How pit facet inclination drives heteroepitaxial island positioning on patterned substrates

We demonstrate the possibility of growing SiGe islands on patterned Si(001) substrates with pits having a continuous variation of the sidewall inclination angle α from α ∼ 4° to α ∼ 54°. Experiments show that the pit-inclination angle critically affects island positioning. While for shallow pits (pit-sidewall inclination angle α < ∼30°) islands are observed solely within the pits, at higher angles islands grow outside the pits. In particular a progressive (complete at α ∼ 54°) decoration of the pit rim by several islands is observed. We use elasticity theory to compare strain relaxation of a single island inside and outside the pit, as a function of α. The theoretical results show that there exists an elastic driving force for island positioning inside shallow enough pits, which reaches its maximum at α ∼ 20° and changes sign for α > 40°. At the same time, the calculations indicate a progressive relaxation of the wetting layer (WL) outside the pit with increasing α. The consistency between numerical results and experimental observations gives a clear indication on the important role played by the elastic relaxation in this system.

Figure 1

Evolution of the pit-mediated island-nucleation behavior with increasing pit angle (α). (a)–(k) 3D AFM images (left) and surface inclination maps (right) of the pits with inclination angles ranging from (a) α = 5.4° to (k) α = 54.7°. The number in the surface inclination maps represents α. While for α < 32° island nucleation occurs inside the pit, for α > 32° islands nucleation is observed around the pit. The color bar represents the local surface slope with respect to the (001) surface. In the bar the known SiGe island facets [{105} (α = 11.3°); {113} (α = 25.2°); {15 3 23} (α = 33.6°); {20 4 23} (α = 41.6°); {23 4 20} (α = 49.4°); {111} (α = 54.7°)] are marked.

Figure 2

(a), (b) Schematic representation of a dome island positioned inside a pit. (a) It is shown that the island inside the pit is composed by a dome sitting on top an IP. (c) A dome positioned at edge position is sketched. In the actual calculations both the lateral and the vertical substrate dimensions were set to 11 times the pit size.

Figure 3

(a) Dependence of the elastic relaxation of a dome island inside a pit on both the pit-inclination angle α and on the degree of pit filling. The filling is measured in terms of the covered depth of the pit. (b), (c), (d) Color maps of the elastic energy distribution in a pit with α = 30° for (b) 0.25, (c) 0.75, and (d) full filling. Panel (e) shows the comparison between the elastic energy densities of the IP+dome structure for Ge contents of x${}_{\mathrm{Ge}}$ = 1 and x${}_{\mathrm{Ge}}$ = 0.35. Both quantities are normalized to the elastic energy of a dome with the same Ge content on flat Si(001).

Figure 4

(a) Elastic-energy density, normalized to the one of a Ge dome on flat Si(001), for the two alternative configurations considered in Fig. 2. While the elastic energy for the edge position (dashed blue curve) continuously decreases with α, the elastic energy for the dome inside the pit (red solid curve) decreases up to α = 20° and then increases to values even higher than on the flat substrate. The calculations for the edge position were made with an island-base size of 1/4 the pit size; calculations repeated halving and doubling the island size did not produce any significant change in the results. Elastic-energy maps for a dome on a flat substrate for a dome inside a shallow pit (α = 20°) and inside a steep pit (α = 60°) are shown in panels (b), (c), and (d), respectively, demonstrating the lower degree of elastic relaxation for islands located inside steep pits compared to shallow ones.

Figure 5

Elastic-energy density normalized to the one of tetragonally strained Ge (ρ${}^{\mathrm{T}}$) for an IP half filling a pit as a function of the pit-inclination angle α.

Figure 6

Side-view color maps of the elastic-energy density of a Ge-pure WL covering (a) a pit with α = 8.1° and (b) a pit with α = 54.7°. The comparison shows that while the elastic relaxation of the WL at the rim of a shallow pit is negligible, the relaxation at the rim of a steep pit is rather significant.