In situ x-ray scattering study on the evolution of Ge island morphology and relaxation for low growth rate: Advanced transition to superdomes

The kinetics of the growth of Ge superdomes and their facets on Si(001) surfaces are analyzed as a function of deposited Ge thickness for different growth temperatures and at a low growth rate by in situ grazing-incidence small-angle x-ray scattering in combination with in situ grazing-incidence x-ray diffraction. At a low growth rate, intermixing is found to be enhanced and superdomes are formed already at lower coverages than previously reported. In addition, we observe that at the dome-to-superdome transition, a large amount of material is transferred into dislocated islands, either by dome coalescence or by anomalous coarsening. Once dislocated islands are formed, island coalescence is a rare event and introduction of dislocations is preferred. The superdome growth is thus stabilized by the insertion of dislocations during growth.

Figure 1

GIXD data: radial scans along the $⟨h0l⟩$ direction, with $l=0.04$, in the vicinity of the Si(400) reflection, for different Ge depositions indicated in the graphs in equivalent monolayers (ML). The vertical lines show the position of the bulk Si(400) and Ge(400) Bragg peaks. The growth temperatures are( a) 773 K (from 0 to 10.3 ML), (b) 823 K (from 0 to 11.1 ML), (c) 873 K (from 0 to 10.3 ML), and (d) 923 K (from 0 to 11.1 ML).

Figure 2

(Color online) GISAXS intensity maps along the [110] azimuth obtained at growth temperatures of (a) 773, (b) 823, (c) 873, and (d) 923 K; the numbers denote the number of deposited Ge monolayers, the arrows are along $⟨113⟩$ (full arrows) and $⟨111⟩$ (dashed arrow).

Figure 3

(Color online) GISAXS intensity maps along the [15 3 0] azimuth obtained at growth temperatures of (a) 773, (b) 823, (c) 873, and (d) 923 K; the numbers denote the number of deposited Ge monolayers, the arrows are along $⟨15323⟩$ (full arrows) and $⟨20423⟩$ (dashed arrow).

Figure 4

(Color online) [(a)–(d)] Four scattering processes in GISAXS. ${\mathbf{K}}_{i,f}$ are the wave vectors of the primary and scattered beams, respectively. (e) Schematic drawing of islands and their corresponding GISAXS intensity map. The width of the streak is inversely proportional to the facet size $L$.

Figure 5

(Color online) (a) AFM images of samples obtained after the deposition of 10–11 ML of Ge at (a) 823, (b) 873, and (c) 923 K, on a large scale, showing the presence of two island “families” with different mean sizes. (d) AFM zoom of a superdome island grown at 873 K. The measured mean sizes of {113} and {15 3 23} facets are $\sim 145$ and $\sim 92\text{nm}$, respectively. They correspond to the simulated values observed in Figs. 8a, 8b. (e) AFM histogram of the equivalent radii of the islands obtained from the island-projected area and (f) AFM histogram of the island heights as a function of the growth temperatures.

Figure 6

(Color online) (a) GISAXS image (azimuth [110], $\theta =10$ ML), from which the line scans in panels (b) and (c) are extracted along the $Q_{\parallel }$ and $Q_{\perp }$ axes. (b) The linear scan extracted from the GISAXS intensity map across the {113} facet streak (points) and its fit by a sum of three $f\left(Q_{\parallel }\right)$ functions (see text); the inset shows the tail of this line scan in a log-log representation. (c) Line scan along the facet streak. From (b) and (c), the $Q_{\perp }^{-2}$ and $Q_{\parallel }^{-3}$ slopes are visible.

Figure 7

(Color online) (a) FEM simulation of the in-plane deformation ${ϵ}_{xx}$ in the island and the Si substrate underneath the island (with respect to Si bulk) in a 100-nm-large dome of pure Ge without dislocations. ${ϵ}_{xx}=4.2\%$ means that Ge atoms are no more strained. In the region of the Si substrate, where ${ϵ}_{xx}<0\%$, the Si lattice is compressed and where ${ϵ}_{xx}>0\%$, the Si lattice is expanded. (b) Experimental and simulated scattered intensities. Finite element simulations of the strain state of coherent dome-shaped islands, and the corresponding simulation of the scattered intensity around the (400) reciprocal-lattice point show that their lattice parameter is much closer to that of Si than experimentally observed.

Figure 8

The dependence of the mean facet sizes $L_0$ on the nominal coverage $\theta$ of the number of the deposited Ge monolayers is shown for the (a) {15 3 23} and (b) {113} facets, respectively. Above 6 ML at 923 K and 6.9 ML for the three other growth temperatures, the data were fitted to a $B{\left(\theta -{\theta }_c\right)}^{1/3}$ function (full lines).

Figure 9

(Color online) Experimental anomalous x-ray diffraction data $\left({\sqrt{I}}_{\text{exp}}\right)$ measured at two energies ($11033$ and $11103\text{eV}$), and Ge and Si structure factors ($F_{\text{Ge}}$ and $F_{\text{Si}}$) calculated from the experimental anomalous x-ray diffraction data. The curves are plotted as a function of lattice parameter for a growth temperature of 873 K, a deposit of 8 ML, and for two growth rates: (a) 0.023 and (b) 0.003 ML/s. (c) Ge content of the islands determined from the ratio of the Ge and Si structure factors versus in-plane lattice constant.

Figure 10

Evolution of the critical coverage $\theta$, for which dislocations appear, as a function of (a) flux $F$ and (b) growth temperatures. The dashed and full lines in (a) indicate the growth rates used in this work and the one used in Ref. 14, respectively.