Supporting information. Heterojunction

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1 Supporting information 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 * yaojie@berkeley.edu 1

2 Methods Synthesis The rippled lateral Bi2Se3/Bi2Te3 heterostructures were synthesized using a one-pot solvothermal synthesis. High-purity polyvinylpyrrolidone (PVP, (C 6 H 9 NO) n, 320mg) was dissolved in ethylene glycol (12ml) to form a clear solution, followed by the addition of bismuth oxide (Bi 2 O 3, 1/3mmol), tellurium (Te, 1/4mmol), selenium (Se, 3/4mmol) and ethylenediaminetetraacetic acid (EDTA, C 10 H 16 N 2 O 8, 110mg) powders at the same time, instead of being added sequentially during the growth process. The resulting suspension was stirred vigorously for one hour with a magnetic stirrer (Benchmark, H3760-HS), and in the same way, four such precursor suspensions were prepared for control experiments and then sealed in four 25ml steel autoclaves. Afterwards, the autoclaves were heated in an oven at a temperature of 200 C for 6, 12, 18 and 24 hours, respectively. After naturally cooling down to room temperature, the synthesized Bi 2 Se 3 /Bi 2 Te 3 heterostructural plates were collected with a centrifuge, and washed with isopropanol (IPA) several times. To explore the effect of EDTA on the width of Bi 2 Te 3 edges and rippling morphology, three other amounts of EDTA (220, 330 and 440mg) were used in addition to 110mg, while the growth time was kept consistent at 24 hours. Growth sequence In all heterostructure nanoplates we have characterized, Bi 2 Se 3 is found to grow first, instead of Bi 2 Te 3 or an alloy. We attribute it to the electronegativity difference between Se and Te, and the reaction energetics. Both Se and Te are chalcogen elements, and Se has higher electronegativity than Te (2.55 for Se, and 2.1 for Te, dimensionless quantity with Pauling scale). 1,2 Se will react with Bi 2 O 3 to form Bi 2 Se 3 until Se is completely exhausted, and then Te will be reduced, generating Bi 2 Te 3 edges. This can also be proved by the energetics of the reaction, 2

3 Bi 2 Te 3 +3Se=Bi 2 Se 3 +3Te. Based on the enthalpy change of the reaction, 62, the Gibbs free energy change,, will be negative, since the entropy ( S) remains almost unchanged (because all the reactants and products are solids with the same molar numbers). 3 Therefore, even if some Bi 2 Te 3 might be produced before Se was fully used up, Te(2- ) in Bi 2 Te 3 would be replaced by Se, and Bi 2 Se 3 would be formed. As a result, Bi 2 Se 3 grows first forming a basal plate, and then Bi 2 Te 3 grows around the plate forming periodic wrinkles to release the lattice mismatch. The alloy region (~50nm) at the interface could be attributed to the atomic inter-diffusion between Bi 2 Se 3 and Bi 2 Te 3. Effects of the growth time and EDTA ratio To demonstrate the effects of growth time and EDTA ratio on the width and thickness of the Bi 2 Te 3 strips, measurements were conducted on the nanoplates from four different growth times (6, 12, 18 and 24 hours, 110mg EDTA), and four different EDTA ratios (110, 220, 330 and 440mg, 24 hours) respectively. For each growth batch, more than twenty nanoplates were characterized. 3

4 Figure S1. The statistical rippling wavelengths and thicknesses of Bi 2 Te 3 strips changing with growth time (a, b) and EDTA ratio (c, d). During the growth process, atoms on the edge of nanoplates are more reactive, due to dangling bonds that more readily accept adatoms, than the chemically saturated Se/Te atoms on the bottom/top surfaces. Therefore, lateral growth overwhelms vertical growth. The average width increases significantly with growth time, while the thickness only slightly increases. As EDTA ratio increases, the edge width and wavelength decrease. According to the nanoparticle growth reported, larger EDTA ratio can result in larger nanoparticles. 4 With more addition of EDTA, it was found that Bi 2 Se 3 parts tend to grow larger in the nanoplates, so Bi 2 Te 3 width will be smaller with a fixed amount of Te source. To sum up, with longer growth time and less EDTA, the nanoplates with wider Bi 2 Te 3 edges and larger rippling wavelength can be grown. Characterization As the nanoplates are freestanding and suspended in IPA, they can be directly deposited onto any substrate, such as SiO 2 /Si and carbon film coated copper TEM grids. The morphology, structure and chemical composition of the rippled plates were characterized with an optical microscope, AFM, SEM, and TEM. The low magnification TEM images with bend contours and the high resolution atomic images were acquired with an FEI F20 UT Tecnai at 200kV, while the STEM-HAADF images and the EDS data were acquired with a FEI Titan at 120kV. 4

5 Figure S2. The morphology of the rippled Bi 2 Se 3 /Bi 2 Te 3 plates drop-cast on SiO 2 /Si substrates. (a, b) The top view SEM images of two plates clearly show the wavelike nature of the edges. (d) The scans parallel to the interface demonstrate that most of the abrupt wrinkle has semisinusoidal profiles. The innermost greyish scan shows the double-hump feature, which may result from the effect of the substrate. (e) The line-scans normal to the interface display that the wrinkle penetrates into the Bi 2 Se 3 regions, with the heights gradually decreasing. 5

6 Figure S3. (a) The SEM image of the rippled plate anchored on carbon film of TEM grid. Scale bar, 2µm. (b) A composite map of the three elements Bi, Se, and Te shows the lateral integration of the two regions identified as Bi 2 Se 3 and Bi 2 Te 3 respectively. Figure S4. HRTEM images at (a)bi 2 Se 3, (b)bi 2 Te 3 and two typical sites of the interface (c, d). After indexing the FFT patterns, the lattice spacings were found to be and nm for Bi 2 Se 3 and Bi 2 Te 3, belonging to {1120 crystal planes. The average spacings of the two typical sites at the interface were calculated as and nm, in-between those of Bi 2 Se 3 and Bi 2 Te 3. No evidence of misfit dislocations was observed at the interface. Figure S5. The low magnification bright field (BF) images of two additional rippled areas (a)(b) illustrating bend contours, and one flat region (c) in between two ripples. 6

7 Figure S6. The SEM and AFM images of the other four rippled plates used for fitting, scale bar, 2µm. Figure S7. For all four plates in Figure 4, the calculated optimal wavelengths corresponding to energy minima match well with the measured ones. With the width increasing, the energy minima shift to larger wavelengths. 7

8 Figure S8. The length control calculations based on fixed width (a,b) or fixed thickness (c,d) respectively. (a)(b) As the width of the Bi 2 Te 3 region increases, the bending energy density almost remains constant, while the in-plane strain energy density decreases proportionally, because the compressive strain is more relaxed in the outer area of Bi 2 Te 3 region through the outof-plane rippling. Consequently, the energy minimum from the balance of bending and strain energies shifts to larger wavelengths for the nanoplates with a wider Bi 2 Te 3 region. (c)(d) When the nanoplates become thicker, both the bending and strain energy density increase. Bending energy is enhanced more intensely (~t 3 ) than strain energy (~t), and similar to the effect of the width, with the thickness increasing, the minimum energy point shifts to larger rippling wavelengths. Increased by the same factor, the thickness will have more influence on the energy change and rippling wavelength compared to the width. 8

9 Figure S9. The integrated strain and arc length along the midway (74 nm) of rippled Bi 2 Te 3 region (W=148 nm, t=11 nm) parallel to the interface for a fixed length of 1000 nm. (a) The strain (x component) is calculated based on Note S1, and as the strain is different for different locations, here the integral along the total fixed length was calculated to reflect the average strain value. The oscillations are from the periodicity of the rippling profile, and after further integration across the whole surface, the oscillation will disappear. Despite the oscillations, the trend is very similar to how the strain energy changes with λ; the minimum strain is located around 250 nm, matching well with the strain energy minimum. (b) For the flat plate under compression (1000 nm) before rippling, the total relaxed length should be around 1060 nm, as the lattice mismatch is about 6%. As the wavelength increases, the arc length demonstrates very similar behavior to the integrated strain and strain energy. The maximum at 250nm approaches the relaxed length, resulting in the minimum strain and strain energy. 9

10 Figure S10. The heights VS of the ripples. The height denotes the vertical distance from the top of the very edge to the substrate, and each data point represents one plate. The error bar is from standard deviation. Note S1 The elastic energy is calculated based on continuum mechanics using the fixed footnote model with a fixed interfacial length from several publications. 5-8 After bending, the total elastic energy consists of bending and in-plane strain energy, the competition of which results in the optimal rippling wavelength and amplitude. The in-plane strain energy has two parts, one of which is residual interfacial strain energy from the strain component parallel to the interface, and the other one results from the stretching energy due to the strain normal to the interface. The out-of-plane bending profile is defined as,, 1exp cos 2 10

11 Where A is the amplitude constant, is the decay parameter, w is the Bi2Te3 edge width, and is the rippling wavelength. x axis and y axis are parallel and normal to the interface respectively. The bending energy density per unit area can be calculated as, 4 21 In which B is the bending stiffness, and can be derived as for 2D materials with more than ten layers. 9 The Young s modulus is taken as 20GPa, and the Poisson s ratio is set as for both Bi 2 Se 3 and Bi 2 Te 3 with ten to fifteen layers due to their similar mechanical properties. 10,11 The in-plane displacement field along x direction can be set as, 4 sin4,<<0 0, 0<< The strain distribution along x direction can be calculated as, 1 2 [ ] The strain distribution along y direction is evaluated as, 1 2 The strain energy density per unit area is derived as, 4 [ ] For a specific width and thickness, the elastic energy is only related to λ, A and β. was fixed, and the energy minimum could be found by varying the A and β values, and then the λ value was 11

12 scanned to find the global minimum. The elastic energy as well as the corresponding amplitude values can be plotted as a function of λ. Table S1. The average widths, thicknesses and wavelengths of the rippled Bi 2 Te 3 edges Plate Average Average Number of Experimental Experimental width (nm) thickness (nm)* quintuple layers wavelength (nm) height (nm) ~ ~ ~ ~ ~ ~ ~ ~ * The thickness of the PVP layer on the surface of the plates was set as 1 nm according to previous estimation, and the average thicknesses here used in the calculation were after subtraction taking the two PVP layers into account Pauling, L. The nature of the chemical bond and the structure of molecules and crystals: an introduction to modern structural chemistry. Cornell University Press: Ithaca, New York, Lu, W. et al. J. Am. Chem. Soc. 2005, 127, Kubaschewski, O. et al. Materials Thermochemistry. Pergamon: Oxford, Qiu, H. et al. J. Mater. Chem. 2011, 21, Nandwana, D. et al. Nano Lett. 2015, 15, Alred, J. et al. Nano Res. 2015, 8, Nandwana, D. et al. J. Appl. Phys. 2015, 117, Landau, L. D.; Lifshitz, E. M. Theory of Elasticity. Pergamon: Oxford, 1970, pp Zhang, D. et al. Phys. Rev. Lett. 2011, 106, Yan, H. et al. Appl. Phys. Lett. 2016, 109, Guo, L. et al. Nanoscale 2015, 7, Kong, D. et al. Nano Lett. 2013, 13,