Growth of spatially ordered Ge nanoclusters in an amorphous matrix on rippled substrates

So far, the growth of spatially ordered nanoclusters by multilayer deposition has been reported and explained satisfactorily only in crystalline materials. Here we demonstrate a method for the growth of spatially ordered nanoclusters in amorphous matrices, where the ordering is achieved in the single large domain. The regular ordering is induced by the deposition of a multilayer on a periodically rippled substrate at an elevated substrate temperature. During the deposition, the nanoclusters self-arrange, following the morphology of the substrate.

Figure 1

(Color online) (a) The atomic-force microscopy picture of a rippled Si surface along with its Fourier transformation in the inset. (b) GISAXS intensity map of the rippled substrate.

Figure 2

(Color online) Structure of a $\left(\text{Ge}+{\text{SiO}}_2\right)/{\text{SiO}}_2$ multilayer deposited on a rippled Si substrate: (a) and (b) transmission electron micrographs of the cross sections of the multilayer taken in the directions across (denoted by $\perp$) and along $(\parallel )$ the ripples, respectively. The arrows indicate the direction of the correlation of the positions of the NCs in different multilayer periods. (c) and (d) Fourier transformations of the TEM images. (e) and (f) GISAXS maps measured on the multilayer containing ten periods in $\perp$ and $\parallel$ configurations, respectively. The arrow indicates a streak coming from the facets of the ripples. (g) and (h) Simulations of the GISAXS intensity distributions shown in (e) and (f), respectively.

Figure 3

(Color online) Schematic view of the arrangement of nanoclusters in the NC lattice formed on a rippled substrate. (a) In-plane view, direction $\parallel$ is set along the ripples; the projection of ${\mathit{a}}_3$ on the sample surface is shown by dashed arrow. To improve visualization, the NCs are shown by alternating rows of dark and light (blue and red online) spheres, directioned along the ripples. (b) and (c) Cross-sectional view showing projections of the positions of the NCs in directions parallel and perpendicular to the ripples direction, respectively. (d) Influence of the ripples morphology on the NC stacking. The asymmetric shape of the ripples described by the angles ${\alpha }_{1,2}$ of the ripple facets with the mean surface $\left({\alpha }_1\ne {\alpha }_2\right)$ causes stacking of NCs different from the expected $ABCABC$ stacking. The fcc-like $ABCABC$ stacking is indicated by dashed circles.

Figure 4

(Color online) Size distribution of the nanoclusters obtained for different growth types. The self-ordering growth is performed on the rippled (red line) and flat (blue line) substrate at $500°\text{C}$ while noncorrelated growth (green line) is realized at room temperature on the flat substrate. The insets show the GISAXS maps from which the size distributions were calculated.