Results

We are conducting the simulation on a thin film with thickness 10. The reasons we do not simulate from the substrate, i.e. the thin film thickness is 0, are the following:
In real experiments of QD growth, the very early stage of the material deposition does not involve the formation of islands. This is due to the wetting potential between the substrate atoms and the deposited atoms. The transition to island nucleation occurs after the atoms accumulate to a critical thickness.[6] And the processes after this critical time are more important to the formation of QDs.
On the other hand, if you are interested in this early stage, updated meshing codes for Abaqus (more elements are added in thickness) should be generated after the film is getting thicker. 

1. Surface flattening:
The reduction of surface area could decrease the free energy of the system. Result shows the surface flattening process from a rough surface. The elastic energy is not considered here.



2. Nucleation process:
The elastic energy is considered here. An initial rough surface evolves into several islands. The surface energy and bulk free energy difference are both considered. Noting that certain coarsening process occurs due to the existence of surface energy.


3. Growth process:
Because of the limited elements we use, we are not able to simulate the growth process of QDs based on the result of 3. Here we manipulate several nucleation sites on the thin film, i.e. several small bumps with amplitude <0.1 here. Result shows the growth of QDs from small bumps(nucleation sites) to islands. The condensation/deposition process is purposely constrained to show the mass conservation of the surface diffusion process. It is clear that the vicinities of the island are lowed when the QDs are growing.


4. Deposition/Condensation:
Result shows that the materials are being deposited on the thin film.
Both surface energy and bulk free energy difference are considered.
Without strain energy:

With strain energy: