Trimeric precursors in formation of Al magic clusters on a Si(111)-$7\times 7$ surface

The formation process of Al magic clusters on the Si(111)-$7\times 7$ surface was investigated by means of a variable-temperature scanning tunneling microscope (STM) in situ and was interpreted using density-functional theory (DFT) calculations. At a growth temperature of 450 ${}^{°}$C, Al atoms hopped among the corner, center, and T4 sites and also across the dimer rows on the Si(111)-$7\times 7$ surface. At low coverage below 0.08 ML, a single Al atom was adsorbed on the corner or center site. When the coverage was increased to 0.08 ML, Al dimers and trimers appeared, and Al magic clusters were also observed. However, no Al tetramers or pentamers were experimentally confirmed. Careful analysis of STM images suggests that Al trimers could be key precursors for the formation of Al magic clusters, and DFT calculations verified this interpretation. Total-energy calculation results using DFT reveal that this is due to the small energy gain from Al trimer to Al tetramer. These results are important for understanding the atomic structure and the formation mechanism of the magic clusters on the Si(111)-$7\times 7$ surface.

Figure 1

(a)–(c) are sequential empty-state STM images (at $+2.0$ V, 0.1 nA) of Al atoms on the Si(111)-$7\times 7$ surface after growth at 450 ${}^{°}$C, which were extracted from one movie observed at 450 ${}^{°}$C. The time interval is 100 s between two images. Al coverage is about 0.12 ML. The scanning size is $20.0\times 20.0$ nm${}^2$. The unit cells of the Si(111)-$7\times 7$ surface are indicated with black lines. The fixed structure outlined by a blue square is used as a marker to show that the three images are in the same area. Dashed (green) rings and solid (yellow) rings show the movement of Al atoms. The observed small and large bright dots are Al atoms and Al magic clusters, respectively.

Figure 2

(a) Empty-state STM image of Al atoms on the Si(111)-$7\times 7$ surface observed at 450 ${}^{°}$C. Sample bias is $+1.5$ V, tunneling current is 0.10 nA, scanning size is $9.0\times 9.0$ nm${}^2$, and Al coverage is 0.03 ML. The unit cells of the Si(111)-$7\times 7$ surface are indicated with black lines. Panels (b)–(d) show candidate adsorption models for a single Al atom on the faulted half-unit cell of the Si(111)-$7\times 7$ surface. Panels (e)–(g) show simulated STM images for the corresponding models (b)–(d). Panel (h) shows the model for the Si(111)-$7\times 7$ unit cell. In one half of the unit cell, six adatoms on the top layer form the triangle. The sites in the corner of the triangle and at the center of each edge of the triangle are defined as the corner and center sites, respectively, while the sites between the two center sites and above the Si atom on the second layer are defined as T4 sites. These three types of sites are common adsorption sites for adsorbates on the Si(111)-$7\times 7$ surface.

Figure 3

(a) Empty-state STM image of Al dimers and Al trimers on the Si(111)-$7\times 7$ surface observed at450 ${}^{°}$C. Sample bias is $+1.5$ V, tunneling current is 0.10 nA, scanning size is $15.0\times 15.0$ nm${}^2$, and Al coverage is 0.08 ML. Half-unit cells of the Si(111)-$7\times 7$ surface are indicated with black lines. Panels (b)–(e) show candidate adsorption models for Al dimers and Al trimers on the Si(111)-$7\times 7$ surface. Panels (f)–(i) are simulated STM images for the corresponding models (b)–(e), respectively.

Figure 4

(a) Empty-state STM image of Al atoms on the Si(111)-$7\times 7$ surface observed at 450 ${}^{°}$C. Sample bias is $+1.5$ V, tunneling current is 0.10 nA, scanning size is $13.3\times 13.3$ nm${}^2$, and Al coverage is 0.27 ML. The unit cells of the Si(111)-$7\times 7$ surface are indicated with black lines. Panels (b) and (c) show the adsorption models for an Al tetramer, panels (d) and (e) show those for an Al pentamer, and panel (f) is the model for an Al hexamer.

Figure 5

(a) Average cluster density per unit cell as a function of the Al coverage, observed with a STM at 450 ${}^{°}$C. (b) Calculated incorporation energy as a function of the Al coverage, defined as the energy reduction of the Al-Si system when one more Al atom is incorporated into the Al${}_{n-1}$ cluster to form the Al${}_n$ cluster, $\Delta E_n=E_n-E_{n-1}$. Here, $E_n$ is the total binding energy per half unit of the Si(111)-$7\times 7$ surface.