Structure effect on intrinsic piezoelectricity in septuple-atomic-layer $\mathrm{MS}{\mathrm{i}}_2{\mathrm{N}}_4$ (M=Mo and W)

Abstract

The recently experimentally synthesized monolayer $\mathrm{MoS}{\mathrm{i}}_2{\mathrm{N}}_4$ and $\mathrm{WS}{\mathrm{i}}_2{\mathrm{N}}_4$ (\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020})) lack inversion symmetry, which allows them to become piezoelectric. In this work, based on ab initio calculations, we report structure effect on intrinsic piezoelectricity in septuple-atomic-layer $\mathrm{MS}{\mathrm{i}}_2{\mathrm{N}}_4$ (M=Mo and W), and six structures (${\alpha }_i$ ($i$=1 to 6)) are considered with the same space group.It is found that $\mathrm{MS}{\mathrm{i}}_2{\mathrm{N}}_4$ (M=Mo and W) with ${\alpha }_i$ ($i$=1 to 6) all are indirect band gap semiconductors. Calculated results show that $\mathrm{MoS}{\mathrm{i}}_2{\mathrm{N}}_4$ and $\mathrm{WS}{\mathrm{i}}_2{\mathrm{N}}_4$ monolayers have the same structural dependence on piezoelectric strain and stress coefficients ($d_{11}$ and $e_{11}$), together with the ionic and electronic contributions to $e_{11}$.Finally, we investigate the intrinsic piezoelectricity of monolayer $\mathrm{M}{\mathrm{A}}_2{\mathrm{Z}}_4$ (M=Cr, Mo and W; A=Si and Ge; Z=N and P) with ${\alpha }_1$ and ${\alpha }_2$ phases expect $\mathrm{CrG}{\mathrm{e}}_2{\mathrm{N}}_4$, because they all are semiconductors and their enthalpies of formation between ${\alpha }_1$ and ${\alpha }_2$ phases are very close. The most important result is that monolayer $\mathrm{M}{\mathrm{A}}_2{\mathrm{Z}}_4$ containing P atom have more stronger piezoelectric polarization than one including N atom. The largest $d_{11}$ among $\mathrm{M}{\mathrm{A}}_2{\mathrm{N}}_4$ materials is 1.85 pm/V, which is close to the smallest $d_{11}$ of 1.65 pm/V in $\mathrm{M}{\mathrm{A}}_2{\mathrm{P}}_4$ monolayers. For $\mathrm{M}{\mathrm{A}}_2{\mathrm{P}}_4$, the largest $d_{11}$ is up to 6.12 pm/V. Among the 22 monolayers, ${\alpha }_1$-$\mathrm{CrS}{\mathrm{i}}_2{\mathrm{P}}_4$, ${\alpha }_1$-$\mathrm{MoS}{\mathrm{i}}_2{\mathrm{P}}_4$, ${\alpha }_1$-$\mathrm{CrG}{\mathrm{e}}_2{\mathrm{P}}_4$, ${\alpha }_1$-$\mathrm{MoG}{\mathrm{e}}_2{\mathrm{P}}_4$ and ${\alpha }_2$-$\mathrm{CrG}{\mathrm{e}}_2{\mathrm{P}}_4$ have large $d_{11}$, which are greater than or close to 5 pm/V, a typical value for bulk piezoelectric materials.

8 pages, 11 figures