Structures and Stabilities of Two-Dimensional Boron Sheets with Point Defects

Borophene with diverse geometries and rich electronic properties has attracted great research interest over the past few years due to its multicenter bonding characteristics derived from the electron deficiency of boron. However, the members of borophene as well as their stability mechanism have not been fully explored yet. In this work, we explored the stabilities of various free-standing (β12-, α1-, β1-, α-, α4-, and α5-phase) borophenes with single/double vacancies (SVs/DVs) and adatom defects using density functional theory methods. Our results show that the most stable configurations of the single-vacant borophene favor the one with the A site vacancy and form the elongated hexagon in defected β12 borophene and hexagonal vacancies in other phase borophenes, respectively. The structures of borophene with DVs favor the ones with two fused hexagonal rings. All of the vacant borophenes are found to be experimentally feasible with low formation energies (Ef_vs) for the lowest-energy SVs/DVs around −1.11 to 1.49 eV. Among them, the Ef_vs of three single-vacant (α-, α4-, and α5-) phase borophenes and two double-vacant (α4- and α5-) phase borophenes are negative, showing that they are more stable than their pristine ones. Besides, the β12-phase borophene is energetically favorable to adsorb the B adatom. Detailed analysis shows that the stability of the defective borophene is sensitive to the ratio of hexagons in the systems. Moreover, the ultrahigh stability of the vacant α-, α4-, and α5-phase borophene can also be derived from the minimization of the imbalance ratio of the σ/π orbital occupation. This study is significant for evaluation of stability in defected borophene and very useful to understand the influence of defects in two-dimensional boron.