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1 Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide Supplementary Figure S1: Commonly-observed shapes in MoS 2 CVD. Optical micrographs of various CVD MoS2 crystal shapes found in different growths. a) Mo- z- z triangles and 6- point star grown on clean Si/SiO2 substrates. Note: the small gold marks are metal alignment marks that were deposited after growth. b) Mo- z- z mirror twin crystal used for electrical devices in Figures 5i- j. c) S- z- z triangles and 5- and 6- point stars. d) Hexagons. e) Gear- like polycrystalline structures grown on dirty substrates. f) 3- point stars grown on dirty substrates. a- c) show the types of crystals achieved in large grain growth, while d- f) show the types of crystals grown as a result of dirty substrates or old precursors. NATURE MATERIALS 1

2 Supplementary Figure S2: Continuous sheet Figure S2a- b show optical images from two different, yet typical, samples similar to Figure 1a. The key difference between the samples is the grain size. On the top left in each image is bare oxide with sparse crystals. In both samples, CVD MoS 2 crystals can grow together to form continuous monolayer sheets (bottom right). The 2 NATURE MATERIALS

3 SUPPLEMENTARY INFORMATION gradients in nucleation density and grain size reflect the substrate proximity to the solid MoO 3 source. The small gold and orange dots, indicated by a red circle, are alignment marks placed after growth. Figure S2c shows two representative histograms of island size (as the square root of the area) extracted from portions of Figure 1a and Figure S2a. In the larger grain growths, such as in Figure S2b, the triangles grow together more to form aggregates and continuous sheets, making accurate measurement of grain size impossible without crystalographically sensitive techniques; For this reason only isolated islands in smaller- grain growths are included in Figure S2c, and regions near continuous sheets are excluded from the measurement. The spread in the histogram demonstrate the wide range of grain sizes and spatial inhomogeneity in all of our samples. NATURE MATERIALS 3

4 Supplementary Figure S3: Raman spectra and mapping a) Raman spectra showing the E 1 2g and A 1g vibrational modes 1 for monolayer (red curve) and bilayer (blue curve) MoS 2 corresponding with the photoluminescence spectra from Figure 1c. b- c) Maps of the peak position for the two Raman modes for monolayer tilt boundary from Figure 5 where b) represents the E 1 2g mode. and c) represents the A 1g mode. Both modes show an upshift of 1 cm - 1 at the grain boundary. While this shift may indicate a change in strain or doping at the boundary, it is difficult to interpret compared to the more marked changes to the photoluminescence seen in Figure 5 of the main text. Scale bar 5 µm. 4 NATURE MATERIALS

5 SUPPLEMENTARY INFORMATION Supplementary Figure S4: High resolution images of edge roughness a) Dark Field TEM image of a single Mo- z- z triangle on a holey amorphous carbon substrate. b- d) STEM images at increasing magnifications from the region inside the red box in a). In c), higher magnification reveals ~ 10 nm edge roughness as highlighted by the orange curve. In d) the MoS 2 lattice is visible, as well as atomic scale edge roughness. The non- uniform background variation in all images is due to the amorphous carbon TEM grid support (the perforated sheet in a). NATURE MATERIALS 5

6 Supplementary Figure S5: DF-TEM imaging of cyclic twin a) Bright- field image of a 6- pointed star. b) Full diffraction pattern shows star has no rotational boundaries. c- e) Dark- field TEM images corresponding with the c) red, d) blue, e) orange spots in the diffraction image. The red and blue [- 1100] spots show opposite intensity because they swap whether the k a or k b spot is captured for each region. The orange spot shows an even intensity over the entire star; this occurs because unlike the [- 1100] spots, the intensity of the [- 2110] spots are 6- fold symmetric (See Figure 1c). f) Bright- field TEM image with overlaid edge orientations extracted from DF- TEM. The outer edges are oriented along the Mo- z- z direction, which demonstrates that the grain boundaries are oriented along the S- z- z directions. 6 NATURE MATERIALS

7 SUPPLEMENTARY INFORMATION Supplementary Figure S6: Simulations of alternate mirror-twin boundaries a) Geometry optimized structure for the experimentally observed grain boundary, as determined by DFT (a). b) The local DOS (LDOS) integrated in the plane of the Mo over a 1.7 ev window inside the band gap of pristine MoS 2 confirms the spatial localization of mid- gap states. c) The energy- resolved density of states for pristine MoS 2 (black curve), the DOS of the structure shown in (a) (red curve), and the DOS projected just onto the atoms in the grain boundary (blue curve). In (c), we have subtracted off the contribution to the DOS arising from the unphysical edge atoms. NATURE MATERIALS 7

8 Analogous calculations are shown for an armchair grain boundary d- f) and for a zig- zag grain boundary g- i); both which are entirely periodic in two dimensions. In panels (b), (e), and (h), the colorscale indicates the magnitude of the integrated LDOS, from 0 (dark) to bohr - 3 (light). Supplementary Figure S7: Time resolved photoluminescence Time- resolved photoluminescence measurements obtained by time- correlated single photon counting with femtosecond excitation by 400- nm laser pulses. Results for exfoliated and CVD MoS 2 samples on oxide layers, after accounting for the instrument response function, yield nearly identical time constants of τ exfoliated=44 ps, and τ CVD=42 ps. The measured emission decay found to varied considerably from sample to sample for both the exfoliated and CVD grown 8 NATURE MATERIALS

9 SUPPLEMENTARY INFORMATION materials, so the similarity of the curves in this figure should not be regarded as having fundamental significance. Supplementary Figure S8: Electrical measurements on a tilt boundary a) Linear and b) logarithmic electrical transport transfer curves of 3 FETs fabricated from the tilt boundary MoS 2 island shown in the inset of (a), which has a tilt angle of 42 (Scale bar 10 μm). The FETs containing the perpendicular (black) and parallel (orange) boundary orientation to the flow of electrons are both 30% lower in conductance than the pristine region (cyan) in the on state (gate voltage = +70 V). NATURE MATERIALS 9

10 Supplementary Methods: Electron Diffraction Simulation: We calculated the diffraction pattern for a monolayer of MoS 2 using Bloch wave simulations to account for the complex scattering that allows the breaking of Friedel s rule and produces this asymmetry (Figure 2). The asymmetry of the Mo and S sublattices separates the [- 1100] diffraction spots into two families : k a={(- 1100), (10-10), (0-110)} and k b= -k a. Our bloch- wave simulations show that the ~10% higher intensity k a spots point toward the Mo sublattice, as indicated by the arrows in Figures 2(a- b). We double- checked this result with high- resolution imaging to confirm that the asymmetric diffraction pattern in Fig 2(b) corresponds to the indicated orientation of the MoS 2 lattice. Identifying triangle edge terminations: Via TEM analyses, we consistently observe that Mo- z- z triangles (Figure 2(b)) have sharper and straighter edges than S- z- z triangles (Figure 2(d)). This morphological difference allows us to rapidly identify the crystal edges and orientation of triangles on the growth substrate simply by optical microscopy. In doing so, we also observe that all crystals from the same growth run have the same morphology, i.e., triangles from a given run will either be dominated by Mo- z- z or by S- z- z edges, a preference we attribute to kinetic effects. Both triangle morphologies exhibit the same range of average sizes from µm. These classifications are important for understanding 10 NATURE MATERIALS

11 SUPPLEMENTARY INFORMATION growth dynamics and suggest the possibility of refined control of edge morphology by tuning the CVD process. DFT calculations: Density functional theory (DFT) calculations were performed with the PW91 generalized gradient approximation for the exchange- correlation functional and ultrasoft pseudopotentials, as implemented in the Quantum Espresso electronic structure package 5. Supercells were generated with about 10 Å separation to ensure negligible interactions between replicas. Structural relaxations were carried out at the gamma point until all components of all forces were less than a.u. Pristine MoS 2 (3.12 and 2.32 Å for Mo- Mo and Mo- S bond lengths, respectively) energy calculations were done with a 16x16 Monkhorst- type k- point grid, confirming the material's direct band gap with a predicted energy of 1.9 ev. Preliminary calculations employing a finer k- point grid for the structural relaxation show minor quantitative but not qualitative changes to the grain boundary geometry and electron structure 6. Because the direction of the experimentally observed grain boundary is incommensurate with the periodicity of the underlying crystal, a system periodic in two dimensions cannot be constructed. Thus we employed the system shown in Figure S6(a) which is periodic along the direction of the grain boundary, but finite in the orthogonal direction such that the edge, terminated by S dimers, is about 10 Å NATURE MATERIALS 11

12 away from the grain boundary. Energy calculations for this 87- atom supercell were performed with 5 k- points in the periodic direction. Local density of states (LDOS) analysis, shown in Figure S6(b) confirms that the electronic effects of the artificial edges are physically confined along the perimeter and so should not affect the properties along the grain boundary. These conclusions are also corroborated by a negligible change in bond length, compared to the bulk, for atoms away from the grain boundary. Analogous calculations on 2D periodic systems with pure armchair and zig- zag grain boundaries, shown in Figure S6 (d- i) similarly yield mid- gap states localized along the boundary, further indicating that the effect is generic and not an artifact of the finite strip size. Estimating non-radiative recombination: Photoluminescence quenching commonly arises from defects in semiconductors, such as the predicted midgap states at the boundaries, which can act as centers for non- radiative recombination 7. While the amount of material structurally modified by the boundary is small compared with the 500- nm laser spot size, the effect can be enhanced by the diffusion of photogenerated excitons to the boundary, which effectively increases the boundary width. Such a process would provide a natural explanation for the strongly reduced PL observed from some boundaries in our samples, since non- radiative recombination may be more efficient in the presence of the localized structures and states of the boundary. Here we estimate the potential impact of this effect using measured values for the carrier mobility and exciton lifetime. 12 NATURE MATERIALS

13 SUPPLEMENTARY INFORMATION The electrical measurements in this paper yielded an electron mobility of µ e = 3 cm 2 V - 1 s - 1 for typical CVD- grown samples. From the Einstein relation for a temperature of T = 300 K, we then obtain an electron diffusivity of = 8 x 10-2 cm 2 s - 1. Since the electron and hole masses are similar, we assume that the exciton diffusivity is half of the electron diffusivity, i.e., D exc = 4 x 10-2 cm 2 s - 1. The scattering mechanisms for electrons and excitons need not be the same, so this should only be considered as an estimate. The characteristic length for diffusion of excitons towards the boundary from the 2- D bulk material over a time τ is given by. For a time interval of τ = 40 ps reported above for the exciton lifetime, we then infer a diffusion length of L = 24 nm. This length, while not negligible, is small compared to the 500 nm spot size of the excitation laser. The quenching of the PL by 50% observed at some grain boundaries must consequently rely primarily, as discussed in the main text, on mechanisms other than exciton diffusion. Supplementary References: 1 Lee, C. et al. Anomalous Lattice Vibrations of Single- and Few- Layer MoS2. ACS Nano 4, Huang, P. Y. et al. Grains and grain boundaries in single- layer graphene atomic patchwork quilts. Nature 469, (2011). 3 Kim, K. et al. Grain Boundary Mapping in Polycrystalline Graphene. ACS Nano 5, (2011). 4 Lahiri, J., Lin, Y., Bozkurt, P., Oleynik, I. I. & Batzill, M. An extended defect in graphene as a metallic wire. Nature Nanotechnology 5, (2010). NATURE MATERIALS 13

14 5 Paolo, G. et al. QUANTUM ESPRESSO: a modular and open- source software project for quantum simulations of materials. Journal of Physics: Condensed Matter 21, (2009). 6 J. Kunstmann, T. B., D. Reichman. Unpublished results. 7 Neamen, D. A. Semiconductor physics and Devices. (McGraw- Hill, 2002). 14 NATURE MATERIALS