Effect of Net Charge on the Relative Stability of 2D Boron Allotropes

We study the effect of electron doping on the bonding character and stability of two-dimensional (2D) structures of elemental boron, called borophene, which is known to form many stable allotropes. Our {\em ab initio} calculations for the neutral system reveal previously unknown stable 2D $\epsilon$-B and $\omega$-B structures. We find that the chemical bonding characteristic in this and other boron structures is strongly affected by extra charge. Beyond a critical degree of electron doping, the most stable allotrope changes from $\epsilon$-B to a buckled honeycomb structure. Additional electron doping, mimicking a transformation of boron to carbon, causes a gradual decrease in the degree of buckling of the honeycomb lattice that can be interpreted as piezoelectric response. Net electron doping can be achieved by placing borophene in direct contact with layered electrides such as Ca$_{2}$N. We find that electron doping can be doubled by changing from the B/Ca$_{2}$N bilayer to the Ca$_{2}$N/B/Ca$_{2}$N sandwich geometry.