Colloquium: Cluster growth on surfaces: Densities, size distributions, and morphologies

Understanding and control of cluster and thin-film growth on solid surfaces is a subject of intensive research to develop nanomaterials with new physical properties. In this Colloquium a review of basic theoretical concepts to describe submonolayer growth kinetics under nonequilibrium conditions is given. It is shown how these concepts can be extended and further developed to treat self-organized cluster formation in material systems of current interest, such as nanoalloys and molecular clusters in organic thin-film growth. The presentation is focused on ideal flat surfaces to limit the scope and to discuss key ideas in a transparent way. Open experimental and theoretical challenges are pointed out.

Figure 1

Illustration of (a) elementary moves during growth after deposition onto a surface and (b) the Ehrlich-Schwoebel barrier for crossing the step edge.

Figure 2

AFM images of ${\mathrm{C}}_{60}$ molecules on ${\mathrm{CaF}}_2(111)$ at a coverage $\Theta =0.1$ for different substrate temperatures between 96 and 217 K. From 80.

Figure 3

Island densities of Ag on Pt(111) at coverages $\Theta =0.12$ in an Arrhenius plot. Analysis of the slope with Eq. (6a) in the low-temperature regime, where $i=1$, gives a diffusion barrier $U=0.168\pm 0.005\mathrm{eV}$. In the high-temperature regime, where $i=2$, the slope yields a dimer bonding energy $E_2=0.15\pm 0.02\mathrm{eV}$. From 16.

Figure 4

Simulated number densities $N$ of stable islands at coverage $\Theta =0.1$ as a function of $D_B/F$, when $AA$ dimers are stable, while $AB$ and $BB$ dimers are unstable. The solid lines correspond to the full solution (14) and the dashed lines indicate the change of scaling behavior associated with the dimer and trimer nucleation routes. From 38.

Figure 5

Number densities of $A$ and $B$ adatoms, $AA$ dimers, and stable islands as a function of the coverage $\Theta$ for a case of mixed dimer stabilities, where $AA$ dimers are stable, while $AB$ and $BB$ dimers are unstable with zero binding energies. Results from the self-consistent approach (solid lines) are compared with KMC simulations (symbols). Parameters are $x_A=x_B=1/2$, $D_A/F={10}^8$, and $D_B/F={10}^7$.

Figure 6

(a) Capture numbers and (b) island size distributions from KMC simulations of kinetic growth with hit-and-stick aggregation on a (100) surface. In (a) the open circles refer to the prediction of the self-consistent theory for $\Theta =0.1$ and $\Gamma ={10}^7$, which for large $s$ deviate strongly from the true ${\sigma }_s(\Theta ,\Gamma )$ (full circles). In (b) the solid lines are the solution of the rate equation (2) with the simulated ${\sigma }_s(\Theta ,\Gamma )$ as input. From 66.

Figure 7

Fraction of covered islands after deposition of 10% of a monolayer of Ag on a Pt(111) surface with size-tailored islands of mean radius $R_0$ at three different temperatures ($i=1$). The symbols refer to the measured data by 14, and the solid and dashed lines (almost identical) refer to fits with the second-layer nucleation theory under neglect [see Eq. (29) or (30)] and inclusion of additional ring barriers between mutually approaching adatoms, respectively. From 56.

Figure 8

STM image of mound formation of Pt after deposition on Pt(111). From 72.

Figure 9

(a) Sketch of atomic movements and energy barriers involved in diffusion processes along and between island edges of $A$ and $B$ type on a (111) surface. (b) Simulated island shapes for $T=300\mathrm{K}$, $F={10}^{-3}\mathrm{ML}/\mathrm{s}$, and the barrier for edge diffusion $E_{\mathrm{edge}}$ decreasing from left to right. In the upper panel, corner diffusion is anisotropic with $E_{\mathrm{c}B}=0.1<E_{\mathrm{c}A}=0.25\mathrm{eV}$, while in the lower panel, corner diffusion is symmetric with $E_{\mathrm{c}B}=E_{\mathrm{c}A}=0.11\mathrm{eV}$. Adapted from 95.

Figure 10

(a)–(c) AFM images of ${\mathrm{C}}_{60}$ islands on ${\mathrm{CaF}}_2(111)$ at three different growth temperatures. (d)–(f) Magnified images of single islands: a compact triangle (d), and hexagonal islands with morphologies I (e) and II (f). (g), (h) Height profiles along line scans shown in (d) and (e). From 67.

Figure 11

Sketch of elementary upward jump processes facilitating the growth of a double-layer triangle. The processes at the $A$ step and the corner between the $A$ and $B$ step involve only two ${\mathrm{C}}_{60}$ and are, therefore, more likely than the process at the $B$ step involving three ${\mathrm{C}}_{60}$ molecules. From 67.

Figure 12

Chemical order for ${\mathrm{CoPt}}_3$ clusters (grains) grown on ${\mathrm{WSe}}_2(0001)$ and ${\mathrm{CoPt}}_3$ films grown on Pt(111) as a function of the growth temperature. $L{1}_2$-type ordering sets in below the bulk disorder or order transition temperature $T\simeq 686°\mathrm{C}$, and vanishes at lower temperatures when the bulk kinetics becomes frozen. For clusters, the vanishing of $L{1}_2$-type ordering occurs at a lower temperature because atomic rearrangements at the advancing surface allow some degree of chemical order in the interior to be built. The occurrence of PMA is schematically indicated for both clusters and films. Adapted from 82.

Figure 13

Sketch of changes in the structure and shape of binary alloy nanoclusters (e.g., ${\mathrm{CoPt}}_3$) with temperature. Atoms of the two components are marked (light) (e.g., Co) and (dark) (e.g., Pt), where the latter tend to segregate at the cluster surface. With increasing $T$ the fraction of side facets increases relative to the top facet and the surface segregation becomes stronger. The two competing effects for PMA lead to a temperature window of its occurrence.

Figure 14

Magnetic anisotropy energies $E_{\mathrm{tot}}$ (solid line), $E_{\mathrm{str}}$ (dotted line), and the chemical order parameter (dash-dotted line) vs temperature of simulated ${\mathrm{CoPt}}_3$ nanoclusters with 1000 atoms for strong surface segregation of Pt ($V_{\mathrm{PtPt}}-V_{\mathrm{CoCo}}=180\mathrm{meV}$) and high exchange rates of Co and Pt at the cluster surface. Adapted from 55.