Influence of surface energy anisotropy on the dynamics of quantum dot growth

We investigate the influence of surface energy anisotropy on the dynamics of quantum dot growth by looking at the long-time dynamics of the morphological (Asaro-Tiller-Grinfeld) instability of a strained thin film driven by surface diffusion during growth and annealing. We derive a continuum model accounting for anisotropic surface energy, wetting, and elastic energies. We obtain a nonlinear nonlocal evolution equation for the film height in the small-slope approximation which we solve numerically given a gamma plot of the surface energy based on experimental properties of silicon-germanium films. A small anisotropy induces a complete change in the coarsening dynamics. The noninterrupted coarsening (Ostwald ripening) at stake for isotropic strained films is destroyed by anisotropy and the system is glued in metastable states. We characterize the statistical properties of the resulting pyramids and show that both their density and mean volume can increase with the total amount of matter. We find an optimal mean film height at which the island size distribution is peaked. These results indicate that different island density or volume may be obtained by varying solely the quantity of matter. Finally, we present an energetic model which describes energetic pathways along which ripening can indeed be suppressed.