Biaxial strain enhanced piezoelectric properties in monolayer g-${\mathrm{C}}_3{\mathrm{N}}_4$

Graphite-like carbon nitride (g-${\mathrm{C}}_3{\mathrm{N}}_4$) is considered as a promising candidate for energy materials. In this work, the biaxial strain (-4%-4%) effects on piezoelectric properties of g-${\mathrm{C}}_3{\mathrm{N}}_4$ 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-${\mathrm{C}}_3{\mathrm{N}}_4$, and almost unchanged electronic contribution, which is different from $\mathrm{M}\mathrm{o}{\mathrm{S}}_2$ monolayer (the enhanced electronic contribution and reduced ionic contribution). To prohibit current leakage, a piezoelectric material should be a semiconductor, and g-${\mathrm{C}}_3{\mathrm{N}}_4$ 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-${\mathrm{C}}_3{\mathrm{N}}_4$ monolayer, which gives a useful guidence for developing efficient energy conversion devices.