  Graphite-like carbon nitride (g-$\mathrm{C_3N_4}$) is considered as a
promising candidate for energy materials. In this work, the biaxial strain
(-4\%-4\%) effects on piezoelectric properties of g-$\mathrm{C_3N_4}$ monolayer
are studied by density functional theory (DFT). It is found that the increasing
strain can reduce the elastic coefficient $C_{11}$-$C_{12}$, and increases
piezoelectric stress coefficient $e_{11}$, which lead to the enhanced
piezoelectric strain coefficient $d_{11}$. Compared to unstrained one, strain
of 4\% can raise the $d_{11}$ by about 330\%. From -4\% to 4\%, strain can
induce the improved ionic contribution to $e_{11}$ of g-$\mathrm{C_3N_4}$, and
almost unchanged electronic contribution, which is different from
$\mathrm{MoS_2}$ monolayer (the enhanced electronic contribution and reduced
ionic contribution). To prohibit current leakage, a piezoelectric material
should be a semiconductor, and g-$\mathrm{C_3N_4}$ monolayer is always a
semiconductor in considered strain range. Calculated results show that the gap
increases from compressive strain to tensile one. At 4\% strain, the first and
second valence bands cross, which has important effect on transition dipole
moment (TDM). Our works provide a strategy to achieve enhanced piezoelectric
effect of g-$\mathrm{C_3N_4}$ monolayer, which gives a useful guidence for
developing efficient energy conversion devices.
