Thermodynamic theory of shape evolution induced by Si capping in Ge quantum dot self-assembly

A quantitative thermodynamic theory has been established to investigate the shape evolution mechanisms induced by Si capping in Ge quantum dot self-assembly. It was found that the decrease in Ge concentration of the quantum dot induced by Si absorption breaks the original balance of composition between the quantum dot and wetting layer. In order to create a new balance, the wetting layer is required to increase its thickness through the Ge diffusion from the quantum dot to the wetting layer, which leads to the shape evolution of the growing quantum dot. The Ge diffusion can suppress the expansion of quantum dots and promote their shrinkage. The theoretical results not only are in well agreement with the experimental observations but also reveal physical mechanisms involved in the Ge quantum dot self-assembly induced by Si capping, which implies that the established thermodynamic theory could be expected to be applicable to address the capping-assisted self-assembly of quantum dots.