Determining layer number of two-dimensional flakes of transition-metal dichalcogenides by the Raman intensity from substrates

Transition-metal dichalcogenide (TMD) semiconductors have been widely studied due to their distinctive electronic and optical properties. The property of TMD flakes is a function of their thickness, or layer number (N). How to determine the N of ultrathin TMD materials is of primary importance for fundamental study and practical applications. Raman mode intensity from substrates has been used to identify the N of intrinsic and defective multilayer graphenes up to N = 100. However, such analysis is not applicable to ultrathin TMD flakes due to the lack of a unified complex refractive index (ñ) from monolayer to bulk TMDs. Here, we discuss the N identification of TMD flakes on the SiO2/Si substrate by the intensity ratio between the Si peak from 100 nm (or 89 nm) SiO2/Si substrates underneath TMD flakes and that from bare SiO2/Si substrates. We assume the real part of ñ of TMD flakes as that of monolayer TMD and treat the imaginary part of ñ as a fitting parameter to fit the experimental intensity ratio. An empirical ñ, namely, ñ(eff), of ultrathin MoS2, WS2 and WSe2 flakes from monolayer to multilayer is obtained for typical laser excitations (2.54 eV, 2.34 eV or 2.09 eV). The fitted ñ(eff) of MoS2 has been used to identify the N of MoS2 flakes deposited on 302 nm SiO2/Si substrate, which agrees well with that determined from their shear and layer-breathing modes. This technique of measuring Raman intensity from the substrate can be extended to identify the N of ultrathin 2D flakes with N-dependent ñ. For application purposes, the intensity ratio excited by specific laser excitations has been provided for MoS2, WS2 and WSe2 flakes and multilayer graphene flakes deposited on Si substrates covered by a 80-110 nm or 280-310 nm SiO2 layer.