The stability of elastically strained nanorings and the formation of quantum dot molecules

Self-assembled nano-rings have recently been identified in a number of hetero-epitaxially strained material systems. Under some circumstances these rings have been observed to break up into ring-shaped quantum dot molecules. A general non-linear model for the elastic strain energy of non-axisymmetric epitaxially strained nano-structures beyond the small slope assumption is developed. This model is then used to investigate the stability of strained nano-rings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of hetero-epitaxial systems for the seif-organisation of quantum dot molecules.