Island formation and dynamics of gold clusters on amorphous carbon films

Samples of Au clusters deposited by laser ablation on an amorphous-carbon substrate are investigated. After a few months’ storage at room temperature, the initially statistically distributed clusters are found to be collected in agglomerates consisting of larger clusters embedded in a Au film typically covering areas of size $25\times 70{\mathrm{nm}}^2$. The Au film is determined to be probably 4 to 8 monolayers but at most $7\mathrm{nm}$ thick. Evidence is found that a number of clusters consisting of less than 50 atoms are pinned at intrusions of the substrate. These results were derived using high-resolution transmission electron microscopy and off-axis holography measurements to characterize the agglomerates as well as the substrate. Monte Carlo simulations were performed to model the film formation process. To this end, the substrate-Au interaction was determined using density functional calculations, while the $\mathrm{Au}–\mathrm{Au}$ interaction was modeled with effective many-body Gupta potentials. The film formation can be understood as diffusion and fusion of clusters of intermediate ($50<N<300$ atoms) size. Larger clusters are more stable at room temperature and remain adsorbed on the Au film.

Figure 1

TEM images of Au clusters deposited on an aC substrate by laser ablation (3000 shots): (a) sample $1\text{day}$ after its preparation. The inset shows the histogram of the size distribution of the clusters. Clusters smaller than $1\mathrm{nm}$ in diameter cannot be resolved unambiguously within the TEM images. (b) Typical island of higher contrast formed on a sample $4\text{months}$ after its preparation. (c) Detail of the island displayed in panel (b). The areas circled show regions exhibiting crystalline structures with differently spaced lattice planes.

Figure 2

Holographic phase shift $\Delta \varphi$ of a segment of the aC substrate with part of an island as shown in Fig. 1b in the far right corner. The image has the size of $28.2\times 28.2{\mathrm{nm}}^2$. The $z$-axis value is proportional to the observed phase shift. In the foreground the almost linear decrease of the aC film thickness towards its edge is visible. (For alternative representations of the data see Figs. 5, 6.)

Figure 3

(Color online) Phase shift distributions as a measure of fluctuations of the phase. Panel (a) shows the result for the vacuum, panel (b) shows the substrate film without adsorbate, and panel (c) shows the distribution for the substrate film with Au adsorbate, albeit at positions without islands. Please note the different scales of the $x$ axes. Histograms are obtained by binning and normalization of the shifted raw data; full lines are Gaussian fits to Eq. (3). The insets show samples of the measured phase shifts. The data used to obtain the histograms amount to 5 to 10 times the data shown in the insets.

Figure 4

(Color online) Au–graphite (squares) and Au–aC substrate potentials (circles) as calculated within the DFT approach. The inset shows the corrugated surface layer of the aC model with the locations of the calculated potentials (a)–(d) indicated by arrows. The fitted potentials used in the MC simulations are shown as solid lines for graphite (g) and the aC model substrate. Dashed lines are guides to the eye.

Figure 5

(Color online) Holographic phase reconstruction image from the same segment as shown in Fig. 2 as an intensity plot. Lighter shades of gray correspond to larger phase shifts with respect to the vacuum. Lines show scans that underwent closer investigation; circles indicate the positions of selected adsorbed clusters.

Figure 6

(Color online) Details of scan 1 in Fig. 5. Panel (a) shows the raw data of the phase shifts together with fitted values (dashed lines; see the text), which average the fluctuations. Panel (b) shows the fluctuations $\Delta \varphi$ obtained from the raw data after subtraction of the fits. Panels (c), (d), (e), and (f) show the binned data of the phase fluctuations form the Au film, the Au-film edge, the substrate, and the substrate edge, respectively. Solid lines are fits from Eqs. (6, 3).

Figure 7

(Color online) Phase shift for two scans (a) and (b) through cluster “C2” in Fig. 5 along the directions indicated in the inset. Dashed lines are linear fits to the background. Panels (c) and (d) show the data of the cluster from panels (a) and (b), respectively, after background subtraction. Dashed lines in (c) and (d) are elliptical fits (see the text).

Figure 8

TEM images of two typical islands (a) before and (b) after in situ annealing at $373\mathrm{K}$ for $2\mathrm{h}$.

Figure 9

(Color online) Fusion of ${\mathrm{Au}}_N$ clusters for (a) $N=55$ and (b) $N=147$. Gray and black circles are obtained in MC annealing runs at $k_{B}T=0.0256\mathrm{eV}$ $(T=297\mathrm{K})$ and $k_{B}T=0.0001\mathrm{eV}$ $(T=1.16\mathrm{K})$, respectively. The full lines are fits for the effective intercluster cohesive potentials Eq. (7). At low temperatures the fusion process comes to an early halt because the energy barrier involved in the atomic rearrangement cannot be overcome.

Figure 10

(Color online) Side view of the shape of adsorbed clusters of size (a) $N=55$; (b) $N=147$; and (c) $N=309$. The initially icosahedral clusters are placed on a planar substrate in the $x\text{‐}y$ plane modeled with a generalized Lennard-Jones potential, Eq. (5), with a depth of the minimum of $V_{\mathrm{LJ},0}=-0.3\mathrm{eV}$ and simulated at room temperature $(k_{\mathrm{B}}T=0.0256\mathrm{eV})$. The clusters are reconstructed in hcp (a), fcc (b), and distorted icosahedral (c) structures as a consequence of the boundary condition imposed by the substrate. (The images were taken after quenching to $T=1.16\mathrm{K}$ in order to eliminate noise.)

Figure 11

(Color online) Side (a) and top (b) view of an ${\mathrm{Au}}_{309}$ cluster surrounded by an Au double layer bound to a substrate as modeled by Eq. (5) with $V_{\mathrm{LJ},0}=0.3\mathrm{eV}$ at room temperature $(k_{\mathrm{B}}T=0.0256\mathrm{eV})$. The ${\mathrm{Au}}_{309}$ was initially icosahedral but reconstructed to a fcc lattice under the influence of the Au(111) double layer. (The images were taken after quenching to $T=1.16\mathrm{K}$ in order to eliminate noise.)

Figure 12

(Color online) Simulation of 200 ${\mathrm{Au}}_{147}$ clusters interacting as described by Eq. (7) on a substrate modeled by Eq. (5) with $V_{\mathrm{LJ},0}=11\mathrm{eV}$ after (a) 3000; (b) $4\times {10}^4$; (c) $4\times {10}^5$; and (d) $4.3\times {10}^7$ MC steps per cluster. The radius of the dots representing the clusters has been chosen as $R_{\min ,147}\left(T_{\text{room}}\right)=0.6\mathrm{nm}$, i.e., touching clusters are fused as shown in Fig. 9b. The side views in panels (a) and (b) show that all clusters are located in a plane touching the substrate (Ref. 70).

Figure 13

(Color online) Time evolution of a system of 298 Au atoms placed randomly on the substrate [Eq. (5)], one ${\mathrm{Au}}_{55}$ and one ${\mathrm{Au}}_{147}$ cluster. Panel (a) 93 MC steps; panels (b) and (c) $6\times {10}^4$ MC steps; panels (d) and (e) $1.18\times {10}^6$ MC steps per atom. Panel (c) shows the formation of the double-layer film, panel (e) the restructuring of the initially icosahedral clusters. (The images were taken after quenching to $T=1.16\mathrm{K}$ in order to eleminate noise.)