Raman spectroscopy polarization dependence analysis in two-dimensional gallium sulfide

Group-III post-transition-metal monochalcogenides like gallium sulfide (GaS) are layered semiconductors with weakly interacting adjacent layers, which allow them to be reduced to the two-dimensional nanometric thickness level by different exfoliation approaches, similar to graphene. Here, we investigate the intensity polarization dependence of the Raman modes for a different number of GaS layers and use symmetry analysis and density-functional perturbation theory to provide further information on these structures. The Raman polarization-dependent behaviors of the bulk relative modes ${\mathrm{A}}_{1g}$ and ${\mathrm{E}}_{2g}$ were found to be independent of the number of layers, being proportional to ${cos}^{2}(\ensuremath{\theta})$ for ${\mathrm{A}}_{1g}$ modes and constant for ${\mathrm{E}}_{2g}$ modes. The computational calculations for two and three layers show Raman active modes emerging at Raman shifts near the bulk Raman modes, with ${\mathrm{A}}_{1g}$ (${\mathrm{A}}_{1}^{\ensuremath{'}}$) and ${\mathrm{E}}_{g}$ (${\mathrm{E}}^{\ensuremath{'}}$) symmetries for an even (odd) number of layers, some of them being observed as ``shoulders'' in the experimental Raman spectra. These phonon modes present Raman tensors with components similar to those observed in bulk, thus explaining the same polar dependencies for different GaS thicknesses. The Raman intensity calculations were made by implementing the specific experimental geometry used here, thus resulting in good qualitative agreement. These results are fundamental for the understanding of the structural and vibrational changes when GaS is reduced to the few-layer limit, layer-number differentiation, and for further symmetry-lowering studies by strain manipulation or substrate interaction, which are routine issues in both fundamental research and device fabrication.