Thickness dependence of wavenumbers and optical-activity selection rule of zone-center phonons in two-dimensional gallium sulfide metal monochalcogenide

Abstract

Gallium sulfide (GaS) stands out as a versatile nonlinear optical material for green–blue optoelectronic and photocatalytic nano-devices. Although it displays an indirect band gap from bulk to monolayer, a small energy difference to the direct band gap results in relevant direct transitions. In addition, the in-plane breaking strain and mechanical strength of layered GaS position it as promising candidate for next-generation flexible nanodevices. The fast and reliable assessment of the number of layers, without sample lost, is key for these applications. Here we unveiled the influence of dimensionality in the structural, mechanical and vibrational properties of GaS by applying density-functional theory based quantum-simulations and group-theory analysis. We found its intralayer structure and interlayer distances to be essentially independent of the number of layers, in agreement with the van der Waals forces as dominant interlayer interaction. The translational symmetry breaking along the stacking direction results in different structural symmetries for monolayer, N-odd layers, N-even layers and bulk geometries. Its force constants against rigid-layer shear, K_LSM = 1.35 × 10¹⁹ N m^-3, and breathing, K_LBM = 5.00 × 10¹⁹ N m^-3 , displacements remain the same from bulk to bilayer structures. The related stiffness coefficients in bulk are C₄₄ = 10.2 GPa and C₃₃= 37.7 GPa, respectively. This insight into GaS interlayer interactions and elastic coefficients reveals it as an excellent lubricant for nano-mechanic applications and to be easy to cleave for thickness engineering, even in comparison to layered graphite and MoS₂. We present the GaS Raman and infrared spectra dependence to the layer number as strategies for sample thickness characterization and derived formulas for distinguishing the number of layers in both high and low-frequency regimes. In addition, our analysis of their optical- activity selection rules and polarization dependencies are applicable to isostructural Group-IIIA chalcogenetes with 2H-layer stacking, as gallium/indium sulphide/selenide. These results contribute to a rapid and non-destructive characterization of the material’s structure, of paramount importance for the manufacturing of devices and the utilization of its diverse properties.