## 3 Results and Discussion  
The sample targeted in this research is illustrated in Figure 1a,b. The bilayer MoS\({}_{2}\) flakes were prepared on the Si wafer covered with 260 nm SiO\({}_{2}\) via an exfoliation process. The flake was exfoliated with pressing the weight as shown in the experimental section. The TFSI molecular treatment was conducted along with the previously reported process; details are the combination of the UV irradiation and immersion into the TFSI acetonitrile solution [31]. Figure 1c,d show PL mapping images for the as-exfoliated and the processed bilayer MoS\({}_{2}\), respectively. The bilayer MoS\({}_{2}\) shows a considerable PL enhancement, more than 100\(\times\) around 1.9 eV, corresponding to a plausible direct band gap nature as seen in monolayers, via the TFSI molecular treatment with UV irradiation. We examined each process for the PL enhancement of the bilayer MoS\({}_{2}\). The UV irradiation process was carried out under an ambient condition, which may generate OH radicals on the surface of MoS\({}_{2}\) (Figure 3). In the previous work, an electronic structure of ML MoS\({}_{2}\) was maintained under UV irradiation, even while some chemical reactions happened on the surface [31,32]. Here, a laterally large (>10 \(\upmu\)m) bilayer MoS\({}_{2}\) was applied to the UV irradiation process for 5 min; as a result, the whole area, regions of interest (ROIs) 1-4 in Figure 3, showed a more direct band gap nature with a single peak around 1.86 eV. The clear signal around 1.64 eV, corresponding to an indirect band gap, was diminished via the UV irradiation. According to the above result, UV irradiation would induce the separation of the top and bottom layers to achieve a ML-like state (Figure 3b). We examined the ML-like sample with UV irradiation by further applying the TFSI treatment (Figure 4). This treatment changed the PL signal dramatically over the whole area (Figure 4b-e). All regions (ROIs 1-4) showed a direct band gap with a single PL signal around 1.88 eV by the TFSI treatment. The factor of the PL enhancement was over 700\(\times\) from the as-exfoliated bilayer flakes. Therefore, the combination of UV irradiation and the TFSI treatment would be useful for modulating the optical property of bilayer MoS\({}_{2}\) to have a strong PL intensity like that of the TFSI-treated ML samples reported previously. The supplemental UV irradiation was applied to the TFSI-treated bilayer MoS\({}_{2}\) but was found not to be so effective (re-UV irradiation for TFSI treated in Figure 4). This indicates that the combination of the first UV irradiation and the TFSI treatment process would achieve saturation of the PL enhancement. In the previous report, the UV irradiation  
Figure 6: (**a**) Optical microscope image of the sample exfoliated without pressing with the weight. (**b**) Raman spectra for the as-exfoliated (original, blue), UV-irradiated (orange), TFSI-treated (green), and re-UV-irradiated (red) bilayer MoS\({}_{2}\). The peak separation between E\({}_{\text{2g}}\) and A\({}_{\text{1g}}\) is about 21.6 cm\({}^{-1}\). (**c**) The plausible situation of the bilayer MoS\({}_{2}\) from the Raman spectra in Figure 6b. This bilayer is a conventional flake. (**d,e**) PL spectra for the bilayer MoS\({}_{2}\) corresponds to Figure 6b; the original is shown in Figure 6d. was applied after the TFSI treatment and was effective in enhancing the PL intensity for ML MoS\({}_{2}\) flakes [31]. We confirmed the same procedure as in the previous report for bilayer MoS\({}_{2}\); a bilayer MoS\({}_{2}\) was treated first with TFSI solution, then by UV irradiation (Figure S1). The TFSI treatment itself changed the bilayer-like nature to a ML-like nature, but the PL intensity was still poor. The subsequent UV irradiation strongly enhanced the PL intensity, and the factor of the enhancement was several hundred times with a single signal around 1.9 eV.