Anomalous Smoothing Preceding Island Formation During Growth on Patterned Substrates

We show that on suitably pit-patterned Si(001), deposition of just a few atomic layers of Ge can trigger a far larger flow of Si into the pits. This surprising effect results in anomalous smoothing of the substrate preceding island formation in the pits. We show that the effect naturally arises in continuum simulations of growth, and we identify its physical origin in the composition dependence of the surface diffusivity. Our interpretation suggests that anomalous smoothing is likely to also occur in other technologically relevant heteroepitaxial systems.

Figure 1

AFM images of patterned substrates showing (a,b) pit array, and (b,c) enlarged view of single pit. Images (a) and (c) are obtained after the deposition of 50 nm of Si buffer, and (b,d) after the subsequent deposition of 3.5 ML of Ge at $720°\mathrm{C}$. The corresponding distribution of surface orientations (e,f) shows which facets are present. (g) AFM linescans passing through pit centers along the [110] direction, for pits shown in (a) and (b). Vertical offset between curves is arbitrary.

Figure 2

(a) Decay of surface corrugation amplitude during Ge deposition. The solid red curve is the full calculation. The dashed curve shows the behavior if we omit the dependence of energy barriers on local composition; omitting Ge surface segregation but including the $c$ dependence gives the dotted curve. Results for $\mathrm{Si}/\mathrm{Si}$ and $\mathrm{Ge}/\mathrm{Ge}$ are shown (labeled) for reference. (b) Evolution of composition of the topmost monoatomic layer during growth. Curves show the behavior including or omitting surface segregation as in (a). (The surface composition is uniform to within 1% across the surface; the average is shown.) (c) Pit profile and composition map after the deposition of 3.5 ML of Ge. (In showing the surface region we exclude the topmost atomic layer, which is roughly 85% Ge.) (d) Same result but assuming a lower value of the Ge diffusion barrier. For reference, the initial pit profile is included as a line in (c) and (d). Misfit strain has been neglected.

Figure 3

Evolution of the pit profile for later stages of Ge deposition comparing the cases (a) without misfit strain and (b) including misfit. The grayed area represents the initial cosine pit profile.

Figure 4

Profile evolution including crystal anisotropy, starting with the same sinusoidal pit as before. (a) Evolution for pure Si. Annealing at $720°\mathrm{C}$ for 5 s gives a faceted profile. Other curves show the profile after the deposition of varying amounts of Si, as indicated, for comparison with Ge deposition. (b–d) Profile and composition maps at different stages of Ge deposition. For reference, the line shows the initial pit profile after annealing. (The topmost layer, $\sim 85\%$ rich in Ge, is not shown).