# Kris's Research Notes

## December 16, 2010

### Droplet Size Experiments — Deposited Gallium Histogram

Filed under: GaAs Simulations — Kris Reyes @ 5:25 pm

This is a follow-up to this post.

In that post, I described how the experiment was run. I deposited 4 monolayers of Gallium, then annealed for 30 seconds. To deposit 4 monolayers of Gallium, I specified that Gallium should be deposited for $4 \times \frac{1}{r_{\downarrow Ga}}$ seconds, since $r_{\downarrow Ga}$ is flux with units monolayers/second. As a result, the experiments will not deposit 4 monolayers exactly. This could be a problem.

Here is a histogram for the amount of monolayers deposited, over all trials:

The sample mean is 4.172 monolayers deposited, and the standard deviation is 0.30132 monolayers. The maximum is 4.8875 monolayers, while the minimum is 3.5076 monolayers. This is a very large difference.

Here is the effect of amount of monolayers deposited as a function of intra-droplet bonding energy $\gamma(G0, G0) \in \left\{ 0.29 , 0.30, 0.35, 0.40\right\} eV$:

As bonding energies increase, hopping rates will decrease. Hopping events will correspond to a larger increase in time for larger energies. However, as bonding energies increase, such events become more unlikely, and so deposition events are more probable. Therefore there is a trade-off: Amount deposited depends of the number of deposition events and the time to deposit. As energies increase, deposition events become more likely, but the window (in terms of Monte-Carlo steps) in which these events can occur decreases because hopping events occupy a larger amount of time. We see this tradeoff in the above graph. Certain experiments have decreasing depth as bonding energies increase, while others tend to increase depth. Note that the maximum depth occurs at $(\gamma, T, r_{\downarrow Ga}) = (0.4, 350, 0.1)$, while the minimum depth occurs at $(0.35, 600, 0.2)$ and at $(0.35, 600, 0.1)$.

Here is depth vs. $r_{\downarrow Ga}$:

Depth seems to be less sensitive to $r_{\downarrow Ga}$, as deposition times are scaled according to this parameter.

Finally here is depth vs. $T$:

Here we note a general decrease in Ga deposited with increasing temperatures. Curves corresponding to equal $\gamma(G0,G0)$ behave similarly. The graph suggests two things. First, as temperature increases, the amount deposited will eventually level off. Second, the value at which the depth asymptotes to decreases with increasing $\gamma(G0,G0)$.