In this note, we present more simulation results of Ga liquid droplet growth and subsequent crystallization at various temperatures, including . In experiments, well-defined “doughnuts” form. Our simulations agree with this.

Recall, we had previously identified energy parameters which agree with experiments via a large search over parameter space. These values were:

eV, eV eV

eV, eV eV.

With these parameters we are able to:

- produce the correct surface concentration diagram for temperatures in the range K and deposition ratios ;
- have step-flow growth for the above growth conditions;
- Grow and crystallize droplets of the correct size and distribution at K;
- Exhibit a transition from nanodots to nanorings around the right temperatures (dots at K, rings at and transitional morphology at .

In this note, we focus on this last point. We repeat the droplet crystallization trials as described in this post, but fixing the energy parameters above. For each temperature , we grow and crystallize droplets in 16 different trials. Here are the trials for K:

The simulations robustly produce quantum dots. There are an average of 8.8 droplets per 1024 atoms, leading to a linear density of 30 droplets per micron. The average droplet width is 39.4 as calculated via thresholding and 30.0 as calculated via auto-correlation function. We may compare these results with experiments understanding that **in experiments 2.9 monolayers of Ga were deposited while 3.5 monolayers were deposited in the simulations**. Hence these are not 1-to-1 comparisons. Experimentally, at 199C the linear droplet density is 48.85 droplets/micron and average droplet diameter is 46.9 atoms. At 191C, the linear density is 51.02 droplets/micron and droplet diameter is 38.15. We may also compare our results with experiments done at 183C after depositing 3.7 monolayers. There the droplets formed were 56.7 atoms wide on average and had a linear density of 40.63 droplets/micron.

Here are the trials for K:

Here we see several types of behavior. We observe fully-formed quantum dots, quantum dots with a liquid Ga core, and the beginnings of nanorings. There are an average of 5.9 droplets per 1024 atoms, a linear density of 20.16 droplets per micron. The average droplet width is 47.7 atoms as calculated via thresholding (which does not notice shallow “valleys” in nanorings) and 33.2 atoms via auto-correlation (which is somewhat sensitive to the valleys).

Here are the trials for K:

Here we see nanoring formation. By inspection, we calculate an average of 2.5 nanorings per 1024 atoms, or about 8.5 rings/micron.

Here are the trials for K:

We see that the simulation results are robust. At K, the simulation produces one large nanoring with the domain of width 1024 atoms, suggesting a linear density of at most 3.4 nanorings/micron.

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