During epitaxial growth, a strained film may relax its strain energy by surface roughening. Recently this mechanism has attracted significant attention since it can be potentially used to grow self-organized quantum dots. A great deal of experimental effort has been devoted to achieving uniform and regular quantum dots, and has revealed tremendous complexity and richness of the processes. Yet to achieve uniform and regular 3D quantum dot arrays through self-organization is still a challenging issue.
We have developed a 3D finite element method to simulate the morphological evolution of a strained film via surface diffusion, with an aim to understanding the self-organization, shape transitions and stability of quantum dots. We model deposition of films on a large lattice mismatched substrate. The film surface diffusion is driven by the gradient of the surface chemical potential, which includes the elastic strain energy, elastic anisotropy, surface energy anisotropy and the interaction between the films and the substrate. For in-plane growth, our simulations reveal that both surface energy anisotropy and elastic anisotropy have a strong effect on the self-organization and shape transitions of the quantum dots. With properly chosen surface energy form, the islands may self-organize into a meta-stable state with relatively uniform island size and spacing. With strong elastic anisotropy, the dots may align up along specific directions. For out-of-plane growth, our simulations demonstrate that the spacer layer thickness and interruption time are crucial for achieving different stacking schemes of quantum dots. In particular, with properly chosen system parameters, after a few layers of growth, the top dots self-organize into an almost perfectly uniform and regular array. Finally the simulation results are compared with experimental results and the potential ways in achieving uniform and regular quantum dot arrays are discussed.