Influence of Quantum Size Effects on Island Coarsening

Surface x-ray scattering and scanning-tunneling microscopy experiments reveal novel coarsening behavior of Pb nanocrystals grown on $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$. It is found that quantum size effects lead to the breakdown of the classical Gibbs-Thomson analysis. This is manifested by the lack of scaling of the island densities. In addition, island decay times $\tau$ are orders of magnitude faster than expected from the classical analysis and have an unusual dependence on the growth flux $F$ (i.e., $\tau \sim 1/F$). As a result, a highly monodispersed 7-layer island height distribution is found after coarsening if the islands are grown at high rather than low flux rates. These results have important implications, especially at low temperatures, for the controlled growth and self-organization of nanostructures.

Figure 1

Island density vs time demonstrates the breakdown of scaling: The curves do not approach each other at long times. These data were obtained from x-ray diffuse scattering measured after the deposition of 1.2 ML of Pb at 208 K for various deposition fluxes $F$. The solid curves are a fit to Eq. (1) with $\beta =1$. The inset shows that the initial island density $n_0$ depends only weakly on flux $n_0\propto F^{0.2}$, whereas the time constant changes quickly with flux $\tau \propto F^{-1}$.

Figure 2

STM images of the coarsening of 1.6 ML Pb deposited on $\mathrm{Si}(111)\mathrm{\text{−}}(7\times 7)$ at 203 K at a flux of $0.5\mathrm{ML}/\min$. The times after deposition are shown for each image. The scale is $250\times 250{\mathrm{nm}}^2$ for (a)–(c) and $500\times 500{\mathrm{nm}}^2$ for (d)–(f). The tunneling parameters were 2 V at 1 nA. Scans take 0.5 min each. The island height is marked on top of each island for (a), (d), and (f) (height is measured with respect to the Pb wetting layer [14].) It can be seen that 3-layer islands are less stable than 4-layer ones and both of these are less stable than 7-layer islands.

Figure 3

Histograms of the island height distribution for 1.6 ML grown at 203 K, measured 5 min after (black) and 74 min after deposition (cross-hatched). (a) shows a high flux rate deposition, $0.5\mathrm{ML}/\sec$, leading to a broad initial island height distribution with fast decay of unstable islands. (b) shows a low flux deposition, $0.05\mathrm{ML}/\min$, leading to a narrower initial island height distribution with little change over time.