  Motived by experimentally synthesized $\mathrm{MoSi_2N_4}$
(\textcolor[rgb]{0.00,0.00,1.00}{Science 369, 670-674 (2020})), the intrinsic
piezoelectricity in monolayer $\mathrm{XSi_2N_4}$ (X=Ti, Zr, Hf, Cr, Mo and W)
are studied by density functional theory (DFT). Among the six monolayers, the
$\mathrm{CrSi_2N_4}$ has the best piezoelectric strain coefficient $d_{11}$ of
1.24 pm/V, and the second is 1.15 pm/V for $\mathrm{MoSi_2N_4}$. Taking
$\mathrm{MoSi_2N_4}$ as a example, strain engineering is applied to improve
$d_{11}$. It is found that tensile biaxial strain can enhance $d_{11}$ of
$\mathrm{MoSi_2N_4}$, and the $d_{11}$ at 4\% can improve by 107\% with respect
to unstrained one. By replacing the N by P or As in $\mathrm{MoSi_2N_4}$, the
$d_{11}$ can be raise substantially. For $\mathrm{MoSi_2P_4}$ and
$\mathrm{MoSi_2As_4}$, the $d_{11}$ is as high as 4.93 pm/V and 6.23 pm/V,
which is mainly due to smaller $C_{11}-C_{12}$ and very small minus or positive
ionic contribution to piezoelectric stress coefficient $e_{11}$ with respect to
$\mathrm{MoSi_2N_4}$. The discovery of this piezoelectricity in monolayer
$\mathrm{XSi_2N_4}$ enables active sensing, actuating and new electronic
components for nanoscale devices, and is recommended for experimental
exploration.
