First-principles calculations of energetics and electronic structure for reconstructed $\mathrm{Si}\left(111\right)-(5\times n)-\mathrm{Au}$ surfaces

We report results of ab initio calculations with various exchange-correlation functionals for the Si(111) surface with a 0.6-monolayer Au decoration. Seven different variations of the recently developed Erwin-Barke-Himpsel and Abukawa-Nishigaya models are studied in detail. Atomic geometries are determined by total-energy minimizations. We find the Erwin-Barke-Himpsel model of the $\mathrm{Si}\left(111\right)-(5\times 4)-\mathrm{Au}$ surface with one Si adatom per unit cell to be the most favorable structure. Seven-member rings and undercoordinated Si atoms of the Abukawa-Nishigaya model are unstable. Scanning tunneling images and band structures are calculated for the controversial geometries. For the ($5\times 4$) adatom geometry the resulting electronic structure agrees with the available experimental data.

Figure 1

Calculated atomic structures proposed by the EBH model for a Si(111)-($5\times n$)-Au surface with $n=1,2,4$ and a Au coverage of 0.6 ML using the vdW-DF functional. (a) Top view of the EBH($5\times 1$) model with ideal Au dimers. (b) Top view of the EBH($5\times 2$) model. (c) Top and sides view of the EBH($5\times 4$) model. The Si and Au atoms are displayed as light blue and yellow balls, respectively. The Si adatoms are represented as green balls. The surface unit cells are indicated by solid black lines. Characteristic geometry parameters (see text) are indicated.

Figure 2

Energy variation vs the dimerization parameter of Au atoms in (a) the EBH($5\times 2$) model without adatom and (b) the EBH ($5\times 4$) model with one adatom for three different XC functionals: PBE-GGA (black), PBEsol (red), and vdW-DF (green).

Figure 3

Calculated atomic structures derived from the surface model originally proposed by Abukawa and Nishigaya [10] for a gold coverage of 0.6 ML using the vdW-DF functional. The Si and Au atoms are displayed as light blue and yellow balls, respectively. The Si adatoms are displayed as green balls. The surface unit cells are indicated by solid black lines. (a) Top view of the relaxed AN($5\times 2$) model with the resulting six-member rings and filled hollows [AN($5\times 2$)a]. (b) Top view of the adatom-free AN($5\times 2$) model [AN($5\times 2$)b]. (c) Top and side views of the AN($5\times 4$) model with one adatom.

Figure 4

Simulated STM images for bias voltages of $\pm 0.5\text{V}$ for (a) the EBH($5\times 4$) and (b) AN($5\times 4$) adatom models. Red (blue) indicates the highest (lowest) tunnel probability. The unit cell is indicated.

Figure 5

Simulated STM images for bias voltages of $\pm 0.5\text{V}$ for the adatom-free, relaxed (a) EBH($5\times 2$) and (b) AN($5\times 2$)b geometries. The highest (lowest) tunneling probability is indicated in red (blue). The surface unit cell is indicated by thin black lines.

Figure 6

Calculated energy bands of Si(111)-($5\times 4$)-Au for the adatom geometries based on the (a) EBH and (b) AN models. The Fermi level is taken as zero energy. The projected bulk Si band structure is displayed as gray areas. The average electrostatic potentials in the slab center and of the bulk Si are used for alignment. The three lowest empty surface bands are labeled by $S_A$, $S_B$, and $S_C$.

Figure 7

Surface-sensitive one-electron density of states projected onto atoms in the uppermost Si atomic layer, the Si adatom, and the Au atoms for (a) EBH($5\times 4$) and (b) AN($5\times 4$). The Fermi level is taken as zero energy. In the case of Au the DOS around zero energy is increased by a factor of 10.

Figure 8

Wave-function squares of the three lowest empty surface bands $S_A$, $S_B$, and $S_C$ for the (a) EBH($5\times 4$) and (b) AN($5\times 4$) models. The partial-charge-density isosurface is shown up to $1.0\times {10}^{-3}$ $e$/Å${}^3$. The Si atoms, Au atoms, and Si adatoms are displayed as blue, yellow, and light green circles, respectively. The $5\times 4$ unit cell is indicated by black solid lines.