Ternary pentagonal BXN (X = C, Si, Ge, and Sn) sheets with high piezoelectricity

The discovery of new and stable two-dimensional pentagonal materials with piezoelectric properties is essential for technological advancement. Inspired by recently reported piezoelectric materials penta-BCN and penta-BSiN, we proposed penta-BGeN and penta-BSnN as new members of the penta-family based on first-principles calculations. Comprehensive analyses indicated that both penta-BGeN and penta-BSnN are thermodynamically, dynamically, mechanically, and thermally stable. In terms of mechanical stability, the elastic constant decreased as lower elements in group 4A of the periodic table were used. Therefore, penta-BGeN and penta-BSnN are softer than penta-BCN and penta-BSiN. In terms of piezoelectric properties, piezoelectric stress and strain tensors increase following the same pattern. In group 4A, penta-BSnN had the highest intrinsic piezoelectricity, especially the e(22) piezoelectric stress. Typically, the piezoelectric strain d(ij) coefficient increases with material softness; penta-BSnN possessed the highest d(ij). Thus, due to its inherent piezoelectricity, penta-BSnN has tremendous potential as a nanoscale piezoelectric material.