Nucleation and growth of Ag islands on fivefold Al-Pd-Mn quasicrystal surfaces: Dependence of island density on temperature and flux

Scanning tunneling microscopy (STM) has been used to investigate the nucleation and growth of Ag islands on the fivefold surface of an icosahedral Al-Pd-Mn quasicrystal. Analysis of the data as a function of deposition temperature, from $127\mathrm{K}\text{to}300\mathrm{K}$, reveals that island density is constant, while at higher temperature it decreases. To model this behavior, we first show that the potential energy surface describing bonding of Ag at various locations on the surface is complex, with a few sites acting as traps for clusters of adatoms. We then develop a rate equation model which incorporates enhanced nucleation at trap sites relative to nucleation at regular sites on terraces. It recovers the temperature dependence of the island density, plus previous flux-scaling data. Our model suggests that the critical size for both types of nucleation sites is large—corresponding to stable clusters of at least 6 Ag atoms—and that binding between atoms at trap sites is significantly stronger than at free terrace sites. The data and the model, combined, provide guidance about the conditions of temperature and flux under which saturation of trap sites can be expected. This, in turn, provides a general indicator of the conditions that may favor localized pseudomorphic growth at low coverage, here and in other systems.

Figure 1

STM images [(a)-(f)] showing the evolution of island density as a function of temperature for deposition of Ag onto $5f\text{−}i\text{−}\mathrm{Al}\text{−}\mathrm{Pd}\text{−}\mathrm{Mn}$ quasicrystal. The size of images is $100\times 100{\mathrm{nm}}^2$. The tunneling conditions are $0.97–0.99\mathrm{V}$ and $0.31–0.47\mathrm{nA}$.

Figure 2

An area based height histogram taken from an STM image at $\theta =0.2$ ML and $T=300\mathrm{K}$. Dotted line shows the threshold which partially separates silver islands from the QC substrate.

Figure 3

Temperature dependence of the average island density, $n_x$, at $F=0.001\mathrm{ML}∕\mathrm{s}$. Solid lines show the predictions obtained from the rate equation model. The inset shows the model’s prediction for the number of islands on regular terrace sites $\left(n_{xf}\right)$ as a function of temperature.

Figure 4

Average island density, ${\mathrm{n}}_{\mathrm{x}}$, versus flux for $\theta =0.2$ ML and $T=300\mathrm{K}$. The solid lines depict predictions from the rate equation model for two cases, set $B$ and set $C$. The expected scaling behavior for homogeneous nucleation for $i=5$ is shown by the dash-dotted line.

Figure 5

Island size distribution from STM images for $\mathrm{Ag}∕\mathrm{Al}\text{−}\mathrm{Pd}\text{−}\mathrm{Mn}$ at $365\mathrm{K}$, 0.26 ML, and $F=1\times {10}^{-3}\mathrm{ML}∕\mathrm{s}$.

Figure 6

(Color online) (a) Potential energy surface $(8.6\times 8.6{\mathrm{nm}}^2)$ for Ag on $i\text{−}\mathrm{Al}\text{−}\mathrm{Pd}\text{−}\mathrm{Mn}$ QC. Darker shades indicate stronger interactions. (b) $8.6\times 8.6{\mathrm{nm}}^2$ STM image of clean fivefold surface of $i\text{−}\mathrm{Al}\text{−}\mathrm{Pd}\text{−}\mathrm{Mn}$ QC ($+0.97\mathrm{V}$, $0.47\mathrm{nA}$). One of the traps is marked both on the STM image and on the PES. (c) Model for nucleation at “trap” sites. $n_{1t}$ is the density of trapped single adatoms; $n_t$ is the density of traps, ${\mathrm{n}}_{1f}$ is the density of free single adatoms, $n_{xf}$ is the density of critical clusters formed on terraces, and $n_{xt}$ is the density of trapped stable clusters.

Figure 7

The rate of nucleation at trap sites, $K_{\mathit{nuct}}$, versus coverage from the rate equation model for set $C$: $n_t=0.035{\mathrm{nm}}^{-2}$, $E_d=0.66\mathrm{eV}$, $E_{bt}=0.090\mathrm{eV}$, $m_{11}=16$, $R=0.20$, $i_f=11$, and $i_t=5$. The inset is an expanded view of the variation in $K_{\mathit{nuct}}$ with coverage for the three lowest temperatures. Flux is 0.001 ML/s.

Figure 8

Predictions for average island density, $n_x$, as a function of flux from the rate equation model. Parameter values correspond to set $C$: $n_t=0.035{\mathrm{nm}}^{-2}$, $E_d=0.66\mathrm{eV}$, $E_{bt}=0.090\mathrm{eV}$, $m_{11}=16$, $R=0.20$, $i_f=11$, and $i_t=5$.