Mechanical properties of monolayer GaS and GaSe crystals

The mechanical properties of monolayer GaS and GaSe crystals are investigated in terms of their elastic constants: in-plane stiffness (C), Poisson ratio $\left(\nu \right)$, and ultimate strength $\left({\sigma }_U\right)$ by means of first-principles calculations. The calculated elastic constants are compared with those of graphene and monolayer ${\mathrm{MoS}}_2$. Our results indicate that monolayer GaS is a stiffer material than monolayer GaSe crystals due to the more ionic character of the Ga-S bonds than the Ga-Se bonds. Although their Poisson ratio values are very close to each other, 0.26 and 0.25 for GaS and GaSe, respectively, monolayer GaS is a stronger material than monolayer GaSe due to its slightly higher ${\sigma }_U$ value. However, GaS and GaSe crystals are found to be more ductile and flexible materials than graphene and ${\mathrm{MoS}}_2$. We have also analyzed the band-gap response of GaS and GaSe monolayers to biaxial tensile strain and predicted a semiconductor-metal crossover after $17\%$ and $14\%$ applied strain, respectively, for monolayer GaS and GaSe. In addition, we investigated how the mechanical properties are affected by charging. We found that the flexibility of single layer GaS and GaSe displays a sharp increase under $0.1e$/cell charging due to the repulsive interactions between extra charges located on chalcogen atoms. These charging-controllable mechanical properties of single layers of GaS and GaSe can be of potential use for electromechanical applications.

Figure 1

Top and side view of monolayer (a) GaS and (b) GaSe. Red dashed lines represent the rectangular unit cell and $a$ and $b$ are the lattice vectors. $h$ is the thickness of the monolayer GaS and GaSe crystals. The charge distribution on the individual atoms for monolayer (c) GaS and (d) GaSe are shown in side view. Increasing charge density is shown by a color scheme from blue to red with linear scaling between zero (blue) and $6.7e/{\AA }^3$ (red). (e) and (f) show the calculated energy-band structure within GGA+SOC and GGA+SOC+GW approximations for monolayer GaS and GaSe, respectively. The Fermi energy $\left(E_F\right)$ level is set to the valence band maximum. The red dashed lines indicate the GW band structure, while blue lines indicate the indirect GGA+SOC band structure.

Figure 2

Calculated energy-band structures within GGA for different applied strain values for monolayer (a) GaS and (c) GaSe. The Fermi energy $\left(E_F\right)$ level is set to the VBM of each structure. The change in the band gap with applied strain for monolayer (b) GaS and (d) GaSe.

Figure 3

In-plane stiffness values: (a) lattice constant, (b) cohesive energy per atom, and (c) work function of monolayer GaS and GaSe crystals. The number near the symbols gives the amount of added charge per unit cell.

Figure 4

Total charge density difference between the bare and 0.1 charged $\left({\rho }_{0.1}\text{−}{\rho }_0\right)$, and 0.2 charged $\left({\rho }_{0.2}\text{−}{\rho }_0\right)$ cases for monolayer GaS and GaSe. Increasing charge density is shown by a color scheme from blue to red with linear scaling between zero (blue) and maximum (red) charge.

Figure 5

Poisson ratio values: (a) lattice constant, (b) cohesive energy per atom, and (c) work function of monolayer GaS and GaSe crystals. The numbers above the symbols refer to the amount of added charge per unit cell.

Figure 6

(a) The change of strain energy and (b) the created stress in the different monolayer materials under applied biaxial strain. (c) The geometries of each monolayer crystal at fracture strain values.

Figure 7

Phonon-band dispersions for monolayer (a) GaS at 17% and (b) GaSe 18% biaxial strains. The three acoustic phonon modes are given in the right panel.