Graphite edge controlled registration of monolayer MoS 2 crystal orientation

Transition metal dichalcogenides such as the semiconductor MoS2 are a class of two-dimensional crystals. The surface morphology and quality of MoS2 grown by chemical vapor deposition are examined using atomic force and scanning tunneling microscopy techniques. By analyzing the moir e patterns from several triangular MoS2 islands, we find that there exist at least five different superstructures and that the relative rotational angles between the MoS2 adlayer and graphite substrate lattices are typically less than 3 . We conclude that since MoS2 grows at graphite stepedges, it is the edge structure which controls the orientation of the islands, with those growing from zig-zag (or armchair) edges tending to orient with one lattice vector parallel (perpendicular) to the step-edge. VC 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License. [http://dx.doi.org/10.1063/1.4919923]

Molybdenum disulfide (MoS 2 ), a layered semiconductor whose layers are weakly bound by the van der Waals force, [1][2][3][4] has a great potential for application in electronic devices.6][7][8][9] Such heterostructures offer the possibility to create devices with new functionalities or better performance in electronic logic and memory devices, [9][10][11] and also offer great potential in the hydrogen evolution reaction. 12Graphene/MoS 2 heterostructures have also been adopted to demonstrate an extremely high photosensitivity and gain 13 as well as the ultrasensitive detection of DNA hybridization. 14Hence, the study of the interfaces between MoS 2 and graphene (or graphite) is critically important and may provide useful hints for various applications. 6,15Shi et al. have recently reported the formation of MoS 2 flakes on the graphene surface via thermal decomposition of ammonium thiomolybdate. 16Although there is a large lattice mismatch between the MoS 2 and the graphene structure, graphene can serve as an epitaxial substrate for MoS 2 .The results encourage the fundamental exploration of the interaction between MoS 2 and hexagonal graphene or graphite.
In this work, we perform atomic force microscopy (AFM) and scanning tunneling microscopy (STM) measurements on sub-monolayer chemical vapor deposition (CVD) grown MoS 2 on a substrate of highly oriented pyrolytic graphite (HOPG). 17,18The CVD process, as opposed to solution transfer used in previous reports, can prevent contaminations such as trapped water at the interface. 19MoS 2 grown using the CVD method has previously been investigated using STM and photoluminescence techniques, 20 but the detailed atomic scale structure at the CVD MoS 2 /HOPG interface has not yet been elucidated.We find that the triangular islands are atomically clean and defect-free, and that clear moir e patterns can be observed, which in general arise due to a lattice mismatch or rotational mis-alignment between a weakly interacting adlayer and substrate. 21By analyzing the atomic lattice and moir e pattern, the stacking orientation between the MoS 2 adlayer and the HOPG substrate can be obtained.We find that there exist at least five possible orientations of MoS 2 islands with respect to the HOPG substrate lattice.An investigation of the superstructure dependent surface energy using ab initio calculations indicates that inter-layer interactions are not sufficient to impose such a constraint on the MoS 2 islands' lattice orientation.However, we find that the MoS 2 islands show a preference for forming with a small relative angle of rotation with respect to the substrate, with angles above a few degrees found to be rare.As ab initio calculations indicate that the difference in surface energy for different orientations is insufficient to explain this tendency, we instead construct a simple model attributing it to the type of graphite edge (zigzag or armchair) at which islands nucleate.These findings offer a microscopic explanation for the apparently ordered orientations of micron sized MoS 2 islands as observed in AFM images.The micrometer-scale AFM morphology of submonolayer MoS 2 on HOPG is shown in Fig. 1.The HOPG substrate's step-terrace morphology is overlaid by triangular MoS 2 thin film islands.Most of these triangles form across an HOPG step, or in contact with the step at one of their edges.Also of interest is the ordered orientation of the islands.Toward the left hand side of Fig. 1(a), the majority of islands are aligned roughly with one corner pointing along the step edge, and one side perpendicular to it.Fig. 1(b) shows MoS 2 islands arranged on a pair of HOPG step edges in another sample location, with the profile taken along the white line indicating a single layer height of around 0.6 nm.Here, it is seen that the islands tend to align with one side against the HOPG edge, and one corner pointing at a nearperpendicular angle to it.This suggests that the apparent order is determined by detailed properties of the substrate, such as the relative orientation between the HOPG edges and surrounding surface lattice, which vary between different regions, but which provide common conditions controlling the growth orientation of separate islands in close proximity.
Fig. 2(a) shows a high resolution STM image taken on an MoS 2 island, using V bias ¼ À1 V.The hexagonal surface lattice corresponds to the outermost layer of S atoms of the MoS 2 monolayer.As well as the periodicity of the atomic lattice, a hexagonal moir e pattern is also observed.Fig. 2(b) shows the STM image scanned in the same region as Fig. 2(a), but with V bias ¼ À0.1 V, within the band gap of MoS 2 , and a current set-point of 50 nA.Interestingly, a different surface lattice is now seen, with a lattice length of 0.246 nm, 17 consistent with the lattice constant of graphite. 21his difference in apparent morphology is attributed to a change in the source of electrons tunneling to the STM tip.A bias voltage of V bias ¼ À1 V draws a tunnel current from the MoS 2 valence band, whereas a bias of V bias ¼ À0.1 V, within semiconductor band gap, should yield almost no contribution from the MoS 2 .Instead, the STM tip descends to probe metallic HOPG bands in order to satisfy the tunneling current set-point, while the MoS 2 layer is effectively electronically transparent at this energy.Tunneling spectra acquired on the MoS 2 island are shown in the supplementary material. 17ecause the HOPG provides the majority of the tunnel current in the latter case, the apparent morphology in the constant current image corresponds to that of the HOPG, rather than the MoS 2 adlayer.In this way, the atomic lattice of the substrate can be observed directly rather than by inference based on measurements of nearby regions of bare substrate.This powerful technique could in principle be generalized to many heterostructure systems in which a thin semiconducting film overlays a metallic substrate or even a semiconducting substrate, provided there is a suitable mis-alignment of band edges between the substrate and adlayer.
Instead of the apparent periodicity of the moir e pattern, we identify a larger unit cell which more correctly characterizes the surface superstructure. 17In the case of the moir e pattern shown in Fig. 2, we describe the superstructure with unit cells containing four moir e peaks, though in general the proper superstructure unit cell may contain any integer number of moir e peaks.Fig. 2(c) shows the schematic diagram of the side view projected along the lattice vectors of this new unit cell (indicated by the black arrows in Figs.2(a) and 2(b)).The lattice constant of MoS 2 in Fig. 2(a) is measured to be 0.315 6 0.001 nm, and in Fig. 2(b) the HOPG lattice parameter is 0.246 nm.The suitable superstructure for this system is thus (0.315 6 0.001 nm) Â 7 ¼ 2.205 6 0.007 nm, which matches 0.246 nm Â 9 ¼ 2.214 nm, over which distance the MoS 2 and HOPG lattices fall out of registry and then back into registry with each other.
In general, moir e superstructures can be formed either by a lattice mismatch between two lattices whose lattice vectors are aligned, by a relative rotation between two layers with equal lattice parameters, or by some combination of these two effects.The MoS 2 island shown in Fig. 2 represents the former case, in which there is no relative rotation, and the pattern arises purely from the fixed lattice mismatch.The superstructure is characterized as R(49/81), meaning the superstructure lattice parameters are ffiffiffiffiffi 49 p times the MoS 2 lattice constant, and ffiffiffiffiffi 81 p times the HOPG lattice constant.In general, however, lattice rotation in MoS 2 islands is also possible, and controls the periodicity of the resulting moir e superstructure.As moir e periodicity varies strongly with inter-lattice angle, even a narrow distribution of angles leads to a broad distribution of Bragg peaks, which is unlikely to be resolved using an area-averaging technique such as Low-Energy Electron Diffraction (LEED).In order to investigate the distribution of relative rotation between the MoS 2 adlayer island and the HOPG substrate, we perform a survey of MoS 2 islands by STM.Various moir e patterns are observed in a collection of high-resolution STM images and classified according to the scheme outlined above and demonstrated in Fig. 2.
Although the superstructure lattice vectors are not parallel with those of the atomic lattice, the periodicity can still be interpreted using the basis expansion of the unit cell vectors of MoS 2 or HOPG.For Fig. 3(a), beyond the moir e pattern period, a repeating superstructure can be found and labeled as R(37/61).The superstructure periodicity is characterized by a unit cell composed of 3i þ 4j or equivalently 4I þ 5J, where the unit-vectors ði; jÞ are the lattice vectors of MoS 2 and ðI; JÞ are those of HOPG.From this information, even without observation of the substrate lattice, we can retrieve information about the orientation of the underlying layer and obtain the relative rotational angle h by using trigonometry.Here, the angle h between the two lattices is $1 .Using the same concept, the superstructures observed in Figs.3(b)-3(d) can be labeled as R(43/73), R(13/21), and R(7/12), respectively.The corresponding relative angles h are 2 ; 3 ; and 11 , respectively.The angles h in these cases were confirmed by measuring the nearby bare HOPG surface.The lattice constants of these five cases are all in the range of 0.315 6 0.002 nm.The details of the atomic structure and the relative rotational angle analysis are collected in the supplementary material. 17n order to elucidate the occurrence of different moir e patterns of MoS 2 on HOPG discovered using STM, we perform a theoretical investigation of the binding energies between the MoS 2 and graphene.Since the strain energy of the MoS 2 layer is known to be smaller than that of graphene, 22 we use a supercell approach to model the system with two planar lattice unit vectors based on the graphene experimental lattice constant (0.2464 nm).The vacuum spacing, used to avoid the spurious interaction among neighboring cells, is 1.5 nm.Calculations were performed in the framework of density functional theory (DFT) 23,24 using the local density approximation (LDA). 25Fig. 4 lists the binding energies (per primitive cell of graphene) of five different superstructures R(n/m) observed in STM versus the lattice constant of the strained MoS 2 layer.The five binding energies show no significant variation within 2 meV.This indicates that the constraint on the orientations of MoS 2 islands does not originate chiefly from inter-layer interactions, and that the explanation for such a constraint must be sought elsewhere.
The atomic resolution STM images and the superstructure analysis offer some explanation as to why the MoS 2 islands have preferred orientations as shown in the AFM image in Fig. 1(a).Besides the five cases shown in Figs. 2   and 3, we find that none of the twelve moir e patterns observed in our experiments correspond to angles greater than 11 , and that for most of them, the angle h is smaller than 3 .For MoS 2 films prepared by transfer printing, we might expect a random distribution of rotations h (between 0 and a maximum of 30 ).However, for CVD grown MoS 2 studied in this work, a small angle h may be enforced by the conditions in the early stages of nucleation and growth of each island.As islands typically form at the edges of an HOPG terrace, we must consider the type of HOPG edge (typically characterized as either a "zig-zag" or "armchair" edge) from which the MoS 2 island grows.Fig. 5 shows schematic representations of MoS 2 islands extending from zigzag and armchair edges.Since a zig-zag edge is necessarily parallel with an HOPG lattice vector, in order that the lattice vectors of MoS 2 maintain a small angle h with respect to the HOPG lattice vectors, one of the MoS 2 lattice vectors in the MoS 2 island growing from a zig-zag edge should remain parallel with the HOPG edge.On the other hand, an armchair edge has an angle of 30 with the HOPG lattice vectors.AFM images presented in Fig. 1, we can now infer that the HOPG terraces shown in Fig. 1(a) likely have armchair edges, while those in Fig. 1(b) likely have zig-zag edges.In other words, the orientation of the MoS 2 on HOPG can be used to characterize the edge structure (zig-zag or armchair) of the top graphene layer in HOPG.
In conclusion, the atomically flat MoS 2 surfaces are clean, with a low defect density, and have a typical scale of several micrometers.Moir e patterns are observed due to the lattice mismatch and rotational mis-alignment with the HOPG substrate.Interestingly, imaging of the substrate directly below the MoS 2 layer is shown to be possible, by tuning the tip voltage into the MoS 2 band gap and probing through it to the metallic substrate below.Analyzing moir e patterns in a collection of STM images, we find that there exist at least five different superstructures, and the rotation between the MoS 2 and HOPG lattices tends to have a small value, typically less than 3 .This tendency is consistent with the observed preferred direction of MoS 2 islands as observed on a micrometer scale in our AFM data.Our ab-initio calculations indicate that modulation of interlayer interactions between the MoS 2 layer and the graphite substrate are not sufficient to provide the necessary constraint on the orientation of the MoS 2 islands.However, we speculate that the type of graphite step-edge from which the MoS 2 island nucleates and grows predominantly controls the island's lattice orientation.The MoS 2 triangle aligns to the graphite step edge depending on the structure (arm chair or zigzag) of the edge of the uppermost graphene layer.MoS 2 islands growing from zig-zag (or armchair) edges tend to orient with one lattice vector parallel (perpendicular) to the step-edge.

FIG. 1 .
FIG. 1. AFM morphology of CVD-grown islands of MoS 2 deposited on an HOPG surface.(a)70 Â 70 lm 2 and (b) 30 Â 30 lm 2 , at another region of the sample.The inset shows the line profile taken along the white line in (b).

FIG. 2 .
FIG. 2. STM atomic resolution images taken on an MoS 2 island.(a) 4.3 Â 4.3 nm 2 , V bias ¼ À1 V, and I set ¼ 10 nA.The lattice constant measured is 0.315 6 0.001 nm.(b) 4.3 Â 4.3 nm 2 , V bias ¼ À0:1 V, and I set ¼ 50 nA.An atomic lattice with a lattice constant of 0.246 nm is now seen.The black arrows label the superstructure period.(c) A schematic diagram shows the side view projected along the superstructure lattice vector of length 7 times the MoS 2 lattice vector and 9 times that of HOPG.