## 3 Results and Discussion
### Chemical Analyses by Nano-Auger Electron Spectroscopy  
Although the variation in optical properties of ML-MoS\({}_{2}\) by the FLI process has been well-studied previously, often in terms of irradiation time, chemical analysis was usually missing or not in detail enough to correlate optical properties with defect states [32; 36; 37; 38]. In this work, on the same locally irradiated ML-MoS\({}_{2}\) sample, sub-nanoscale chemical analyses were conducted with the use of the n-AES technique. The n-AES spectra were measured successively by moving the focused electron beam along the white dashed line in Figure 3c from the origin 0 to the spot of \(d=\) ~6.41 \(\upmu\)m with the interval of ~0.53 \(\upmu\)m across the irradiated region (Figure S1). Figure 4a includes a set of representative n-AES spectra in the derivative form of \(E(dN(E)/dE)\) vs. \(E\), where \(E\) is the kinetic energy of detected Auger electrons, as designated previously, and \(N\) is the number of detected Auger electrons dependent on \(E\), respectively. The strong peaks are related to the S LMM Auger transitions, while the two other peaks originated with the Mo MNN Auger transitions [45]. Since the peak-to-peak intensity, \(I_{\text{pp}}\) (i.e., the difference between the maximum point of the up peak and the minimum point of the down peak), is proportional to the number of elemental atoms related to the corresponding Auger transition [45]. Therefore, in this study, the \(I_{\text{pp}}\) of S LMM Auger transitions at \(E=150.0\) eV, \(I_{\text{pp}}\), S, and that of Mo MNN Auger transitions at \(E=186.5\) eV, \(I_{\text{pp}}\).Mo, were used for chemical analyses [45].  
In Figure 4b, the variations in two representative optical and chemical parameters, the \(I_{\text{A+A}^{-}}\) of ambient PL and \(I_{\text{pp}}\),S, respectively, with \(d\), are shown to be closely related to each other. As expected, when the \(I_{\text{pp}}\),S decreased (i.e., the S deficiency increases), \(I_{\text{A+A}^{-}}\) is enhanced, and vice versa. The plot of \(I_{\text{A+A}^{-}}\) vs. \(I_{\text{pp}}\),S normalized to the value at \(d=0\) is also shown in Figure 4c. Since the two data sets were measured almost along the same white dashed line in Figure 3c but with different intervals, to match them with the same \(d\) values, \(I_{\text{pp}}\),S corresponding to the \(d\) values for the \(I_{\text{A+A}^{-}}\) data were determined approximately by linear interpolation. The ambient PL was observed to increase effectively when the normalized \(I_{\text{pp}}\),S is lower than ~0.873, demonstrating that even the un-irradiated region of the ML-MoS\({}_{2}\) flake not close to the irradiation spot has the fluctuation of the detected amount of S atoms as ~93.7 \(\pm\) 6.0%, probably due to the existence of nanoscale defects such as nano-voids and nano-cracks, and local structural distortion by surface and interfacial contaminants [26]. Therefore, based on the plots of normalized \(I_{\text{pp}}\)s of S and Mo elements in Figure 4d, the actual S deficiency is determined to be ~13.4 \(\pm\) 3.5% in the region around the irradiation center (\(d>\) 3.5 \(\upmu\)m), and similarly, the actual Mo deficiency is estimated to be ~6.4 \(\pm\) 4.8%. By the FLI process, Mo defects seemed to be formed to some degree, although the Mo deficiency is not large like that of light S atoms. It is worth notingthat the nanoscale fluctuation of the detected amount of atoms on ML-MoS2 revealed in this work should be considered carefully when 2D materials are analyzed by a chemical analysis tool of a relatively lower spatial resolution. Moreover, from Figure 4c, the PL intensity was found to be almost saturated below the normalized \(I_{\text{PP-S}}\) \(\sim\)0.778.