# Kris's Research Notes

## July 11, 2011

### More on “Fast” Adatom Diffusion

Filed under: GaAs Simulations — Kris Reyes @ 3:34 pm

I ran 128 identical runs depositing 1 monolayer of Ga at a rate of 0.1 monolayers/second. I calculated mean $\mathbb E[N_d]$ and variance $Var(E_d)$ of the number of resulting droplets $N_d$ formed at the end of the trials. This was done for both fast adatom diffusion turned on and off.

First, we examine the results when fast adatom diffusion was turned on. The runs performed about 240,000,000 updates on average and took about 2115 seconds to complete. The empirical mean and variance are: $\mathbb E[N_d] = 13.2422, Var(N_d) = 1.6810$. Here is a sample result.
(Note: on average, there were about 385,000,000 hops total and about 1300 times where the simulation couldn’t hop adatoms for the full number of hops)

When fast adatom diffusion was turned off, the runs performed about 620,000,000 updates (2.58 times more than above) and took about 3659 seconds (1.73 times more than above). The empirical moments are given by $\mathbb E[N_d] = 11.7109, Var(N_d) = 1.262$. Here is a sample result.

Here are the histograms for $N_d$ for both cases (red for the trials with fast adatom diffusion turned on, blue is for those trials with it turned off):

We see from the above that there is some separation between the two distributions. That the $\mathbb E[N_d]$ is larger when fast adatom diffusion is on suggests that Ga adatoms are not diffusing as fast in that case than the case when fast adatom diffusion is off. Indeed, examining the two sample results above we see that there are several more Ga adatoms on the surface when fast adatom diffusion is turned on. This results in more and smaller droplets in this case. Here is an example of the surface for when the fast diffusion is both turned on (left) and turned off (right).

We see that for the normal diffusion model, Ga adatoms are usually isolated. This is not the case when fast diffusion is on.

Here are sample droplets for both cases: