Dilute nanostructures built of dimers: Kinetic Monte Carlo study of Co on Cu(111)

The growth of Co on Cu(111) at coverage 0.03 monolayer is studied by kinetic Monte Carlo simulations performed above temperature of dimer formation (20–21 K) in order to find a nanostructure composed primarily of dimers as an analog of the dilute nanostructure formed of monomers. Both of the nanostructures are stabilized by a long-range surface-state-mediated interaction between adatoms. In order to obtain the largest possible fraction of dimers the simulation procedure consists in deposition of adatoms at low temperature (7 K) and simulated annealing at higher temperatures. After 60–200 s of annealing at 21–22 K, about 87% of adatoms belongs to dimers. The dimers form dilute islands with a local hexagonal order and an average nearest-neighbor distance of $12.0\left(5\right)\text{Å}$. The nanostructure in the dimer state is stable up to 200 K.

Figure 1

(Color online) The pair-interaction energy between Co adatoms on Cu(111) incorporated in KMC simulations. Adatoms are separated by a distance $r$ shown in the units of Cu(111) surface parameter $a=0.256\text{nm}$. The distances indicated in the figure relate to the following energies: $V_{eq}\left(r_{eq}\right)=-1181.74\text{meV}$, $V_0\left(r_0\right)=29.60\text{meV}$, and $V_1\left(r_1\right)=-2.01\text{meV}$. For reasons of scale, on the energy axis the short-range interaction with the ordinary dimer energy $V_{eq}$ is not shown. For $r<11a$ the curve is based on the energy values taken from Refs. 8, 25 whereas for longer distances a fit based on Eq. (1) is used.

Figure 2

(Color online) Snapshots of 0.03 ML of Co on the Cu(111) surface. The size of the simulation cell is $100a\times 111a$. (a) Random configuration of adatoms deposited at 7 K at a flux 0.01 ML/s. (b) The nanostructure made up of monomers ($T=16\text{K}$, annealing time $t=500\text{s}$). (c) The nanostructure composed of dimers ($T=22\text{K}$, $t=140\text{s}$). White arrow points at monomer trapped among dimers. The marked region is shown in Fig. 5.

Figure 3

(Color online) Relative number of adatoms in the form of dimers and trimers as a function of annealing time. The annealing temperature is a parameter of the curve. For clarity, curves for trimers at $T=19$ and 21 K are not shown.

Figure 4

(Color online) Snapshots of 0.031 ML of Co on the Cu(111) surface. The size of the simulation cell is $100a\times 111a$. (a) Lattice of monomers taken as initial configuration for annealing at 20 K. The monomers are located in fcc sites. In superstructure matrix notation the lattice can be described as fcc(111)-$\left[\genfrac{}{}{0ex}{}{50}{26}\right]$. (b) First stage: A dilute percolating island formed after 8 s of annealing, where 73% of adatoms is in the form of monomers and 27% in the form of dimers. (c) Second stage: dilute islands formed after 270 s of annealing, where 6.5% of adatoms is in the form of monomers, 86% is in the form of dimers, and 7.5% is in the form of trimers.

Figure 5

(Color online) Map of lateral energy of a test adatom that was placed in the vacant fcc sites marked by diamonds. Size of the mapped region is $50a\times 50a$. The map relates to the fragment of Fig. 2c marked by a square, that was additionally annealed at 22 K by 6 s. The disks represent adatoms. They form an island, which consists of dimers and one linear trimer (pointed by arrow). Monomer pointed by the arrow in Fig. 2c now is a part of this trimer. The map shows also three dimers that do not belong to the island. One of them is in hcp-hcp configuration, two of them in fcc-fcc configurations. The repulsive energy at fcc sites is presented in the logarithmic scale with the base 10. The regions of attractive energy are black, independent of the energy value.