Defects in Functional Materials. Группа авторов

7(h), the migrating Mo lattice atom neighboring the Mo vacancy is highlighted in blue and purple, with arrows indicating the distance and direction of the next hopping. Again, in the vacancy hopping, the defect migration still obeys the random walk behavior without directional preference, typical of the Brownian motion of particles. Also, the Mo vacancy hopping only occurs within the sublattice of Mo and would never enter the S sublattice. Consistent with the DFT calculation, statistical analysis confirms the ground-state V_Mo and metastable (Figs. 8(a) and 8(b), which suggest us a most likely kinetic pathway for vacancy migration.

      As shown in Figs. 8(c) and 8(d), the DFT-calculated energetics in the V_Mo → →V_Mo pathway give an initial migration barrier of 2.9 eV, which is much higher than the simple surface migration of Mo adatom. This contrasting energy barrier is easy to understand since the migration of Mo atom in the vacancy migration case is confined within the central Mo atomic plane of the sandwiched trilayers. Fewer degrees of freedom in the confined space and the breaking and reorganization of Mo–S bonds in the vacancy migration would account for its high energy barrier, compared with the simple adatom migration. The presence of only one metastable state also reflects the decreased degree of freedom in the in-plane vacancy diffusion, since more metastable states appear in the adatom migration [31].

      Figure 8. States of vacancy and their evolution. (a) and (b) Statistical counts and dwell time of vacancies and their metastable states during the migration of an Mo vacancy. (c) DFT-calculated migration pathway of Mo vacancy. The dynamic process is shown by the inset atomic models with arrows illustrating the migration pathway of the neighboring Mo atom. (d) Detailed atomic dynamics of Mo vacancy migration with top-view and side-view, respectively. Note the V_Mo → → V_Mo transition in c is symmetric: hence, only the first half process of vacancy migration (right red arrow in (c)) is drawn in detail in (d). Reproduced from Jin et al. (2017) with permission.

      

      Such a high energy barrier of 2.9 eV also indicates that the vacancy migration must be induced by the beam–atom scattering interaction, since this order of energy barrier is not accessible by thermal activation at room temperature. Hence, the observed vacancy migration is a process driven by the electron beam which transfers enough energy to excite the target atom/defect into its metastable states.

       3.3. Grain/domain boundaries in MBE-grown MoSe2

      Domain/grain boundaries are very common defects in polycrystalline materials, playing a dominating role in their mechanical and electric properties. Xie et al. found that ordered grain boundaries existed quite commonly in the atomically thin transition metal dichalcogenides (TMDs) synthesized by molecular beam epitaxy (MBE) [33–40]. These defects are recently characterized in atomic resolution by STM and ADF-STEM, named as inversion domain boundary (IDB) or mirror twin boundary. They emerge in the matrix of the as-grown monolayer MoS₂ and MoSe₂ and link one with another in a triangular network and run along the zigzag directions. Figure 9(a) shows an STM image of the IDB-decorated MoSe₂ surface, while the close-up image of Fig. 9(b) reveals some fine details where each IDB defect manifests by two closely spaced mirror-symmetric lines with intensity modulations of period ∼1 nm. From the STS measurements (see Fig. 10(f)), one notes that these IDBs introduce mid-gap states at the Fermi level; thus, they act as metallic channels, where charge density wave transition may occur at a low temperature [33, 42], and thus lead to the intensity modulations. Another cause of the modulations has been suggested to reflect the quantum confinement effect of the metallic states or the Tomonaga-Luttinger liquid [33–35].

      Figure 9. (a) STM image (size: 50 × 50 nm², bias: −1V) of an as-grown MoSe₂ on HOPG. (b) A close-up STM image (size: 13 × 13 nm², bias: −1.46V) revealing the twin lines associated with each defect and the intensity undulations along the lines. Reproduced from H.J. Liu et al. (2014) with permission.

      Figure 10(a) shows the atomically resolved ADF-STEM imaging of monolayer MoSe₂ grown by MBE, where Se2 columns are brighter than the Mo lattices [42]. Its fast Fourier transform (FFT, Fig. 10(a) inset) presents abnormally sharp lines connecting the first-order diffraction spot, indicating the existence of some ultranarrow and long line defects emerging in the monolayer MoSe₂. And also, these line defects have a specific directional distribution rather than in random directions. These line defects are actually IDBs, highlighted in blue (Fig. 10(b)) among those golden-colored triangular domains. Nanostripe-like IDBs are connecting with each other in a network form. Figure 10(c) provides a closer look at the atomic resolution ADF-STEM image of an IDB defect, where obvious four-membered rings are arranged in the zigzag direction and both domains are in a mirror symmetry in structure, as shown in Fig. 10(d). This DFT-relaxed IDB structure shows significant reorganization of Mo–Se bond lengths, which enlarges the horizontal Se–Se distance from 5.67 Å (d₀) to 6.16 Å (d₁). Then each IDB induces an uncommon lateral shift of 0.49 Å to the original Se–Se period of 5.67 Å, a fractional lattice translation, giving rise to diverse stacking orders if two such IDB-nested monolayers stack onto each other.

      Figure 10. Inversion domain boundaries in MBE-grown monolayer MoSe₂. (a) Atomically resolved ADF–STEM image of monolayer MoSe₂. The inset FFT shows the quasi-periodicity of the ultra-narrow and long nanostructures. Scale bar: 2 nm. (b) False colored domains and boundaries. These dense inversion domain boundaries connect with each other like a wagon wheel. Scale bar: 2 nm. (c) Experimental and simulated ADF-STEM images of the boundary. Scale bar: 0.5 nm. (d) DFT relaxed atomic model of the boundary where orange balls represent Se atoms and cyan ones represent Mo atoms. (e) ADF-STEM intensity profiles along the long sides of the rectangular stripes marked in (c). (f) DFT-calculated DOS and experimental STS spectra from the domain center and the boundary. The calculated DOS were from boundary or domain Mo atoms highlighted in blue and red in (d), respectively, since Se atoms make negligible contribution to the DOS around the pristine bandgap. Reproduced from