Alloyed $\mathrm{Ge}\left(\mathrm{Si}\right)∕\mathrm{Si}\left(001\right)$ islands: The composition profile and the shape transformation

Atomistic simulations combining a Monte Carlo algorithm and molecular static relaxations were carried out to predict the alloying profile in pyramid and dome shaped $\mathrm{Ge}\left(\mathrm{Si}\right)∕\mathrm{Si}\left(001\right)$ islands. The results show that the composition profile is dominated by the surface segregation of Ge and segregation of Si to the substrate island interface. Within the interior of the island the composition profile is found to be uniform. An analysis of the energetics of the alloying shows that at typical growth temperatures, the lowering of the energy achievable through the formation of a nonuniform alloying profile would be too small to overcome the tendency towards randomization driven by the entropy of mixing of the system. The shape transformation from the pyramid to the dome shape is shown to be predicted accurately by the modeling.

Figure 1

(Color online) The distribution of Ge and Si in pyramid and dome shaped islands calculated at a temperature of 900 K at a concentration of 33% Ge, 50% Ge, and 66% Ge in the island. The steps on the surface of the islands represent surface steps in the atomistic model.

Figure 2

(Color online) (a) and (c) show the composition in shells parallel to the island surface for pyramids and domes respectively. (b) and (d) show the composition in layers parallel to the substrate–island interface for pyramids and domes, respectively.

Figure 3

(Color online) The composition profile on a cutting plane through the center of a dome shaped island with an average Ge content of 50% at a temperature of 8 K.

Figure 4

The strain energy density for a range of compositions calculated for pyramids and domes, using finite element analysis (FEA), and from the atomistic models with uniform and nonuniform composition profiles (before and after compositional equilibration).

Figure 5

The average probability to accept an unfavorable step if the energy difference equals the average strain energy is shown as a function of temperature for two different lattice mismatches.

Figure 6

(Color online) The critical pyramid side length for different aspect ratios of the dome shape and a comparison with experimental data (Ref. 39, 40).

Figure 7

(Color online) The dependence of the critical pyramid size on the surface composition and the surface reconstruction [values for the {001} surface from Stekolnikov et al. (Ref. 37)].