Effect of disorder on Raman scattering of single-layerMoS2

We determine the effect of defects induced by ion bombardment on the Raman spectrum of single-layer molybdenum disulfide. The evolution of both the linewidths and frequency shifts of the first-order Raman bands with the density of defects is explained with a phonon confinement model, using density functional theory to calculate the phonon dispersion curves. We identify several defect-induced Raman scattering peaks arising from zone-edge phonon modes. Among these, the most prominent is the $\mathrm{LA}(M)$ peak at $\ensuremath{\sim}227\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ and its intensity, relative to the one of first-order Raman bands, is found to be proportional to the density of defects. These results provide a practical route to quantify defects in single-layer $\mathrm{Mo}{\mathrm{S}}_{2}$ using Raman spectroscopy and highlight an analogy between the $\mathrm{LA}(M)$ peak in $\mathrm{Mo}{\mathrm{S}}_{2}$ and the $D$ peak in graphene.