and crumpled morphology. Preliminary progress towards the transfer of 3D


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structures is being made. However, cracks arise with residual polymeric contamination (Figure S7 in the supporting information of Ref. 18). This limits the compatibility of these 3D architectures with the technologies that are based on rigid solid substrates. Moreover, the preparation process of 3D architectures usually involves multiple steps from the synthesis and transfer of 2D materials to the manipulation of substrates, and a one-step synthesis and assembly method is greatly preferred, but has not been reported yet. Here we report a freestanding 3D heterogeneous architecture combining a basal Bi2Se3 nanoplate with rippled Bi2Te3 sheets using one-pot solution synthesis. Both constituents are typical van der Waals 2D materials.21 In fact, 2D heterostructures have enabled a wide spectrum of new physical phenomena and device applications. 22-25 Generation of periodic ripples by the interfacial strain in 2D lateral heterojunctions has been theoretically demonstrated and analyzed by Alred et al., 26 and almost concurrently shown for lateral graphene/h-BN heterostructure with molecular dynamic simulations.27,28 However, for 2D materials directly grown on substrates, the interaction between the materials and the substrates restrains the out-of-plane deformation. Instead, the interfacial strain from the lattice mismatch results in the interfacial misfit dislocations and random strain distribution.23,24 In order to minimize the substrate effect, we utilize a substrate-free solution method and successfully prepare freestanding 2D lateral Bi2Se3/Bi2Te3 heterojunctions. In the following sections, we show that due to the large lattice mismatch of around 5.9%, the as-grown Bi2Te3 indeed buckles up and down, forming periodic ripples around the edges of the Bi2Se3 nanoplate (Fig. 1), just like what has been anticipated in the graphene/h-BN system. Our calculation verifies that the out-of-plane deformation can dramatically reduce the elastic energy from the lattice mismatch to accommodate coherent interfaces, and the balance of the bending and strain energies results in the characteristic rippling


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wavelengths and amplitudes. Moreover, the dimensions of ripples are found to be dependent on the width and thickness of the Bi2Te3 region, therefore 3D structures can be generated in a controllable way. The ripples can potentially change topological surface states and thermoelectric properties on wavy edges, and the lateral heterojunction could have distinct surface and bulk transport properties across the interface.29,30,31 Our approach will not only shed new light on the design of 3D nanostructures in 2D materials, but can also work as a platform to engineer the electronic structure and transport properties for optoelectronic, electromechanical and magnetic applications.32,33,34 RESULTS AND DISCUSSION Different from 2D materials grown by the widely-used chemical vapor deposition (CVD) method, the rippled Bi2Se3/Bi2Te3 heterojunctions are synthesized using a one-pot solution method (see methods section), and the as-grown nanoplates form suspensions in ethanol. They can be drop-cast on required substrates as needed in different characterizations or applications. As Bi2Te3 has a ~5.9% larger lattice constant than Bi2Se3, when coherently bonded, Bi2Te3 will be compressed while Bi2Se3 is under tension along the interface as shown in Figure 1a. The outof-plane deformation with the formation of periodic ripples can effectively release the interfacial strain and minimize the total energy, leading to a more stable state. To clearly demonstrate the 3D structure, scanning electron microscope (SEM) images are captured. Figure 1c displays a plate deposited on SiO2/Si substrate with three ripples showing up along every edge. The sample is slightly tilted to give a better angle to observe the ripples. Another plate is found to be folded as in Figure 1d, which demonstrates the morphology of the back side, and indicates that for a freestanding hexagonal wavy plate, the edges actually buckle up and down forming nearly sinusoidal ripples (top views of the two plates as Supplementary Figure S2a, b). When drop-cast,


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the parts that originally buckle downwards on the edges are flattened and adhere to the substrate due to the van der Waals interaction. The thickness of the former nanoplate is about 16 nm as measured with atomic force microscopy (AFM) (Figure 1e), and the width of the Bi2Te3 strips is around 560 nm. The red line scan parallel to the edge demonstrates that the ripples have a semisinusoidal profile with a peak to peak distance of around 1.3µm.

Figure 1. The schematic plots and basic morphology of the rippled Bi2Se3/Bi2Te3 plates dropcast on SiO2/Si substrates. (a) Without rippling, the Bi2Se3 part is in tension while the Bi2Te3 part is in compression due to the large lattice mismatch around 5.9% (magnitude of the mismatch is exaggerated in the schematic to illustrate the difference). (b) For the coherent interface, the outof-plane deformation is an effective way to reduce the in-plane strain energy. (c) The tilted view SEM image shows three ripples buckling up at each edge of the plate. (d) Another folded plate reveals the morphology of the back surface, and indicates that the edge has a wavelike nature when suspended in solvents. (e, f) The thickness of the plate in (c) is around 16 nm, and the red line scan shows a semi-sinusoidal profile with an average peak to peak distance of 1.3µm along the edge. Scale bar, 2µm.


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The scanning transmission electron microscope (STEM) image using high-angle annular darkfield (HAADF) detection in Figure 2a shows increased contrast between the two parts, due to the mass/thickness dependent electronic scattering. The peripheral regions appear brighter since they are richer in the heavier tellurium (Te) atoms, which is also verified by the elemental mapping with the energy dispersive X-ray spectroscopy (EDS). As shown in the elemental images in Figure 2(b-d), bismuth (Bi) is uniformly distributed throughout the whole plate, while selenium (Se) and Te show clear segregation, with Se in the center and Te in the peripheral regions. The EDS linescan profile of the elemental distribution in Figure 2e clearly shows the opposite composition changing trends of Se and Te across the interface. The high resolution TEM (HRTEM) images of flat regions on both sides of the heterojunction in Figure 2f and 2g exhibit parallel lattice fringes. Fast Fourier transformations (FFT) insets show that both of the two materials have hexagonal lattice structures. We indexed the FFTs and find the lattice spacings to be 0.207 and 0.220 nm respectively, which belong to {1120} crystal planes of Bi2Se3 and Bi2Te3, consistent with previous reports.35Unlike previous reports where dislocations instead of 3D structures were formed to relax strains,21,36 no evidence of misfit dislocation was observed in the HRTEM images taken at the interface between Bi2Se3 and Bi2Te3 (Figure S4 in the supporting information), as the interface is not abruptly sharp and the out-of-plane rippling can effectively relieve the strain from lattice mismatch.


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Figure 2. TEM-EDS and HRTEM analysis on the rippled Bi2Se3/Bi2Te3 nanoplates. (a) STEMHAADF image shows the contrast between the outer edges rich in heavier tellurium (Te) atoms and the inner part with lighter selenium (Se) atoms. The bright stripe at the right-top corner is due to the thicker part of carbon film. (b-d) Elemental images from TEM-EDS prove that bismuth (Bi) is uniformly distributed throughout the whole plate, while Se and Te are segregated, with Se in the center and Te in the peripheral regions. (e) EDS profile across the interface shows the segregation of Se and Te. The interface is not abruptly sharp, but instead shows a transition region (~50 nm) from Bi2Se3 to Bi2Te3. (f)(g) HRTEM images of both the inner and marginal flat regions exhibit parallel lattice fringes. Insets: Fast Fourier transformations (FFT) show that both of the two materials have hexagonal lattice structures, and by indexing them, the lattice spacings are found to be 0.207 and 0.220 nm respectively, which belong to {1120} crystal planes of Bi2Se3 and Bi2Te3. Figure 3 displays the low magnification bright field (BF) images of two wrinkled areas and one flat region in-between the two ripples (more images of rippled areas and flat regions in


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Supplementary Figure S5). Clear symmetric contrast fringes are observed in the wrinkled areas, unlike the relatively uniform contrast in the flat region. These fringes are bend contours, which occur when a particular set of diffraction planes is not parallel everywhere, and the planes that satisfy the Bragg condition exhibit constructive interference. 37 According to the diffraction conditions, the more the sample is bent, the more contours occur from the higher-order diffraction.38,39 The symmetric bend contours reveal that the wrinkle is heavily bent with a mirror symmetry about the center line, demonstrating the high quality of the ripples and the singlecrystalline nature of the material.

Figure 3. The low magnification bright field (BF) images of two wrinkled areas (a)(b) and one flat region (c) in between two wrinkles. At the two wrinkled areas, dark symmetric contrast fringes appear, which are bending contours from constructive diffraction according to the Bragg condition. The symmetric dense bending contours reveal that the wrinkle is heavily bent with a mirror symmetry about the center line. After characterizing heterostructured nanoplates with different rippling dimensions as shown in Figure 4 (more sample images in Supplementary information), strong correlation is found between the ripple morphology and the width and thickness of the Bi2Te3 strips. We define a characteristic wavelength, ‘λ’, as the average distance between adjacent peaks in a ripple, and ‘A’ as the rippling amplitude. As the Bi2Te3 width decreases, the number of ripples on each edge


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increases, i.e., the rippling wavelength decreases. Meanwhile, the heights of ripples, partially revealing the amplitudes in freestanding nanoplates, are measured based on the AFM scanning, and statistically analyzed as listed in Table S1. As the Bi2Te3 edges narrow down, the heights (amplitudes) reduce. To gain deeper understanding of the rippling formation, the elastic energy is calculated based on continuum mechanics (detailed assumptions and calculation process in Supplementary Note 1).26-28,40 The calculated results shown in Figure 5a are based on a sample with the Bi2Te3 strip width (~150 nm) and thickness (~11 nm). As the rippling wavelength () increases, the amplitude (A) increases almost linearly (Figure 5a inset). The two parameters determine the arc length of the ripple, which reflects the release of the compressive strain from

the lattice mismatch. Bending energy ( ) is dependent on the bending curvature, ~ ,

in which is the bending profile, and ~ , R is the radius) is the curvature. With an increase of the rippling wavelength λ, the plate tends to be flatter and less bent (R increases), and

the curvature decreases.40 As a result, the bending energy goes down quickly, showing a dependence, in agreement with the previous theoretical calculation.28

Figure 4. SEM (a-d) and AFM (e-h) images of four rippled Bi2Se3/Bi2Te3 nanoplates. As the width of Bi2Te3 edges increases, both the wavelength and amplitude increase. Scale bar, 2µm.


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As the wavelength decreases, the strain energy density goes down to the minimum (λ ≈250 nm), and then increases again. The variation of the strain energy can be explained with both the arc length and calculated strain of the ripple, as shown in Figure S9 of the supporting information. With more rippling ( decreasing), the arc length increases, and the compressive strain from the lattice mismatch is more released through the out-of-plane bending. Consequentially, the strain energy density goes down, approaching the minimum where the compressive strain from lattice mismatch is nearly fully relaxed ( ~250 nm). Then if the wavelength further decreases, the arc length will decrease, and the strain energy increases again. The optimal wavelengths and amplitudes of ripples emerge at the energy minimum from the competition between the ripple bending energy and in-plane strain energy. The calculated optimal wavelength corresponding to minimum energy of around 530 nm matches well with the experimental measurement of around 515 nm, so do the other plates (Figure 5d and Supplementary Figure S7). The corresponding amplitude is derived to be about 52 nm, in agreement with the height (~62 nm) considering the distortion caused by the substrate. Some ripples might undergo more intense deformation compared to others, which may appear abrupt (Figure 1c and 1e, at 1PM site). Though the abrupt site resembles the ‘D-loop’ defect reported in the graphene nanoribbons of carbon fiber, 41 combining the AFM and HRTEM images (Figure S2, Figure 2 and S4), after careful analysis, no evidence for the existence of D-loop defects was found, and the Bi2Te3 strips are continuous. To explore the effects of the Bi2Te3 width and thickness on rippling wavelengths, calculations based on fixed thickness or fixed width are carried out respectively. With the width of the Bi2Te3 region increasing, the bending energy density, which is determined by the curvature, stays almost unchanged, so the total bending energy linearly increases with the width (Supplementary Figure S8a). The in-plane strain energy density decreases proportionally as the width gets larger, so the


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total strain energy does not change much (Supplementary Figure S8b), because the compressive strain is relaxed more in the outer majority of Bi2Te3 region through the out-of-plane rippling, and the in-plane strain energy is mainly concentrated in the region nearby the interface. Consequently, the energy minima from the balance of bending and strain energies shift to larger wavelengths for the nanoplates with wider Bi2Te3 region, as shown in Figure 5b. Besides the width, thickness also makes a significant impact on the rippling parameters. With the nanoplates becoming thicker, both the bending and strain energy density increase (Supplementary Figure S8c and S8d). Intuitively, the flexural rigidity is larger for thicker samples, which are stiffer and more resistant to bending. As a result, thicker plates are more difficult to bend, and tend to exhibit larger wavelengths and amplitudes. From the energy consideration, bending energy is enhanced much more intensively (~t3) than strain energy (~t).38 Similar to our finding of the dependence on width, when the thickness increases, the minimum energy point shifts to larger rippling wavelengths. It is also found that for a comparable change, the thickness will have more influence on the energy change and rippling than the width.


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Figure 5. The rippling wavelength dependence on the Bi2Te3 edge widths (w) and thicknesses (t). (a) The elastic energy is calculated based on continuum mechanics with the measured width and thickness of the 1st plate in Figure 4. The wrinkles’ optimal wavelengths and amplitudes emerge at the total energy minimum from the competition between the ripple bending energy and in-plane strain energy. Inset shows the amplitude dependence on wavelength. (b)(c) The control calculations for fixed width and thickness respectively. With either of them increasing, the energy minima move to larger wavelengths. (d) The wavelengths show a linear dependence on

√ . For the experimental measurement, all wavelengths, widths and thicknesses are obtained

from the SEM and AFM images, and the calculation results are marked as blue circles. The error bar represents standard deviation. (e, f) The width of Bi2Te3 strips changes with growth time and ethylenediaminetetraacetic acid (EDTA) ratio. For each growth batch, more than twenty nanoplates were measured, and the error bar represents standard deviation.


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To acquire the quantitative relationship between the rippling wavelength, and the width together with thickness of Bi2Te3 edges, all the parameters are experimentally measured. A clear relation between the periodicities, and the widths as well as thicknesses can be found in Fig. 5d, confirming Ref. 26’s theoretical prediction when fitted to Eq. 5 there,26 as,

λ = 21 in which is the wavelength, w is the Bi2Te3 edge width and t is the thickness. The coefficient ‘21’, we think, is decided by the balance between the bending and strain energy. On the other hand, the amplitude of ripples on the freestanding nanoplates are inevitably affected by the substrates when they are drop-cast. Nevertheless, the height of the ripples, partially reflecting the

amplitude in freestanding plates, still demonstrates a clear monotonic correlation with √ , as shown in supplementary Figure S10. Consequently, by controlling the Bi2Te3 edge width and thickness, the rippling wavelengths and amplitudes can be tuned over a large range. The width and thickness of the Bi2Te3 strips can be affected by changing the synthesis conditions, such as the growth time and the ratio of EDTA, as shown in Figure 5e and 5f as well as Figure S1 of supporting information. The results show that with longer growth time and less EDTA, the nanoplates with wider Bi2Te3 edges and larger rippling wavelengths can be grown. Such mechanism allows 2D lateral heterostructure to act as a platform to controllably design and fabricate 3D architectures for elaborate functionality manipulation. CONCLUSIONS We demonstrate a freestanding rippled Bi2Se3/ Bi2Te3 lateral heterojunction synthesized with a simple one-pot solution method. With a large lattice mismatch of around 5.9%, the Bi2Te3 region developed periodic ripples around the edges of Bi2Se3. With the out-of-plane buckling and ripple formation, the lateral heterostructure can coherently accommodate the large lattice mismatch, as


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the warping can dramatically decrease the total elastic energy. More importantly, the rippling wavelengths and amplitudes are found to be strongly dependent on the widths and thicknesses of the Bi2Te3 edges, due to the competition between bending energy and in-plane strain energy. A

linear proportionality to √ has been verified from our experimental data.26 Therefore, the 3D morphology of the heterostructure can be well controlled. The freestanding rippled heterojunction presents a new way to construct 3D nanostructures based on strained 2D materials, and fabricate nanoscale devices for various potential applications, including strain engineering of the topological states, thermoelectric properties on both wavy edges and the interface, and unique optoelectronics, quantum optics and electromechanics.

ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the ACS Publication website. The methods; The top view morphology of the rippled Bi2Se3/Bi2Te3 plates drop-cast on SiO2/Si substrates; The SEM image and the composite elemental map of the rippled plate anchored on carbon film of TEM grid; The HRTEM images at the interface; The low magnification bright field (BF) images of two additional rippled areas and one flat region; The SEM and AFM images of the other four rippled plates used for fitting; The calculated optimal wavelengths for all four plates in Figure 4, matching well with the measured ones; The control calculations based on fixed width or fixed thickness; The integrated strain and arc length along the midway of rippled

Bi2Te3 region; The heights VS √ of the ripples; The detailed calculation process based on continuum mechanics analysis; The average widths, thicknesses and wavelengths of the rippled Bi2Te3 edges.


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AUTHOR INFORMATION Corresponding Author *Email: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS This work was supported by the Samsung Advanced Institute of Technology under the grant 037361-003 and Bakar Fellows Program at University of California, Berkeley. The TEM characterization was done at the Molecular Foundry in Lawrence Berkeley National Laboratory. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. The authors are grateful to Prof. Ertekin, Y. Xiao, Z. Gong, Q. Li, Y. Wang, K. Dong, C. Wang and H. Zhu for their valuable discussions.

1. Wang, Q.; Zhao, X. Beyond Wrinkles: Multimodal Surface Instabilities for Multifunctional Patterning. MRS Bull. 2016, 41, 115-122. 2 . Deng, S.; Berry, V. Wrinkled, Rippled and Crumpled Graphene: an Overview of Formation Mechanism, Electronic Properties, and Applications. Mater. Today 2016, 19, 197-212. 3. Silverberg, J.; Evans, A. A.; Mcleod, L; Hayward, R. C.; Hull, T.; Santangelo, C. D.; Cohen, I. Using Origami Design Principles to Fold Reprogrammable Mechanical Metamaterials. Science 2014, 345, 647650. 4. Rogers, J.; Huang, Y.; Schmidt, O. G.; Gracias, D. H. Origami MEMS and NEMS. MRS Bull. 2016, 41, 123-129. 5. Overvelde, J. T.B.; de Jong, T. A.; Shevchenko, Y.; Becerra, S. A.; Whitesides, G. M.; Weaver, J. C.; Hoberman, C.; Bertoldi, K. A Three-dimensional Actuated Origami-inspired Transformable Metamaterial with Multiple Degrees of Freedom. Nat. Commun. 2016, 7, 10929-10936. 6. Cho, J.; Keung, M. D.; Verellen, N.; Lagae, L.; Moshchalkov, V. V.; Van Dorpe, P.; Gracias, D. H. Nanoscale Origami for 3D Optics. Small 2011, 3, 1943-1948. 7. Akinwande, D.; Brennan, C. J.; Bunch, J. S.; Egberts, P.; Felts, J. R.; Gao, H.; Huang, R.; Kim, J.; Li, T.; Li, Y. et al. A Review on Mechanics and Mechanical Properties of 2D Materials-graphene and beyond. Extreme Mech. Lett. 2017, 13, 42-72. 8. Shen, J.; Zhu, Y.; Jiang, H.; Li, C. 2D Nanosheets-based Novel Architectures: Synthesis, Assembly and Applications. Nano Today 2016, 11, 483-520.


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29. Liu, Y.; Li, Y. Y.; Rajput, S.; Gilks, D.; Galindo, P. L.; Weinert, M.; Lazarov, V. K.; Li, L. Tuning Dirac States by Strain in the Topological Insulator Bi2Se3. Nat. Phys. 2014, 10, 294-299. 30. Min, Y.; Roh, J. W.; Yang, H.; Park, M.; Kim, S, I.; Hwang, S.; Lee, S. M.; Lee, K. H.; Jeong, U. Surfactant-free Scalable Synthesis of Bi2Te3 and Bi2Se3 Nanoflakes and Enhanced Thermoelectric Properties of Their Nanocomposites. Adv. Mater. 25, 1425-1429, (2013). 31. Bhowmick, S.; Singh, A. K.; Yakobson, B. I. Quantum Dots and Nanoroads of Graphene Embedded in Hexagonal Boron Nitride. J. Phys. Chem. C 2011, 115, 9889-9893. 32. Duerloo, K. N.; Reed, E. J. Flexural Electromechanical Coupling: a Nanoscale Emergent Property of Boron Nitride Bilayers. Nano Lett. 2013, 13, 1681-1686. 33. Resta, R. Towards a Bulk Theory of Flexoelectricity. Phys. Rev. Lett. 105, 1276011-4, (2010). 34. Yang, S.; Wang, C.; Sahin, H.; Chen, H.; Li, Y.; Li, S.; Suslu, A.; Peeters, F. M.; Liu, Q.; Li, J.; Tongay, S. Tuning the Optical, Magnetic, and Electrical Properties of ReSe2 by Nanoscale Strain Engineering. Nano Lett. 2015, 15, 1660-1666. 35. Lu, W.; Ding, Y.; Chen, Y.; Wang, Z.; Fang, J. Bismuth Telluride Hexagonal Nanoplatelets and their Two-step Epitaxial Growth. J. Am. Chem. Soc. 2005, 127, 10112-10116. 36. Fei, F.; Wei, Z.; Wang, Q.; Lu, P.; Wang, S.; Qin, Y.; Pan, D.; Zhao, B.; Wang, X.; Sun, J. et al. Solvothermal Synthesis of Lateral Heterojunction Sb2Te3/Bi2Te3 Nanoplates. Nano Lett. 2015, 15, 59055911. 37. Williams, D. B.; Carter, C. B. Transmission Electron Microscopy. Springer: New York, 2009; pp 407415. 38. Lee, J.; Loya, P. E.; Lou, J.; Thomas, E. L. Dynamic Mechanical Behavior of Multilayer Graphene via Supersonic Projectile Penetration. Science 2014, 346, 1092-1096. 39. Mckenna, A. J.; Eliason, J. K.; Flannigan, D. J. Spatiotemporal Evolution of Coherent Elastic Strain Waves in a Single MoS2 Flake. Nano Lett. 2017, 17, 3952-3958. 40. Landau, L. D.; Lifshitz, E. M. Theory of Elasticity. Pergamon: Oxford, 1970, pp 38-57. 41. Gupta, N.; Artyukhov, V. I.; Penev, E. S.; Yakobson, B. I. Carbonization with misfusion: fundamental limits of carbon-fiber strength revisited. Adv. Mater. 2016, 28, 10317-10322.


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Three-dimensional Architecture Enabled by Strained Two-dimensional

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