Self-assembled nanorings have recently been identified in a number of heteroepitaxially 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 nanostructures beyond the small slope assumption is developed. This model is then used to investigate the stability of strained nanorings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. The model predicts a region of stability for rings below a critical radius, and also a region for larger rings which have a proportionally small thickness. The predictions of the model are shown to be consistent with the available results. For the heteroepitaxial InP on In 0.5 Ga 0.5 P system investigated by Jevasuwan et al. (2013) , the nanorings are found to be stable below a certain critical size. This is in good quantitative agreement with the model predictions. At larger sizes, the rings are unstable. The number of dots in the resulting quantum dot molecule is similar to the mode number for the fastest growing mode. Second order terms show that the number of dots is expected to reduce as the height of the ring increases in proportion to its thickness. The strained In 0.4 Ga 0.6 As on GaAs nanorings of Hanke et al. (2007) are always stable and this is in accordance with the findings of the analysis. The Au nanorings of Ruffino et al. (2011) are stable as well, even as they expand during annealing. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of heteroepitaxial systems for the self-organisation of quantum dot molecules. • Epitaxially strained, semiconductor nanorings have been observed to break-up into discrete mounds forming a so-called quantum dot molecule. • The non-linear, second order elastic strain energy of a generalised in-plane surface traction expressed in polar coordinates acting on an isotropic half-space is derived. • This is used to determine the stability of nanorings subject to circumferential perturbations. • Stability maps show that nanorings below a certain radius or thickness are always stable. • The growth mode of unstable perturbations is shown to closely correlate with the observed number of mounds in observed quantum dot molecules.
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