Molecular-beam epitaxy of monolayer MoSe₂: growth characteristics and domain boundary formation

On HOPG and graphene, MoSe₂ growth proceeds over a wide range of growth conditions via the nucleation of 2D islands on the surface. The epitaxial growth mode is layer-by-layer according to the RHEED and STM observations. The RHEED patterns are streaky throughout the deposition process and the STM micrographs reveal the typical terrace-and-step morphology of the surfaces. As an example, figure 1(a) shows the surface of a MoSe₂ film, which is 1.4 MLs thick and deposited on HOPG at 390 °C. Despite the variations in film thickness across the sample due to the >1 ML deposit coverage and the kinetics of MBE, the surface appears atomically smooth, revealing ML high islands or steps as exemplified by the line profile in the inset. The RHEED pattern of the sample (also shown in the inset) is streaky, affirming the flat morphology of the film. Inter-diffraction streak spacing is found to match well with a strain-free MoSe₂, therefore the film is unstrained despite the lattice misfit with the substrate. In other words, the substrate lattice does not provide a constraint for strained MoSe₂ epifilms, a property characteristic of vdW epitaxy [16–18].

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While one might expect the 2D layer-by-layer growth mode of a layered material because it would lead to a diminishing proportion of lateral chemical bonds present at the island edges, such a growth mode for epitaxial MoSe₂ on HOPG (and graphene) is not in full agreement with a recent theoretical prediction of TMD growth on graphene [21]. Instead, the three-dimensional (3D) or Volmer–Weber mode has been suggested for TMD deposition on graphene based on adhesion energy considerations. The stronger adhesion between TMD MLs than that between the TMD and graphene favors the Volmer–Weber growth mode [21]. In the same study, however, it has also been suggested that the 2D mode of growth could be achieved on nitrogen-doped or defected graphene due to the enhanced deposit–substrate interaction as facilitated by the defects. Our observation of the 2D growth mode of epitaxial MoSe₂ on HOPG and graphene might thus indicate either that our substrates were defected (e.g. containing the Stone–Wales defects) or that other factors existed stabilizing the 2D film. We did not introduce nitrogen doping, so the doping effect could not be relevant here. One factor that might have stabilized the 2D growth of MoSe₂ is the kinetics of MBE. As is described in detail in the following text, we find MoSe₂ growth on HOPG proceeds by the nucleation of small islands at the step edges on the substrate surface. This growth process may have changed the character of the deposit–substrate interaction and dominates over the otherwise vdW interaction between the two materials on flat interfaces. In a study by Tenne [22], it was shown that free-standing 2D islands or small clusters of TMDs could be unstable against the formation of nanotubes or fullerene-like structures, by which the lateral chemical bonds at the island edges became saturated or diminished. This is similar to C-nanotube or C60 formation out of graphene sheets. Our observations of the 2D growth mode of MoSe₂ on HOPG/graphene over a wide range of deposition conditions may thus indicate the presence of kinetic factors suppressing 3D nanostructure formation during the MBE of MoSe₂. On the other hand, under certain conditions nanorod features, illustrated in figure 1(b), are indeed observed on the surface of epitaxial MoSe₂, seemingly conforming to the results of Tenne [22]. Nevertheless, we wish to point out that the nanorods in figure 1(b) are substrate-supported rather than free-standing. Furthermore, the chemical identity of the nanorods in figure 1(b) is not yet determined to be MoSe₂ or some other phases. Lowering the temperature of deposition seems to favor nanostructure formation, which is also at odds with the thermodynamic considerations. Further studies are needed to elucidate the origin of such nanostructures.

Returning to the 2D growth of MoSe₂, STM examinations reveal that its growth proceeds via 2D island nucleation at ascending steps of the substrate as exemplified in figure 2(a), depicting the surface of 0.05 ML MoSe₂ deposited on HOPG at 250 °C. The low growth temperature would favor the island nucleation mode of growth over the step-flow mode due to reduced adatom diffusion. However, it is noted in figure 2(a) that the large terraces in between the surface steps remain void of MoSe₂ islands, suggesting the long diffusion length of adatoms even at 250 °C. This may be explained by the weak vdW interaction between the deposit and the substrate. The long diffusion length leads to step-flow growth characteristics where adatoms are captured by the pre-existing steps on the surface rather than aggregate to form MoSe₂ islands on flat terraces. On the other hand, because of the lateral chemical bond at the step edges, adatoms captured by steps would diffuse at slower rates along the steps, making the steps kinetically roughened. By inspecting figure 2(a), however, one notes distinct triangular islands attached to the ascending steps rather than the roughened step edges. Since the C-bonds at the steps of HOPG do not conform to those of MoSe₂, the natural lateral bonding of the two materials for a smooth transition from graphene to MoSe₂ at the steps is not viable. Thus it is likely that the steps on the substrate merely act as heterogeneous nucleation sites facilitating MoSe₂ nucleation and subsequent growth.

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There is an apparent asymmetry in the island population at ascending versus descending steps in figure 2(a), and the nucleation islands appear to heavily populate at ascending steps on the surface (i.e. on the lower terrace of a step rather than on the upper terrace). However, as the deposition continues and the coverage increases, MoSe₂ islands become apparent on the upper terrace as well (see figure 2(b)). Line profile measurements across the islands on both terraces show a height difference corresponding to a graphene step. So we suggest the nucleation of MoSe₂ on the upper terrace is facilitated by the height difference between ML graphene and ML MoSe₂, therefore a new step of the opposite sense is created upon nucleation of the MoSe₂ islands on the lower terrace of a graphene step. In other words, an ascending step changes into a descending one and vice versa upon MoSe₂ nucleation and growth at the step, promoting continuous growth of MoSe₂ on both terraces. This mechanism of growth is schematically illustrated in figure 2(c). Such a growth process obviously results in locally multilayer high films, which is undesirable for obtaining uniform 2D samples. Therefore stepped substrates are less favored for growing high quality 2D crystals of uniform thicknesses.

Another aspect of the morphology in figure 2 is the triangular shape of MoSe₂ islands, reflecting the three-fold symmetry of ML MoSe₂. Such an island shape suggests a dependence of step energy on crystallographic orientation. Only low energy steps are exposed and bound the islands [23]. For ML MoSe₂, the low energy edges may be either Mo- or Se-terminated $\langle 10\bar{1}0\rangle$ steps, which depends also on the possible edge–atom reconstruction and/or chemical saturation [24]. For unsaturated edges without edge–atom reconstruction, Se-terminated ones have a lower energy than that of Mo-terminated steps. Comparing Mo₆Se₂₀ (i.e. Se-edged cluster) and Mo₁₀Se₁₂ (Mo-edged cluster) on graphene by density functional theory calculations, we find an ∼70 meV/atom formation energy gain of the former. It is thus likely that the triangular islands are bounded by the Se-terminating steps, and this is consistent with some previous studies [25]. This consideration might also account for the observed triangular island shape of CVD-grown TMD films [8, 12]. For MBE growth, however, there are complications due to the kinetics of adatom attachment/detachment at steps, diffusion across step corners, etc that may also play a role in determining the island shapes [26, 27].

Next we comment on the epitaxial relation between MoSe₂ and the substrate. As the HOPG substrate is highly textured in the plane parallel to the surface, epitaxial MoSe₂ is similarly textured, preventing us from establishing the exact epitaxial relation, if any, by in situ LEED measurements. Indeed, the LEED patterns taken from such samples usually show a ring feature (figure 3(a)), implying random in-plane rotation domains over the size of the electron beam of the LEED (∼0.2 mm²). On the other hand, as shown in figure 3(b), a selected area (<1 μm²) transmission electron diffraction (TED) pattern obtained using a transmission electron microscope (TEM) (working at 200 keV) clearly indicates crystallography information about the epitaxial relationship between MoSe₂ and graphene. Two sets of highly aligned diffraction patterns (from MoSe₂ and graphite, respectively) are identified, which are labeled by '(1)' and '(2)' in the figure.

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In order to affirm such an aligned epitaxial relation over larger areas of the sample, we have grown a film on a graphene-on-SiC substrate, where the bilayer graphene film has larger domain sizes. One of the LEED patterns of epitaxial MoSe₂ on graphene/SiC is shown in figure 3(c). Clearly, the ring feature of figure 3(a) has broken up into arcs, implying rotation domains of reduced angles (∼20 degrees) over the area of the beam size of the LEED. Notably, these diffraction arcs are aligned with the pattern of the substrate, so setting aside the rotation domains, epitaxial MoSe₂ follows the lattice of graphene, i.e. [0001]_MoSe2||[0001]_graphene and ${{[10\bar{1}0]}_{{\rm MoSe2}}}$||${{[10\bar{1}0]}_{{\rm graphene}}}.$ On the other hand, the six-fold symmetry of the diffraction pattern implies the presence of inversion domains of about equal proportions in the film. The fact that a defined epitaxial relation exists between MoSe₂ and graphene suggests non-negligible deposit–substrate interaction at the heterointerface, which marks another characteristic feature of the vdW epitaxy [16–18].

STM of samples grown on graphene/SiC and on HOPG showed little difference; because the SiC wafers are highly resistive, STM data of such samples are rather limited for a more comprehensive comparison. On the other hand, as HOPG is conductive, it is better suited for STM studies. We nevertheless expect the two substrates, HOPG and graphene-on-SiC, to behave the same in supporting epitaxial MoSe₂ during MBE, as the top surface layer is of the same graphene. Over small areas of the STM measurement (<1 μm²), rotation domains can hardly be detected. In fact, even for samples grown on HOPG, which, according to the LEED, are highly textured, STM images rarely reveal such texturing. This is in agreement with the TED result shown above. The LEED measurements sample much larger areas than STM, so the LEED result can be more representative in revealing the crystallinity of the epifilms. By comparing figures 3(a) and (c), we thus infer that epitaxial MoSe₂ on graphene/SiC is superior to that on HOPG.

Inspection of STM images of the MBE-grown films at energies corresponding to the gap region of MoSe₂ reveal strikingly bright line features intertwined into triangular networks. An example is shown in figure 4 measured at −1.0 eV relative to the Fermi level (due to unintentional doping, the sample has the Fermi level close to the conduction band minimum). Similar networks of these bright lines in STM images had been reported in the early 1990s and attributed to moiré interference patterns or related effects [28, 29]. Our experiments show that such networks exist not only in MoSe₂ on HOPG (graphene) but also on Au(110) substrates [14]. Together with the observation that the density changes with the MBE conditions (see below), we rule out the moiré interference effect. TEM studies of the films establish that the bright lines seen in STM images actually reflect inversion domain boundary (DB) defects, which have given rise to mid-gap electronic states [14]. It is such DB defects that intertwine to form the triangular network. The abundance of DBs, which delineate inversion domains in the film, is consistent with the six-fold symmetry of the LEED and TED patterns as noted earlier. To help to understand the formation process of the DB defects in MBE-grown MoSe₂, we carry out deposition experiments at sub-ML coverages and at different temperatures. Figures 5(a)–(c) shows surfaces of a set of samples of different deposit coverages, and figures 6(a)–(c) compares samples prepared at different temperatures. From figures 5(a)–(c), one makes an interesting observation that the DB defects are not born from the start of MoSe₂ island nucleation. Rather they form and develop only after some critical coverage of the deposit has been grown. At low coverage (figure 5(a)), few DB defect can be found. The island edges show bright STM contrasts because the edge atoms introduce in-gap electronic states contributing to the STM contrasts [25, 30]. As the deposit coverage increases, isolated lines of defects start to appear in the interior of the island (figure 5(b)). Continuing growth leads to more lines of defects being introduced, which become increasingly denser and regular in distribution at the central region, whereas in regions close to the edges of the islands, they remain relatively sparse (figure 5(c)). These line defects do not seem to be caused by coalescence of the nucleation islands. If they were, a more random distribution of the lines would be expected and their density would not show the dramatic dependence with film coverage.

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Formation of the DBs in crystalline films can be energetically costly and their nucleation is usually the response of a film to stress. For epitaxial MoSe₂ on HOPG along the c-axis, the hetero-interface is of weak vdW bonding and can barely sustain large lattice misfit strain. As noted earlier, epitaxial MoSe₂ is strain-free even at the very early stage of deposition. Another source of stress is thermal, which is inevitably introduced during temperature ramping after film growth. We have examined the relevance of thermal stress by varying the ramping rate of the substrate temperature but observed little effect. However, as shown in figures 6(a) and (b), the temperature used during MoSe₂ deposition does affect the defect density—the higher the temperature, the lower the density. Even more dramatic is post-growth annealing, and we find that the DBs may be completely annealed out at high temperatures as exemplified in figure 6(c).

The DB formation in epitaxial MoSe₂ appears kinetic driven. Upon high temperature annealing whereby the sample becomes DB-free, bringing the sample back to the growth temperature does not seem to reintroduce the defects. Annealing under different environments, e.g. in vacuum or in Se over-pressure, shows a noticeable difference in the diminishing rate of defects: they anneal out faster under Se flux than in vacuum. Moreover, as-grown WSe₂ films do not show similar networks of DBs despite similar MBE conditions [31]. These findings may help to identify the reason and mechanism of DB formation in MBE MoSe₂.

Lastly we show that DB defects significantly affect the optical properties of the materials. Because the conductive HOPG substrate effectively quenches the photoluminescence of the sample, and the epifilms are also textured on HOPG (see figure 3), we compare the optical properties of samples grown on graphene/SiC in the following text. While films that have undergone the annealing procedure clearly show direct band-edge PL emission at 800 nm (see figure 7 inset), those without annealing do not show clear band-edge luminescence due to the high density of non-radiative defects in the film. Raman spectroscopy measurements reveal a wavenumber shift of the A_1g, out-of-plane, vibration mode between samples with versus without DB defects. Figure 7 (main panel) compares two spectra from ML MoSe₂ grown on graphene/SiC containing, respectively, (i) high and (ii) low density of DB defects due to annealing or not. In the spectra, the vibrational modes of SiC and epitaxial MoSe₂ are all identified, and the peak at 239.6 cm⁻¹ in (ii) (red) and at 240.6 cm⁻¹ in (i) (black) corresponds to the A_1g mode of MoSe₂. There is an obvious wavenumber shift by ∼1 cm⁻¹, which may reflect a difference of interaction strength at the film–substrate interface. As spectrum (i) is for a sample containing a high density of DB defects and its Raman peak is at a higher frequency, implying enhancement of the hetero-interface interaction, it is likely that the defects contribute to the strengthening of the deposit–substrate interaction.

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