Atomic structure of the $\sqrt{3}\times \sqrt{3}$ phase of silicene on Ag(111)

The growth of the $\sqrt{3}\times \sqrt{3}$ reconstructed silicene on Ag substrate has been frequently observed in experiments while its atomic structure and formation mechanism is poorly understood. Here, by first-principles calculations, we show that $\sqrt{3}\times \sqrt{3}$ reconstructed silicene is constituted by dumbbell units of Si atoms arranged in a honeycomb pattern. Our model shows excellent agreement with the experimentally reported lattice constant and STM image. We propose a new mechanism for explaining the spontaneous and consequential formation of $\sqrt{3}\times \sqrt{3}$ structures from $3\times 3$ structures on Ag substrate. We show that the $\sqrt{3}\times \sqrt{3}$ reconstruction is mainly determined by the interaction between Si atoms and have weak influence from Ag substrate. The proposed mechanism opens the path to understanding of multilayer silicon.

Figure 1

(a) Formation of the dumbbell building block units starting from buckled silicene. Atomic structure of (b) $\sqrt{3}\times \sqrt{3}$ trigonal dumbbell silicene (TDS), (c) $\sqrt{3}\times \sqrt{3}$ honeycomb dumbbell silicene (HDS), (d) $1\times 1$ full dumbbell silicene (FDS), and (e) $2\times 2$ large honeycomb dumbbell silicene (LHDS). The unit cells are delineated by solid black lines. Atoms having different environment are represented by balls having different colors.

Figure 2

(a) The phononic band dispersions of TDS, LHDS, HDS, and FDS structures. The K and M points in the BZs of the $1\times 1$, $2\times 2$, and $\sqrt{3}\times \sqrt{3}$ unit cells are indicated by subscripts. (b) The electronic band dispersions of TDS, LHDS, and HDS structures unfolded to the BZ of the free-standing $1\times 1$ silicene. The contribution from each state to the unfolded band is represented by a blue circle having a radius proportional to the weight of that state. The bands of FDS structure don't need to be unfolded because it has $1\times 1$ periodicity. The superimposed electronic band structures of the free-standing $1\times 1$ silicene are shown by green lines.

Figure 3

(a) Growth of $\sqrt{3}\times \sqrt{3}$ HDS structure on Ag(111) surface. (b) Structural transformation from $3\times 3$ to $\sqrt{3}\times \sqrt{3}$ reconstructed silicene on Ag substrate. The height difference between two phases is approximately 2 Å. (c) Ball and stick models and calculated STM images of $3\times 3$ reconstructed silicene and $\sqrt{3}\times \sqrt{3}$ HDS. Note that the bright spots in STM images coincide with protruding atoms shown by red balls. The numbers in the ball and stick model represent the bond lengths in angstroms. $3\times 3$ supercells are delineated by green lines.