Layer-dependent second-order Raman intensity of MoS2 and WSe2 : Influence of intervalley scattering

Abstract

Acoustic-phonon Raman scattering, as a defect-induced second-order Raman scattering process (with incident photon scattered by one acoustic phonon at the Brillouin-zone edge and the momentum conservation fulfilled by defect scattering), is used as a sensitive tool to study the defects of transition-metal dichalcogenides (TMDs). Moreover, second-order Raman scattering processes are closely related to the valley depolarization of single-layer TMDs in potential valleytronic applications. Here, the layer dependence of second-order Raman intensity of $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$ is studied. The electronic band structures of $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$ are modified by the layer thicknesses; hence, the resonance conditions for both first-order and second-order Raman scattering processes are tuned. In contrast to the first-order Raman scattering, second-order Raman scattering of $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$ involves additional intervalley scattering of electrons by phonons with large momenta. As a result, the electron states that contribute most to the second-order Raman intensity are different from that to first-order process. A weaker layer-tuned resonance enhancement of second-order Raman intensity is observed for both $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$. Specifically, when the incident laser has photon energy close to the optical band gap and the Raman spectra are normalized by the first-order Raman peaks, single-layer $\mathrm{Mo}{\mathrm{S}}_{2}$ or $\mathrm{WS}{\mathrm{e}}_{2}$ has the strongest second-order Raman intensity. This layer-dependent second-order Raman intensity can be further utilized as an indicator to identify the layer number of $\mathrm{Mo}{\mathrm{S}}_{2}$ and $\mathrm{WS}{\mathrm{e}}_{2}$.