Morphological stability analysis of the epitaxial growth of a circular island: Application to nanoscale shape control

In this paper, we present a comprehensive morphological stability analysis of a single, epitaxially growing, perturbed circular island by using a Burton–Cabrera–Frank (BCF) island dynamics model. We show that there exists a critical deposition flux for which a single mode perturbation remains unchanged. In the absence of an additional far-field mass flux, there exists a naturally stabilizing radius, so that beyond this radius, growth is always stable. Up to this radius, taking fluxes larger than the critical flux results in instability. The presence of kinetics makes sufficiently small islands grow stably, even without line tension or surface diffusion. The presence of desorption further introduces a range of parameters and island radii for which both stable and unstable shrinkage may occur. The presence of a far-field mass flux in the BCF model can eliminate the naturally stabilizing radius and unstable growth may be achieved for a wide range of island radii. We then demonstrate how these results may be exploited to control the shape of the island using the deposition flux and far-field mass flux as control parameters.