Diffusion Dynamics during the Nucleation and Growth of $\mathrm{Ge}/\mathrm{Si}$ Nanostructures on Si(111)

We report a low energy electron microscopy study of the relation between self-organized $\mathrm{Ge}/\mathrm{Si}(111)$ nanostructures and their local environment. By comparison with Monte Carlo simulations, three-dimensional islands are shown to display a substantial tendency towards self-ordering. This tendency may result from the diffusive nature of the nucleation processes. The size of individual nanostructures does not significantly correlate with the distance between neighboring islands. Thus energetic factors are thought to govern the competition among coexisting nanostructures to capture the deposited mass.

Figure 1

$2.6\times 2.6\mu {\mathrm{m}}^2$ LEEM image of a sample prepared by depositing 10 ML Ge on a clean Si(111) substrate kept at 400 °C. Black lines indicate the perimeters of the Voronoi tessellation as associated with the positions of the centers of mass in the islands’s distribution. White dotted lines enclose the areas of individual 3D structures.

Figure 2

Selected values of $\Im$ at different $\sigma$, showing the statistics of the Voronoi cell areas at given amounts of order. The panels at the left display selected examples of the probability distributions employed to generate the quasihexagonal arrangement of islands in our MC simulations.

Figure 3

Comparison between the experimental distributions (ticks on the horizontal axis), the random limit (light shadowed curves), and the best fits to the function of $\sigma$ (continuous dark gray lines). The right panel displays the dependence of the distortion parameter $\sigma$ on $T$.

Figure 4

Relationship between the island areas and the relevant Voronoi cell areas. Although the linear parameter $b$ is positive at every $T$ (as shown by the 99.73% confidence bands superimposed on the image), Pearson’s $r$ is consistently indicative of a poor correlation (the value $r=0.92$ was calculated by comparing islands grown at different $T$). The lower panel displays the behavior of the linear coefficient $b$ (slope of the linear fit) and of $r$ as a function of $T$.