Scanning tunneling microscopy and kinetic Monte Carlo investigation of cesium superlattices on Ag(111)

Cesium adsorption structures on Ag(111) were characterized in a low-temperature scanning tunneling microscopy experiment. At low coverages, atomic resolution of individual Cs atoms is occasionally suppressed in regions of an otherwise hexagonally ordered adsorbate film on terraces. Close to step edges Cs atoms appear as elongated protrusions along the step edge direction. At higher coverages, Cs superstructures with atomically resolved hexagonal lattices are observed. Kinetic Monte Carlo simulations model the observed adsorbate structures on a qualitative level.

Figure 1

(Color online) (a) STM image of two adjacent terraces of Ag(111) covered with 0.03–0.04 ML Cs deposited at room temperature and imaged at 7 K. A monatomically high step separates the terraces (voltage $V=200\text{mV}$, current $I=0.2\text{nA}$, size $97\times 97{\text{nm}}^2$). (b) Close-up view of Cs adatoms on a terrace $\left(35\times 35{\text{nm}}^2\right)$. (c) Close-up view of the adsorbate arrangement in the vicinity of a step edge $\left(20\times 20{\text{nm}}^2\right)$.

Figure 2

Dipole-dipole interaction energy (gray) and surface-state-mediated interaction energy (black) between Cs adatoms on Ag(111) calculated according to Eqs. (2, 3) with parameters $p=0.09e\text{nm}$, $A_0=0.3$, ${\delta }_0=\pi /2$, $E_0=-0.06\text{eV}$, and $k_F=0.813{\text{nm}}^{-1}$. At the experimentally observed lattice constant of the adlayer, $a\approx 1.5\text{nm}$ (dashed line), the surface-state-mediated interaction and the dipole-dipole interaction energy have similar values.

Figure 3

(Color online) [(a) and (b)] Density plots and [(c) and (d)] defect fractions calculated by kinetic Monte Carlo simulations at $T=7\text{K}$ and $E_D=17\text{meV}$ for particle coverages 0.0383 ML in (a) and (c) and 0.0395 ML in (b) and (d). The density plots of $g_{\tau }\left(\mathbf{r}\right)$ are calculated at 1000 s using a time averaging interval of $\tau =16\text{s}$. The image size corresponds to $26\times 26{\text{nm}}^2$. The time evolution of the defect fraction $q_{\tau }$ in (c) and (d) is shown for a disordered (triangles) and a hexagonally ordered (circles) initial particle arrangement. In the initial equilibration period between 0 and 30 s the defect fraction changes rapidly until the stable or metastable state is reached. The asymptotic stable phase is reached within 800 s.

Figure 4

(Color online) Density plot of $g_{\tau }\left(\mathbf{r}\right)$ in the vicinity of a (111) (upper part) and a (100) (lower part) step edge. The simulation area corresponds to an image size of $30\times 30{\text{nm}}^2$. The density plot was generated for $T=7\text{K}$, $\tau =12\text{s}$, and $E_D=17\text{meV}$.

Figure 5

(Color online) (a) Quasi-three-dimensional representation of constant-current STM image of Ag(111) covered with 0.11 ML of Cs ($V=0.25\text{V}$, $I=0.1\text{nA}$, $10\times 10{\text{nm}}^2$). Cesium adatoms which appear as almost circular protrusions exhibit a mutual distance of 0.74 nm. Inset: atomically resolved Ag(111) lattice. The dashed line indicates that adlayer and substrate lattice have the same orientation. (b) STM image of Cs-covered Ag(111) at 0.15 ML ($V=1.2\text{V}$, $I=0.2\text{nA}$, $80.4\times 80.4{\text{nm}}^2$). Lines on terraces which contain irregularly shaped structures appearing as depressions at the applied tunneling voltage are boundaries between translational domains of the adsorbate lattice. Inset: Atomically resolved Cs domains. While the orientation of the adjacent domains is identical, the lattices are translated by half a superlattice constant (see dashed line).

Figure 6

(Color online) Arrangement of 340 particles according to kinetic Monte Carlo simulations using a time averaging interval of $\tau =12\text{s}$ and a substrate temperature of $T=7\text{K}$. The coverages are indicated at the top right of each plot. The horizontal (inclined) arrow indicates the crystallographic direction of the substrate (particle lattice). The rotation angle is defined as the smaller angle enclosed by the two arrows.

Figure 7

(Color online) Rotation angle of the superlattice with respect to the substrate lattice. Experimental data are depicted as circles and calculated data as triangles. The dashed line indicates a coverage at which two phases with different rotation angles coexist.