Mechanical exfoliation and layer number identification of MoS2 revisited

In this paper we accurately revisit the mechanical exfoliation and layer number determination of MoS2. By modelling the exfoliation itself as a random vertical (lateral) exfoliation (fragmentation) phenomenon, a rationale is given to optimise the number of iterations in the scotch-tape peeling technique and we rigorously demonstrate that since the second cleavage the occurrence of monolayers is the most likely. For the unambiguous layer number identification, experiments have been carried out with a unified complementary approach based on optical microscopy, atomic force microscopy, resonant and non resonant Raman spectroscopy, and photo-luminescence spectroscopy. The experimental analysis has been carried out on a statistically significant set of few-layer MoS2 flakes (from one to five layers). The work stresses the strong need of such complementary multitechnique approach to really unambiguously determine the layer number of flakes (that neither optical microscopy, nor AFM alone can give). Optical microscopy contrast analysis experiments (carried out on flakes deposited onto 270 nm SiO2/Si(100) substrates) demonstrate that for fewlayer MoS2 (from the mono to the epta-layer) the optical contrast is weakly depending on the radiation wavelength and is a non-monotonic function of the layer number. Thus, flakes from ten to twelve layers exhibit the same contrast of monolayers, as demonstrated by parallel AFM analysis. AFM clearly shows that the stacking between the silicon oxide substrate and the first MoS2 layer is strongly unpredictable and likely depending on the degree of surface contamination of the substrate. A parallel systematic resonant Raman study is performed ranging from one to five layers clearly exhibiting systematic layer dependent spectral features in the one-five layers range. For the first time a layer estimation number based on a quantitative analysis of resonant Raman and PL spectra is proposed.