The recently experimentally synthesized monolayer $\mathrm{ MoSi_2N_4}$ and $\mathrm{ WSi_2N_4}$ (\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 $\mathrm{ MSi_2N_4}$ (M=Mo and W), and six structures ($\alpha_i$ ($i$=1 to 6)) are considered with the same space group.It is found that $\mathrm{ MSi_2N_4}$ (M=Mo and W) with $\alpha_i$ ($i$=1 to 6) all are indirect band gap semiconductors. Calculated results show that $\mathrm{ MoSi_2N_4}$ and $\mathrm{ WSi_2N_4}$ 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 $\mathrm{ MA_2Z_4}$ (M=Cr, Mo and W; A=Si and Ge; Z=N and P) with $\alpha_1$ and $\alpha_2$ phases expect $\mathrm{ CrGe_2N_4}$, 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 $\mathrm{ MA_2Z_4}$ containing P atom have more stronger piezoelectric polarization than one including N atom. The largest $d_{ 11}$ among $\mathrm{ MA_2N_4}$ materials is 1.85 pm/V, which is close to the smallest $d_{ 11}$ of 1.65 pm/V in $\mathrm{ MA_2P_4}$ monolayers. For $\mathrm{ MA_2P_4}$, the largest $d_{ 11}$ is up to 6.12 pm/V. Among the 22 monolayers, $\alpha_1$-$\mathrm{ CrSi_2P_4}$, $\alpha_1$-$\mathrm{ MoSi_2P_4}$, $\alpha_1$-$\mathrm{ CrGe_2P_4}$, $\alpha_1$-$\mathrm{ MoGe_2P_4}$ and $\alpha_2$-$\mathrm{ CrGe_2P_4}$ have large $d_{ 11}$, which are greater than or close to 5 pm/V, a typical value for bulk piezoelectric materials.
Categories: cond-mat.mtrl-sci