Immersion structures of monovalent metal adatoms on $\mathrm{Ag}∕\mathrm{Si}\left(111\right)\sqrt{3}\times \sqrt{3}$: First-principles study

We present first-principles calculations for the adsorption of monovalent metal adatoms (noble and alkali metals) on the $\mathrm{Ag}∕\mathrm{Si}\left(111\right)\sqrt{3}\times \sqrt{3}$ surface, a tunable two-dimensional electron gas system by electron-doping adatoms. The noble metals and Li immerse spontaneously into the topmost Ag layer with a significant amount of structural relaxation. The clustering of Ag adatoms is investigated, and the cluster with three-immersed-adsorbates is found to be the most stable one. The calculated atomic structures with one and three immersed Ag adatoms well reproduce the measured scanning tunneling microscopy features at low dopant coverages, called “star” and “propeller,” respectively. The present results provide a unified view of the atomic structures of metal adatoms on the $\mathrm{Ag}∕\mathrm{Si}\left(111\right)\sqrt{3}\times \sqrt{3}$ surface, which play an important role in the surface electronic states.

Figure 1

(Color online) (a) Top and (b) side views of the IET structural model with the metastable adsorption sites (SiT, ${\mathrm{LT}}_a$, ${\mathrm{LT}}_b$, and ST) indicated by small circles. The white, small gray, and dark spheres represent the Si atoms forming triangles, Si atoms in deep layers, and substrate Ag atoms, respectively. (c) Energy variation during immersion of the adatom from the ${\mathrm{LT}}_a$ to the most stable ${\mathrm{LT}}_b$ site as a function of adatom height $\left(z\right)$ from the Ag overlayer. In (a) the lightly shaded spheres denote the optimized positions of the substrate Ag atoms in the most stable ${\mathrm{LT}}_b$ adsorption structure and the dashed parallelogram shows the $\sqrt{3}\times \sqrt{3}\text{unit}$ cell.

Figure 2

(Color online) Adsorption structures of a single Ag adatom: (a) and (c) on a ST and (b) and (d) on a LT site of the $\sqrt{3}\text{−}\mathrm{Ag}$ surface at $1∕48$-ML adatom coverage. In (a) and (b) the lightly shaded spheres and triangles denote the position of the substrate Ag atoms on the pristine IET structure and the small triangles, respectively, for reference. The largest spheres stand for the Ag adatoms, and the others are the same as those in the Fig. 1.

Figure 3

(Color online) Total energies as a function of the adatom height $z$ with respect to the substrate Ag layer for (a) noble metals and (b) alkali metals. All adatoms are positioned on the ST site.

Figure 4

(Color online) (a), (b) Simulated STM images for a single Ag adatom on the ST site with filled and empty biases and (c), (d) corresponding experimental-STM images taken from Figs. 2(d) and 2(a) in Ref. 11, respectively. In (a) and (b), biases are $-1.5\mathrm{V}$ and $1.0\mathrm{V}$, respectively, and in (c) and (d) $-1.0\mathrm{V}$ and $1.3\mathrm{V}$, respectively. In all the images, the calculated equilibrium structure of Fig. 2a is superimposed.

Figure 5

(Color online) Ag adatom clusters on the $\sqrt{3}\text{−}\mathrm{Ag}$ substrate with (a) two, (b) three, and (c) four Ag adatoms. (d) Cluster energy as a function of cluster size. The cluster energy $\left(E_{\mathit{cl}}\right)$ is calculated by $E_{\mathit{cl}}=E_b^n-n{E}_b^1$, where $n$ and $E_b^n$ are the size of the cluster and adsorption energy of the $n\text{−}\mathrm{Ag}$ cluster relative to the $\sqrt{3}\text{−}\mathrm{Ag}$ substrate. This definition removes the effect of the substrate. The symbols representing atoms are the same as those in Fig. 2.

Figure 6

(Color online) (a), (b) Simulated STM images for the three-Ag-adatom cluster on the $\sqrt{3}\text{−}\mathrm{Ag}$ substrate and (c), (d) corresponding experimental-STM images taken from Figs. 2(d) and 2(b) in Ref. 11, respectively. Biases are $-1.0\mathrm{V}$ for the filled-state images of (a) and (c) and $0.5\mathrm{V}$ and $1.0\mathrm{V}$ for the empty-state images of (b) and (d). In all images, the calculated equilibrium structure of Fig. 5b is superimposed.