Self-healing monovacancy in low-buckled silicene studied by first-principles calculations

A new type of monovacancy (MV), MV-1, with a planelike $s{p}^3$ hybridization at its defect core has been found in two-dimensional (2D) low-buckled silicene by using the first-principles study, which has never been found to exist stably in the 2D single-layer nanostructures, including other previously studied graphene, $h$-BN sheets, and single-layer ${\mathrm{MoS}}_2$. In addition, other two possible monovacancies (MV-2 and MV-3) with higher energies have also been found to exist in 2D low-buckled silicene. More importantly, it is found that the new type MV-1 is the most stable ground structure among the three possible MVs. And the high-energy MV-3 is unstable, easily decaying into MV-1, but metastable MV-2 could coexist with MV-1 at low temperatures less than 10 K. The diffusion coefficient of MV-1 is calculated to be $2.3\times {10}^{-5}{\mathrm{cm}}^2/\mathrm{s}$, much higher than that of the MV in graphene. Finally, electronic structures of the defective silicene with MV-1 and MV-2 are calculated, showing both of them are metallic.

Figure 1

Top views of the optimized geometric structures of the possible Si MVs in the smaller (6 × 6) supercell. (a) A pristine Si MV, called MV-0, is shown by a circle in the left part in which the gray ball indicates the ejected Si atom, and its three equivalent neighbors are marked Si-1, Si-2, and Si-3, respectively. Also, a reconstructed Si MV, called MV-1, is given in the right part in which the center Si atom bonds with its four nearest Si atoms, inducing a planelike $s{p}^3$ hybridization. (b) Other two possible reconstructed Si MVs in 2D silicene, denoted MV-2 and MV-3, respectively. The side views: (c) MV-1, (d) MV-2.

Figure 2

The possible diffusion paths of MV-1: (a) Initial MV-1 configuration and its possible diffusion process. Here the dashed arrows indicate the moving directions of several numbered Si atoms around the MV-1 core. (b) New position of MV-1 by its diffusion. (c) The corresponding transition energy barriers of the MV-1 diffusion.

Figure 3

The electronic band structures of the reconstructed 2D low-buckled silicene with (a) MV-1 and (b) MV-2 in the (6,6) supercell. For comparison, that of the pure low-buckled one is given in (c). The dashed red lines denote the Fermi level, which is set to zero. The integrated charge-density isosurfaces $(0.006e/\AA$${}^3)$, marked as 1, 1′, 2, and 3 in (a) and (b), are given in (d)–(g), respectively. The dashed rhombuses indicate the used unit cells in our calculations.