Molecular-beam epitaxy of monolayer and bilayer WSe₂: a scanning tunneling microscopy/spectroscopy study and deduction of exciton binding energy

Figure 1(a) presents an STM image of an as-grown WSe₂ film of nominal thickness of 1.2 MLs. The film is predominantly ML WSe₂, but there is also appreciable coverage of BL domains/islands and holes of exposed substrate due to the kinetics of the MBE process. The terrace-and-step morphology of the surface and the streaky RHEED pattern (see inset) suggest layer-by-layer growth mode of WSe₂ on HOPG resembles that of MoSe₂ growth on the same substrate [12]. However, we note a striking difference between epitaxial WSe₂ and MoSe₂. As reported in an early publication, the MBE-grown MoSe₂ film often contains a high density of the DB defects intertwined into a triangular network [7]. These DB defects manifest in the STM micrographs as bright lines when imaged at the bias conditions, corresponding to the gap region of MoSe₂ (see figure 3(a) below). In epitaxial WSe₂, on the other hand, no such bright line is found. In the atomic-resolution STM image of figure 1(b), one only observes regular moiré patterns due to the lattice misfit between WSe₂ and graphite but no sign of the DB defect. Given the same crystal structure and similar lattice parameters between WSe₂ and MoSe₂, it is somewhat surprising that the two materials behave so differently during MBE growth on HOPG. The WSe₂ film is thus more attractive and advantageous for studying the intrinsic properties of ultrathin TMDs.

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In figure 1(c), we present two differential conductance spectra obtained by the STS measurements on the ML and BL regions of the same sample and at fixed positions far from steps. Both curves reveal a semiconductor property with sizable energy gaps. The Fermi level (0 eV) is found close to the middle of the energy gaps, indicative of low background doping of the film. This also contrasts the MoSe₂ film grown by MBE, which is often electron-doped, and the Fermi level is close to the conduction band edge (refer to figure 3(b)). Comparing the two spectra in figure 1(c), one clearly notes a gap-narrowing effect upon the film thickness increase from ML to BL.

We follow the method of references [8, 10] (see the supplementary materials) to locate the band edges from the dI/dV spectra of figure 1(c) and thus determine the energy bandgaps of ML and BL WSe₂. They are 2.59 ± 0.07 eV and 1.83 ± 0.10 eV for ML and BL WSe₂, respectively. The value of 2.59 eV for ML WSe₂ is consistent with an early reported result [13], but as suggested in a recent study, the experimental spectral edge may not reflect the true electronic band edges of ML WSe₂, and consequently the 'apparent' energy gap is usually overestimated in the STS spectrum by as much as the spin-split Δ_SO at the K point of the Brillouin zone (BZ) [8, 14]. For ML WSe₂, the Δ_SO is as high as 0.4 eV [8, 14]. Figures 1(d) and (e) present the calculated energy bands by the density functional theory (DFT) for ML and BL WSe₂, respectively, taking into account the spin–orbit coupling. The fact that the valence states at K are mainly of the d_x2−y2 and d_xy components of the metal atoms and that they have large in-plane momenta (k_||) makes them less sensitive to STS measurements [8, 15]. The experimental spectral edge below Fermi energy does not necessarily reflect the K_v state of the valence band maximum (VBM) (see figure 1(d)) [8, 15], and, according to Zhang et al [8], the first peak close to the spectral edge of the valance band coincides with the lower spin-split band K₂, which is at −1.61 eV in figure 1(c) (black). Given the 0.4 eV spin-splitting, the VBM is thus more likely located at −1.21 eV, as marked in the figure. For the conduction band, there is an ambiguity where the conduction band minimum (CBM) lies—the K or the Q valley—and the latter is approximately midway between Γ and K (refer to figure 1(d)) [14]. Recent STS experiment [8] suggested the Q-valley to be 0.08 eV below K_c. In any case, as the Q_c-state contains much of the p-orbital component of the chalcogen atoms and has a lower k_|| than the K_c-state, the STS spectral edge above the Fermi energy likely corresponds to the Q_c-state as marked, and it is found to be at +1.18 eV. Therefore, we derive the indirect bandgap (i.e., Q_c–K_v) of ML WSe₂ to be about 2.39 eV.

For BL WSe₂, the CBM is affirmed at Q_c, which can be found at +0.99 eV in figure 1(c) (green). For the VBM, the energy difference between Γ_v and K_v (refer to figure 1(e)) is small. But as the STS measurement is more sensitive to the Γ-states, the spectral edge at −0.84 eV likely reflects the Γ_v-state, and we derive an energy gap of BL WSe₂ to be 1.83 ± 0.10 eV, which corresponds to the indirect gap between Q_c and Γ_v.

Because the two spectra in figure 1(c) are from two close-by positions of the same sample but of different thickness domains, it is reasonable to assume that the ML and BL share the same Fermi level. In figure 1(c), one notes the different magnitudes of the band-edge energy shifts of the valence- versus conduction-band edges: 0.37 eV for the VBM and 0.19 eV for the CBM, which give rise to an overall bandgap narrowing of 0.56 eV in BL WSe₂ over that of ML. While the 0.19 eV shift of the CBM is for the same Q_c bands, which may reflect the inter-layer coupling of the p-orbital electrons in BL WSe₂, the 0.37 eV energy shift of the VBM may, however, be thought of as the change of the VBM from the K valley in ML WSe₂ to Γ in BL film. On the other hand, we also note a band-bending effect at the boundary (i.e., step) of ML and BL domains. The latter may cause an additional shift of the band-edges, as illustrated in figure 2(a) and discussed below.

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Band-bending close to the boundary of ML and BL domains is evidenced by the STS spectra taken at varying distances from a step, as shown in figures 2(b) and (c) for the ML and BL regions, respectively. Upon approaching the step, the spectra show a blue-shift for both domains, as illustrated in figure 2(a). The magnitudes of the upward shift (i.e., the band-bending) can be different in ML versus BL domains. This will result in an 'apparent' electronic band misalignment even far from the step where the spectra in figure 1(c) were measured.

The upward band-bending at both sides of the junction is unusual and interesting. We attribute it to the Fermi level pinning by the in-gap states associated with the edge atoms at the step. It was demonstrated that edge atoms of ML MoS₂ clusters could induce in-gap states close to the VBM [16]. If the bulk of the film (i.e., away from the step) is nearly intrinsic, i.e., the Fermi level is in the middle of the bandgap, as suggested by figure 1(c), then the edge atoms at the junction will induce an upward band-bending, resulting in the band diagram of figure 2(a). This type of band-bending implies depletion of conduction electrons but accumulation of holes at the step, which may lead to some interesting electronic and optical effects.

We now make a comparison with the STS results from ML and BL MoSe₂. Figure 3(a) shows an as-grown MoSe₂ film of 1.4 MLs nominal coverage. As pointed out earlier, such films contain networks of the DB defects in both ML and BL domains. The conductance spectra presented in figure 3(b) were taken from points away from both steps and the DB defects in order to reveal the intrinsic properties of MoSe₂ layers. Following the same procedure, we derive the energy gaps of ML and BL MoSe₂ to be 2.25 ± 0.05 eV and 1.72 ± 0.05 eV, respectively, from the STS spectra. Unlike WSe₂, there is no ambiguity about the CBM for ML MoSe₂, which is in the K valley. The valence bands at K are spin-split by ∼0.18 eV [17]. Given that the STS does not necessarily reveal the band edges at K, the measured gap of 2.25 eV may represent an upper bound of the true gap of ML MoSe₂. As for BL MoSe₂, the VBM is known to be shifted to Γ_v, while the CBM is at Q_c. Both are sensitive to STS measurements, so the STS-measured gap of 1.72 eV more likely reflects the true indirect gap (Q_c–Γ_v) of BL MoSe₂. Finally, similar to WSe₂, both the conduction and valence band edges are seen shifted upon going from the ML to the BL of the sample.

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Having determined the electronic bandgaps by the STS of ML and BL WSe₂ and MoSe₂ in the above, we estimate exciton binding energies in these materials by comparing them with the PL results of the same materials. Indeed, giant excitonic effect in ultrathin TMDs, originating from enhanced Coulomb interaction between electrons and holes due to spatial confinement and reduced dielectric screening, is one of the remarkable properties of the 2D systems, which are attracting extensive theoretical and experimental attention lately [10, 14, 18–27]. The reported size of exciton binding energy, a key quantity describing the strength of excitonic effects, has not been very consistent, ranging from ∼300 meV to about 1.0 eV for ML TMDs [10, 14, 18–27]. Despite such variations, they represent an order of magnitude increase over that in the bulk [28] and in conventional 2D semiconductor quantum wells [29].

It is unfortunate that the PL measurements of the same MBE samples studied by the STS above are not successful. No band-edge emission was detected, and it was likely due to the quenching effect by the highly conductive HOPG substrate. We thus performed the PL experiments on exfoliated samples instead. Although non-ideal, the results still provide evidence of large exciton binding energies of the direct emissions in ML WSe₂ and MoSe₂ as well as reduced exciton binding energies in BL films for the indirect exciton emissions.

Figures 4(a)–(d) present the PL spectra for both MoSe₂ (a, b) and WSe₂ (c, d) ML and BL samples. Because the luminescence intensities of the ML samples are around one order of magnitude higher than the BL counterparts, we have shown the normalized PL intensities in all plots for clarity. Comparing figures 4(a) and (b), we find that the normalized PL spectra from MoSe₂ are almost identical for the ML and BL films in both the emission peak position and the intensity ratio. The only noticeable difference is the intensity shoulder, seen in figure 4(b) around 1.6 eV, which can be attributed to the indirect exciton emission, according to its temperature-dependent behavior, as elaborated in the supplementary materials. The strong PL peaks at 1.657 eV and 1.629 eV are the direct exciton and trion emissions, respectively [17]. As ML MoSe₂ has an energy bandgap of 2.25 eV, one deduces that the exciton binding energy in ML MoSe₂ is about 0.59 eV, which likewise represents an upper bound due to the overestimate of the bandgap by STS. For BL MoSe₂, the STS-measured gap (1.72 eV) reflects the indirect gap between Q_c and Γ_v, while the dominant exciton emission (1.657 eV) is from the direct emission at K valley. So a simple subtraction of the two energies is not very meaningful. As noted earlier, the weak intensity shoulder at about 1.6 eV in figure 4(b) reflects the indirect exciton emission. By multiple peak fitting of the PL spectrum, we locate the indirect exciton emission peak at 1.602 eV, which we attribute to Q_c–K_v emission by consideration of the second-order Moller–Plesset perturbation [29]. The local minimum in the conduction band at Γ is much higher than that at K (see figure 1(e)). According to the Moller–Plesset perturbation theory [30], phonon-assisted indirect emission Q_c-K_v would overwhelm that of Q_c–Γ_v. By noting that the energy gap between Q_c and K_v is ∼1.81 eV, one deduces that the binding energy of indirect exciton in BL MoSe₂ is about 0.21 eV.

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For WSe₂, our PL experiments have revealed complications, showing some unknown peaks when measured at 10 K (see supplementary materials). These peaks are likely related to defects or traps in the sample, and their presence hinders accurate assignments of exciton emission energies. On the other hand, we have found the PL spectra are clearer at lifted temperatures. The data measured at 77 K are used for extracting the exciton binding energies in WSe₂, as shown in figures 4(c) and (d). For ML sample (figure 4(c)), the exciton and trion emissions are identified at 1.735 and 1.703 eV, respectively. By comparing with the STS-measured bandgap at the same temperature (2.39 eV), one deduces the exciton binding energy of 0.72 eV. For BL WSe₂, we do not observe trion emission but a broad peak at about 1.56 eV (figure 4(d)). The broad peak vanishes at high temperatures (e.g., 180 K). So this peak is again likely related to defects. The PL evolution as a function of temperature (10–300 K) and the multi-peak fitting of the spectrum lead to the direct and indirect exciton emission peaks at 1.694 and 1.605 eV at 77 K, respectively. As we only know the indirect bandgap of BL WSe₂ from the STS measurements (1.83 eV), noting further that there is a small energy difference between Γ_v and K_v, we deduce the indirect exciton binding energy in BL WSe₂ to be about 0.23 eV. The reduced exciton binding energy in BL TMD is the result of the indirect gap, where the electron and holes do not share the same crystal momentum. The significant difference of the exciton binding energy between ML and BL TMD thus reflects the band-edge shift. Unfortunately, due to the ambiguity of the direct gap (K valley) in the STS measurement, we cannot estimate the direct-gap exciton binding energy of BL.

Table 1 summarizes the deduced exciton binding energies for both ML and BL WSe₂ and MoSe₂. We note that the binding energy of 0.59 eV for ML MoSe₂ is in reasonable agreement with that found in ML MoSe₂ grown on graphene/SiC (0.55 eV) [10], while that of ML WSe₂ (0.72 eV) appears consistent with the previously reported value of 0.79 eV in reference [24] and 0.6 ± 0.2 eV in [25]. For BL TMD films, the exciton binding energies become smaller, but they are of the indirect excition emissions as compared to the direct emission in ML films.