Breaking Elastic Field Symmetry with Substrate Vicinality

We present a novel approach to engineer the growth of strained epitaxial films based on tailoring the elastic-interaction potential between nanostructures with substrate vicinality. By modeling the island-island interaction energy surface within continuum elasticity theory, we find that its fourfold symmetry is broken at high miscuts, producing directions of reduced elastic-interaction energy. As a consequence, it is possible to direct the Ge island growth on highly misoriented Si(001) substrates towards desired pathways.

Figure 1

(a) Interaction energy surface of Ge domes on the flat Si(001) surface and (b) corresponding contour plot. (c) Interaction energy surface of Ge domes on 10°-miscut Si(001) surface and (d) corresponding contour plot. Angular distribution of impingement directions measured (e) on 8°-miscut Si(001) substrates and (f) on 10°-miscut Si(001) substrates at 7.5 ML of Ge coverage.

Figure 2

(a) Shape evolution of Ge islands on flat (●), 8°-miscut (★), 10°-miscut (▪) Si(001) surface. The dashed lines show the $h/b$ linear dependence for different aspect ratios. In the inset, the morphology of the domes on flat and misoriented substrates is sketched. STM images at 7.5 ML of Ge coverage: (b) Ge superdomes on the flat Si(001) surface. A coalescence event is highlighted by a white circle. (c) Later stage of coalescence. Typical morphology of a superdome formed by (d) coarsening and (e) coalescence on the flat surface. Line scans along the [110] direction of superdomes formed (f) by coarsening and (g) by coalescence.

Figure 3

STM images at 7.5 ML of Ge coverage: (a)–(b) Formation of Ge superdomes by coalescence on the 8°-miscut Si(001) surface. (c)–(d) Ge superdomes presenting the typical wedge defect after coalescence.

Figure 4

STM images: (a)–(b) Formation of Ge superdomes by coalescence on the 10°-miscut Si(001) surface at 7.5 ML of Ge coverage. (c) Highly dislocated Ge islands after coalescence at 8 ML of Ge coverage. (d) Same sample of panel (c) after 30 min annealing at $720°\mathrm{C}$: flat-top superdomes are formed.