Figure 4: Thickness metric.

(a) Representative overview AFM images of a surfactant-exfoliated MoS₂ dispersion deposited on Si/SiO₂ wafers (scale bar, 1 μm). (b) Zoomed-in AFM images of the regions indicated in a. (c) Height profiles of the nanosheets in (b). (d) Heights of steps observed on deposited MoS₂ nanosheets such as that displayed in the inset (scale bar, 250 nm). The step height is found to be a multiple of 1.9 nm. (e) Raman (integrated A_1g phonon area, scale bar, 1 μm) and (f) PL maps (excitation 532 nm, integrated area from 640–700 nm, scale bar 1 μm) of the region shown in a. (g) Photoluminescence spectra of the areas marked by circles (colour coded). The blue circle and spectrum, respectively, is associated with a flake of apparent height 3 nm (Fig. 4c). Inset: zoom-in of PL from multi-layered flakes marked by red and green circles associated with flakes of apparent thickness 5–7 nm (Fig. 4c). (h) Example (fraction F2) of a layer number histogram after conversion of AFM height to number of layers. (i) Plot of the mean number of layers as obtained from AFM thickness analysis versus the wavelength associated with the A-exciton measured from both extinction and absorbance spectra. The vertical error bars represent the standard error of the AFM height distribution. The red filled diamond represents free-standing micromechanically cleaved MoS₂ monolayer, where λ_A was obtained from the PL peak position. The experimental findings are consistent with literature data on the photoluminescence of free-standing MoS₂ extracted from Mak et al.⁵¹ NB profiles in c are colour coded with the lines in b.