Determining by Raman spectroscopy the average thickness and N-layer-specific surface coverages of MoS₂ thin films with domains much smaller than the laser spot size

Raman spectroscopy is a widely used technique to characterize nanomaterials because of its convenience, non-destructiveness, and sensitivity to materials change. The primary purpose of this work is to determine via Raman spectroscopy the average thickness of MoS₂ thin films synthesized by direct liquid injection pulsed-pressure chemical vapor deposition (DLI-PP-CVD). Such samples are constituted of nanoflakes (with a lateral size of typically 50 nm, i.e., well below the laser spot size), with possibly a distribution of thicknesses and twist angles between stacked layers. As an essential preliminary, we first reassess the applicability of different Raman criteria to determine the thicknesses (or layer number, N) of MoS₂ flakes from measurements performed on reference samples, namely well-characterized mechanically exfoliated or standard chemical vapor deposition MoS₂ large flakes deposited on 90 ± 6 nm SiO₂ on Si substrates. Then, we discuss the applicability of the same criteria for significantly different DLI-PP-CVD MoS₂ samples with average thicknesses ranging from sub-monolayer up to three layers. Finally, an original procedure based on the measurement of the intensity of the layer breathing modes is proposed to evaluate the surface coverage for each N (i.e., the ratio between the surface covered by exactly N layers and the total surface) in DLI-PP-CVD MoS₂ samples.