On the energetic origin of self-limiting trenches formed around Ge∕Si quantum dots

At high growth temperatures, the misfit strain at the boundary of Ge quantum dots on Si(001) is relieved by formation of trenches around the base of the islands. The depth of the trenches has been observed to saturate at a level that scales linearly with the base-width of the islands. Using finite element simulations, we show that this self-limiting behavior is consistent with the energetics of trench formation that involves a competition between the relaxation of the strain energy at the base of the island and the energy cost for creating the trench surface. The close quantitative agreement of the computed trench depths with the experimental measurements of Chaparro et al. [Appl. Phys. Lett. 76, 3534 (2000)] suggests an energetic rather than kinetic origin for the observed saturation behavior.