Phase-Field Simulation of Shape Evolution and Bimodal Size Distribution of Self-Assembled Quantum Dots

The strain-induced self-assembly of islands in heteroepitaxial systems is a promising approach to the fabrication of quantum nanostructures for optoelectronic devices. In this study, a phase-field model which can simulate the growth process of self-assembled SiGe/Si quantum dots during deposition is developed. The novel feature of this model is that it can simulate the morphological changes of islands, i.e., from single-faceted pyramid to multifaceted dome, by taking a high anisotropy and a sixteen-fold anisotropy of surface energy into account. By using the developed model, two-dimensional simulations are performed on a large computational model. As a result, island nucleation on the surface of a wetting layer, island morphological change and Ostwald ripening due to an interaction between two neighbor islands were well reproduced. The bimodal distribution of island size, which is a very important phenomenon in self-assembled quantum dots, could also be generated. Furthermore, it is clarified that the bimodal distributions are largely affected by island morphological change from pyramid to dome. The variations of island size and energy variations are estimated for single island in detail. As a result, it is concluded that the island morphology transitions occur so as to reduce the elastic strain energy.