The enhanced vertical piezoelectricity in Janus C₃HFX (X = Si and Ge) monolayers based on the born effective charges dipole-moment

Recently, two-dimensional (2D) piezoelectric materials are widely studied, and the vertical piezoelectric properties of 2D materials are highly required to be known in the related theory research works and experiments, so it becomes very important to explore the intrinsic mechanism of piezoelectricity in the 2D materials. Herein, we systematically study the piezoelectricity of Janus C₃HFX (X = Si and Ge) monolayers with semiconductor property, which are carbon-based 2D materials, using the first-principles calculation. The remarkable enhancements on the absolute values of the vertical piezoelectric coefficient of C₃HFSi-1 (e₃₃ = 11.27 × 10⁻¹⁰ C/m) and C₃HFGe-4 (e₃₃ = −12.78 × 10⁻¹⁰ C/m) are larger than that of C₄HF (e₃₃ = −2.28 × 10⁻¹⁰ C/m) by 5 and 6 times, respectively. It indicates that the atom replacement at appropriate positions in the multiatomic monolayer can significantly enhance the vertical piezoelectric properties based on the appropriate distribution of polarization charge. We define the concepts, the Born effective charges center (BECs-center) and the BECs-dipole-moment in this work, to explain these large vertical piezoelectric coefficients’ variation. The larger BECs-dipole-moment will enhance the vertical piezoelectricity for these C₃HFX monolayers than that of the C₄HF monolayer. These concepts defined in this work will deepen the understanding of the internal physical mechanism about the piezoelectricity.