slight deviation of the symmetry of the ADF-STEM intensity in Fig. 10(c) is due to the presence of unintentional residual aberration such as three fold astigmatism A2 in the focused electron probe. Considering this residual aberration in electron optics, quantitative ADF-STEM image was simulated in the lower panel of Fig. 10(c) and compared with the experimental image in the upper panel. Figure 10(e) shows the intensity line profiles extracted along the long sides of the stripes in the experimental and simulated images, both in a high consistency, confirming an Se2-core boundary structure. In others words, neighboring triangular domains share the same line of Se2 columns to form the Se2-core IDBs everywhere [42].
Scanning tunneling spectra from the IDBs and domain center in Fig. 10(f) show distinctive characteristics especially around Fermi energy. The STS from the domain center is almost similar to the density of states (DOS) of a normal semiconductor with a bandgap of ∼2.0 eV, while that of IDBs has a remarkable midgap state at −0.41 eV and another two peaks at −1.8 eV and 0.6 eV. This metallic midgap state around Fermi level is characteristic of the IDB defects. The DFT-calculated DOS of IDB and the domain center both agree well with the experimental STS in the midgap states and bandgap characteristics, except the slight undrestimation of the bandgap.
3.4. Stacking-band structure diversity in bilayer MoSe2
Network-like IDBs will induce fractional lattice translation to the adjacent domains. If two layers with IDBs stack together, then diverse stacking orders will inevitably appear, which occurs exactly in the MBE-grown bilayers [42]. Figure 11(a) shows the atomically resolved ADF-STEM image of a typical MoSe2 bilayer without interlayer rotation. Random size of the non-periodic domains in a relatively large area rules out the possibility of Moiré patterns but confirms that they are stacking-dependent domains. This is quite different from the lattice-mismatch-induced Moiré stacking orders in hetero-bilayers [43].
After careful checking of the triangular bilayer domains, the difference in ADF-STEM imaging of different domains indicates distinctive stacking orders in the bilayer [42]. To specify the detailed stacking structure in each domain, construction of the stacking model and image simulation will be necessary. Starting from the initial high-symmetry AB–0 and AA–0 (Fig. 11(b)) configurations, the upper layer is shifted horizontally (H1, H2) or vertically (V1–V7), both parallel to the fixed bottom layer to yield various types of stacking orders, as shown in Figs. 11(b). The corresponding simulated ADF-STEM images demonstrate clearly the distinctiveness and diversity of these stacking sequences. Note that AB–0 and AA–V3 (Fig. 11(b)) stackings are actually bilayer structures in the well-known 2H and 3R phases, respectively. These simulated ADF-STEM images of each stacking structure act as fingerprints of each stacking sequence, and hence, can be directly compared with the experimental image in Fig. 11(a). Each domain can be assigned with a stacking order when the experimental images match the simulated images. As shown in Fig. 11(a), each domain is marked by triangles in different colors. Each color indicates one type of stacking order with its stacking name marked, as AB–V4, AB–V6, etc. Besides the high-symmetry configuration AB–0 and AA–V3, all the other experimentally observed stackings in low symmetry survive and get stabilized due to the confinement of the IDBs. Through this combination and comparison of the experiment/simulation results, each domain of the large-area bilayer can be unambiguously identified with one of the diverse stacking orders.
Figure 11. Diverse atomic structure of MoSe2 bilayer domains. (a) Experimental HAADF image of a typically continuous and uniform bilayer MoSe2. Those domains marked by triangles in the same color indicate the same stacking order. Scale bar: 2 nm. (b) Atomic model and the simulated ADF-STEM images of diverse bilayer stacking orders. The atomic structures of each domain in (a) are assigned by the comparison of experimental and simulated ADF images. Reproduced from Jin et al. (2017) with permission.
It’s expected that diverse stacking bilayer structures would have different electronic structures, and distinctive electronic density of states near the fermi level. To probe the dependence of electronic structure on the stacking order, scanning tunneling spectroscopy was thus utilized to measure the electronic states from the domain centers. As shown in Fig. 12(a), experimental STS spectra collected from different domains present three types of features: olive spectra with band tail (BT) states; the pronounced peak of valence band splitting into double peaks (DP) with an obvious separation; low-conductance (LC) spectra.
Figure 12. Distinctive electronic structures of the diverse bilayer domains. (a) DFT calculated LDOS of several typical bilayer stacking structures. (b) Experimental STS spectra measured at different domains. The inset is a STM image of the corresponding domains. The valence band edge is dependent on the stacking order. The different valence band DOS should arise from the diverse stacking orders of bilayer domains. (c)–(d) Band structures of the frequently observed stacking orders AB–V4 and AA–V3. Reproduced from Jin et al. (2017) with permission.
Three most common stackings were found in experiments: AB–0, AB–V4, AA–V3, whose electronic structure was calculated by DFT in Fig. 12. The calculated valence band DOS of AB-V4 (black curve) has an obvious double peak feature, and that of AA–V3 shows a band-tail structure and its bandgap get reduced, compared to the normal DOS of AB–0. The experimental STS in olive with band-tail feature can be assigned to the BT category, where the frequently observed AA–V3 is a typical stacking. And AB–V4 could be one possible stacking responsible for the observed “DP” spectra in black in Fig. 12(a). Further calculated band structure of AB–V4 in Fig. 12(c) shows that the VBM at K and the second valence band extreme at Γ with a 130-meV separation result in the double-peak feature of the valence band of AB–V4. While for AA–V3, the VBM was, however, found at Γ, nearly degenerated with the 59-meV-lower second valence band extreme at K. This band extreme crossover results in the band tail state, in AA–V3.
For various bilayer stackings, the relative energy increases linearly with the interlayer distance d, suggesting an attractive interlayer interaction [42]. The smallest interlayer distance d means the highest stability, as proved by the most common AB–0, AA–V3 with small d. The observed band tail state is a fingerprint for smaller-interlayer-distance stacking orders, in STS measurements. DFT-calculated K-Q and Γ-Q gaps increase exponentially with interlayer distance d, while the Γ-Q gap is more sensitive to interlayer distance. This is because the VB at Γ primarily comprises Mo dz2 and Se-pz orbitals and is more sensitive to the interlayer interaction than the VB at K point.