Spatial correlation of self-assembled isotopically pure Ge/Si(001) nanoislands

By using a statistical method based on Voronoi tessellation, we investigated the nucleation of strain-driven self-assembled Ge/Si(001) nanoislands and their dynamic interaction with the local environment. The evolution of the composition and strain during the growth process was also studied by Raman scattering. The use of isotopically purified ${}^{76}\text{G}\text{e}$ source allows the observation of faint features in the three-dimensional nanoisland Raman signal at the early stage of the growth. The nucleus critical sizes are deduced from the scaling behavior of the Voronoi cell areas and the grown island volumes. The relatively small critical size suggests a stabilizing role of Si atoms and surface imperfections. Additionally, we found that the nucleation process on the metastable two-dimensional layer cannot only be described by the capture of newly deposited Ge atoms, but it is strongly governed by the diffusive interaction with the SiGe alloyed layer.

Figure 1

(Color online) Distributions of the island volumes as a function of the corresponding Voronoi cell areas at 0.2, 0.4, 0.6, 0.8, 1.0, and 2.0 ML. The insets display AFM images $\left(1\times 1\mu {\text{m}}^2\right)$ for the Ge deposition of 0.2, 0.8, and 2.0 ML. The network superimposed on AFM images shows the Voronoi tessellation calculated from the center of each island. The horizontal dotted line shows the critical volume of $V_c=1.2\times {10}^4{\text{nm}}^3$ separating between small pyramids and large domes. The solid lines are the best linear fits to obtain the correlation coefficients. The vertical broken line denotes the average Voronoi cell area at the steady-state regime.

Figure 2

Evolution as a function of the coverage of: (a) the correlation coefficient $r$; (b) the island density; (c) the Ge content; (d) the Si content; and (e) the compressive biaxial strain (solid circles). Open circles in (c) and (d) show the total amounts of Ge and Si atoms in 3D islands calculated from the effective thickness on the wetting layer. The broken line in (c) shows the amount of deposited Ge atoms.

Figure 3

(Color online) (a) Scaled distributions of Voronoi cell areas (vertical bars) fitted to two different scaling functions of the SGD (solid curves) and the GWD (short-broken curves), and scaled distributions of the experimental island size (open circles) in the submonolayer deposition range of 0.2, 0.8, and 1.0 ML on the wetting layer. $x$ is the Voronoi cell area scaled with its average area, and $y$ is the island volume scaled with its mean value. (b) Average area of the Voronoi cells (solid circles) and both coefficients of $\alpha$ (open downward triangles) and $\beta$ (open upward triangles) as a function of Ge amount deposited on the wetting layer.

Figure 4

Raman spectra obtained for different ${}^{76}\text{G}\text{e}$ deposition amounts on the wetting layer. All spectra are normalized to the Si-Si mode of the substrate. For comparison, Raman spectrum of the wetting layer having the critical thickness (the bottom spectrum) is overlapped as the dotted curves with each spectrum.