Formation of Ge Nanoripples on Vicinal Si (1110): From Stranski-Krastanow Seeds to a Perfectly Faceted Wetting Layer

Ge growth on high-indexed Si (1110) is shown to result in the spontaneous formation of a perfectly $\{105\}$ faceted one-dimensional nanoripple structure. This evolution differs from the usual Stranski-Krastanow growth mode because from initial ripple seeds a faceted Ge layer is formed that extends down to the heterointerface. Ab initio calculations reveal that ripple formation is mainly driven by lowering of surface energy rather than by elastic strain relief and the onset is governed by the edge energy of the ripple facets. Wavelike ripple replication is identified as an effective kinetic pathway for the transformation process.

Figure 1

STM images of Ge on Si (1110) deposited at $550°\mathrm{C}$ recorded at coverages of (a) 3.7 ML, (b) 4.0 ML, and 4.5 ML for (c) and (d). Note the different scale of the images. The insets in (a) and (c) depict the surface orientation maps (SOM) calculated from larger STM images, revealing complete $\{105\}$ facetation of the Ge surface at thicknesses exceeding 4.2 ML. Only isolated mounds and preripples are seen for lower coverages. The insets in (b) and (d) show the 2D FFT power spectra of the STM images. For the perfectly faceted Ge surface at 4.5 ML, FFT satellite peaks (indicated by circles) up to the second order are observed.

Figure 2

(a) RHEED intensity of the specular spot (SS, blue line) and a facet diffraction spot (FS, black line) plotted as a function of Ge coverage on Si (1110), indicating an abrupt morphological transition at a critical coverage of 4.2 ML. RHEED patterns recorded at different coverages are shown in (b) to (d). The schematic illustration of the flat 2D wetting layer (WL) and the perfectly faceted (PF) ripple surface are shown in (e) and (f), respectively. Panel (g) shows the evolution of the surface profile along [$-110$] as a function of Ge coverage. The shaded regions below the profiles represent the respective total Ge amount deposited in each case and the horizontal dashed lines the location of the $\mathrm{Ge}/\mathrm{Si}$ heterointerface. For clarity, the profiles are offset in the vertical direction.

Figure 3

Energy difference $\Delta E_{\mathrm{tot}}/L-3\Gamma (=\Delta E_{\mathrm{vol}}/L+\Delta E_{\mathrm{surf}}/L)$ calculated using Eqs. (2, 3) between an infinitely long $\{105\}$ faceted ripple on a $N$ ML thick WL and the $N+1$ ML thick 2D WL with the same volume plotted as a function of ripple base $b$ at different coverages $N$ (left axis). The horizontal line represents the value of $-E_{\mathrm{edge}}/L=-3\Gamma =-370\mathrm{meV}$ obtained by comparison with experiments (vertical shaded bar). The right-hand axis shows the total energy $\Delta E_{\mathrm{tot}}/L$ of the system using this value.

Figure 4

(a) Wave propagation mechanism starting from an isolated ripple (top) on a WL, creating first two asymmetric satellites (middle) with satellite base $b_2$, finally leading to full faceting (bottom). (b) Energy difference between the configurations of the single ripple with $b_1=10\mathrm{nm}$ and the ripple with two satellite ripples as a function of the final satellite base $b_2$ for different $N$ values.