The MoS2 monolayers grown on a c-cut single crystalline sapphire (Al2O3) substrate investigated in this study are randomly orientated, as shown in Fig. 1(a), which was taken using an optical microscope. Figure 1(a) also defines the crystallographic correlation between MoS2 monolayers and sapphire substrate, in which we assign the stacking angle \(\left(\theta \right)\)=0 for the coherent alignment through MoS2[11\(\stackrel{-}{2}\)0]/Al2O3[11\(\stackrel{-}{2}\)0], as labeled in Fig. 1(a). The MoS2 monolayers with varying \(\theta\) rotating clockwise can be observed on the sapphire substrate, which may be due to the growth mechanisms lacking preferred and coherent nucleation site during the chemical vapor deposition [24–26]. Figure 1(b) demonstrates the correlation of the varying \(\theta\) in reference to the crystallography of the sapphire substrate. It should be noticed that, the period of the varied \(\theta\) indeed shows a 6-fold symmetry based on the crystallographic correlation between MoS2 monolayers and sapphire substrate. Therefore, the resulting stacking patterns are demonstrated in Fig. 1(c), in which the pattern appears to be in a 6-fold periodicity, providing a model system to use spectroscopy studying the effect of stacking coherency between MoS2 monolayers and sapphire substrate.
Figure 2(a) displays the \(\theta\)-dependent Raman spectra for the MoS2/sapphire heterostructure. It shows the characteristics at \({E}_{2g}^{1}\) and \({A}_{1g}\) appear to be no significant difference or drifting although there is minor fluctuation at \({A}_{1g}\), i.e. the spectrum taken at 30 degrees. The wave number difference (\(\varDelta k\)) between \({E}_{2g}^{1}\) and \({A}_{1g}\) are all approximately 20 cm-1, which stands for the fingerprint of the MoS2 monolayer. The \(\theta\)-dependent Raman spectra suggests varying \(\theta\) didn’t modify the structural vibration significantly, however, another scenario can be observed through the \(\theta\)-dependent PL spectra as exhibited in Fig. 2(b). The PL feature mainly reflects the exciton state in MoS2 monolayer, which also serves as a spectroscopic signature of monolayer as a result of the direct band gap. Differing from the Raman spectra, the \(\theta\)-dependent PL spectra show significant 6-fold periodicity. Note that, both Raman and PL spectra taken at \(\theta\)=75, 90, and 105 degrees are arbitrarily selected for reference to verify the periodicity of the \(\theta\)-dependence because those stacking are crystallographically identical as the cases taken at \(\theta\)=45, 30, and 15 deg, respectively. In order to clearly demonstrate the 6-fold periodicity, Fig. 2(c) displays the plots of the exciton energy versus the change of \(\theta\) for MoS2/Al2O3 heterostructure alongside the results taken from the MoS2/SiO2 heterostructure. The former one follows an ideal 6-fold periodicity as expected from the schematic diagram in Fig. 1(c) and the quench of 6-fold periodicity in latter case should be attributed to the amorphous nature of SiO2, giving rise to the absence of crystallographic correlation while stacking. Again, the data of \(\theta\)>60 degrees were selected for arbitrary references because those are crystallographically repeated as demonstrated in Fig. 1(b) and Fig. 1(c).
A systematic investigation to resolve the \(\theta\)-dependence at different positions of MoS2 monolayer on sapphire substrate was performed to examine the site-associated effects on exciton energy and the \(\theta\)-dependence. Figure 3(a) displays the PL spectra taken at the different sites of MoS2 monolayer, as labeled in the inset, and the corresponding PL spectra are shown in the main panel. It has been shown that the exciton energy underwent a red-shift transition while taking the PL spectra from the center, edge, to corner of MoS2 monolayer, standing for the site with different degrees of symmetry degradation. The red-shift transition as indicated in Fig. 3(a) may suggest the reduced exciton energy as a result of the less structural confinement from center\(\to\)edge\(\to\)corner [27–29]. Moreover, the PL intensity drops quickly in response to the site-dependent probe, suggesting the structural symmetry indeed plays an important role of hosting exciton luminescence [30]. Interestingly, while plotting the exciton energy acquired at center and corner as a function of \(\theta\), both cases show a similar 6-fold symmetry, but the variations of exciton energy acquired at the corner features a weaker variation amplitude than the those acquired at the center. The result may suggest the corner of MoS2 monolayers may be still structurally coupled to the sapphire substrate reflected on the 6-fold periodicity although those sites feature significant symmetry breaking, thus leading to the reduced variation on the amplitude of exciton energy versus \(\theta\).
Thus far, the PL characterization has illustrated chromatic tuning of the exciton energy, achieved by manipulating the specific Moiré correlation between MoS2 monolayers and the sapphire substrate. A significant concern has emerged regarding the aging effect on the variation of exciton energy versus θ. In Fig. 4(a), the exciton energy taken at the center of the MoS2 monolayer is plotted as a function of θ at various aging times, revealing a reduction in the 6-fold correlation with increasing aging time. It's important to note that the sapphire/MoS2 samples were maintained in a moisture-proof environment during the aging treatment. Interestingly, after the aging treatment, the exciton energy acquired from all θ migrates towards the energy state as initially obtained at θ = 30 degrees as a minimum throughout the system, suggesting aging does indeed influence the chromatic properties of MoS2 monolayers. Figure 4(b) displays the plots of exciton energy taken at θ = 0 degrees and the amplitude of exciton energy variation versus θ at different aging times. As a result, both the exciton energy and the changes in periodicity amplitude decrease with aging time, suggesting that the destination of the exciton state in MoS2 monolayers is bound towards the state as initially obtained at θ = 30 degrees.