grains and grain boundaries in highly crystalline ... · amorphous carbon ... non-radiative...

Grains and grain boundaries in highly-crystalline monolayer molybdenum

disulfide

Supplementary Figure S1: Commonly-observed shapes in MoS2 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.

Grains and grain boundaries in highly crystalline monolayer molybdenum disulphide

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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 MoS2 crystals

can grow together to form continuous monolayer sheets (bottom right). The

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gradients in nucleation density and grain size reflect the substrate proximity to the

solid MoO3 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.




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Supplementary Figure S3: Raman spectra and mapping

a) Raman spectra showing the E2g1 and A1g vibrational modes1 for monolayer (red

curve) and bilayer (blue curve) MoS2 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 E2g1 mode. and c)

represents the A1g 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.





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 MoS2 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).





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 ka or kb 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.





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 MoS2 confirms the spatial

localization of mid-‐gap states. c) The energy-‐resolved density of states for pristine

MoS2 (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.





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 0.025 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 MoS2 samples on oxide layers, after accounting for

the instrument response function, yield nearly identical time constants of

τexfoliated=44 ps, and τCVD=42 ps. The measured emission decay found to varied

considerably from sample to sample for both the exfoliated and CVD grown





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 MoS2 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).





Supplementary Methods:

Electron Diffraction Simulation:

We calculated the diffraction pattern for a monolayer of MoS2 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 : ka={(-‐

1100), (10-‐10), (0-‐110)} and kb= -ka. Our bloch-‐wave simulations show that the

~10% higher intensity ka 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 MoS2 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 30-‐70 µm. These classifications are important for understanding





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 package5. 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 0.001 a.u.

Pristine MoS2 (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 structure6.

Because the direction of the experimentally observed 8-‐4-‐4 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





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 recombination7. 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.





The electrical measurements in this paper yielded an electron mobility of µe = 3

cm2V-‐1s-‐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 cm2s-‐1. Since the electron and hole masses are similar, we assume that the

exciton diffusivity is half of the electron diffusivity, i.e., Dexc = 4 x 10-‐2 cm2s-‐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, 2695-‐2700.

2 Huang, P. Y. et al. Grains and grain boundaries in single-‐layer graphene atomic patchwork quilts. Nature 469, 389-‐392 (2011).

3 Kim, K. et al. Grain Boundary Mapping in Polycrystalline Graphene. ACS Nano 5, 2142-‐2146 (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, 326-‐329 (2010).





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, 395502 (2009).

6 J. Kunstmann, T. B., D. Reichman. Unpublished results. 7 Neamen, D. A. Semiconductor physics and Devices. (McGraw-‐Hill, 2002).





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