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

TL;DR

This paper investigates the formation of trenches around Ge quantum dots on Si(001), revealing that their self-limiting depth results from a balance between elastic relaxation energy and surface energy costs, supported by simulations matching experimental data.

Contribution

It introduces a finite element simulation model that explains the energetic origin of self-limiting trenches around Ge/Si quantum dots, aligning with experimental observations.

Findings

Trench depth saturates depending on island base-width.

Trench depth increases linearly with island radius.

Simulation results agree quantitatively with experiments.

Abstract

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 depends on the base-width of the islands. Using finite element simulations, we show that the self-limiting nature of trench depth is due to a competition between the elastic relaxation energy gained by the formation of the trench and the surface energy cost for creating the trench. Our simulations predict a linear increase of the trench depth with the island radius, in quantitative agreement with the experimental observations of Drucker and coworkers.