# Kris's Research Notes

## December 2, 2010

### Droplet Size Experiments – Part 2

Filed under: GaAs Simulations — Kris Reyes @ 7:59 am

This is a follow-up to this post.

Previously, we had observed that the droplet widths we had previously obtained were wrong because we did not have enough droplets to meaningfully calculate such statistics. So I repeated the experiments on a lattice of width 8192 atoms.

Recall the parameters we had used in the experiment. We had fixed surface Ga bond strength $\gamma(G2, A4) = 1.0 eV$ and inner-droplet Ga bond strength $\gamma(G0, G0) = 0.3 eV$. I varied temperature

$T \in \left\{450, 475, 500, 525, 550, 575, 600\right\} K.$

I varied Ga flux

$r_{\downarrow Ga} \in \left\{ 0.1, 0.2, 0.3, 0.4\right\}$ monolayers/sec.

In each trial, I deposited 4.0 monolayers of $Ga$ on a $GaAs$ substrate. I then annealed for 30 seconds. I ran 16 trials for each pair $(T, r_{\downarrow Ga}),$. This allows me to calculate for each $(T, r_{\downarrow Ga})$ pair:

• the mean autocorrelation, averaged over the 16 trials;
• the histogram of droplet heights, taken over all 16 trials;
• the histogram of droplet widths, taken over all 16 trials;
• the histogram of droplet mass, taken over all 16 trials;
• the mean number of droplets, averaged over all 16 trials;

To calculate the above histograms, I used a thresholding method. For a height profile $h(x)$, I determined the minimum height $min(h)$ and considered a site $x$ to be part of a droplet if

$h(x) > min(h) + \tau,$

for a threshold value $\tau$. Here we set $\tau = 5$. We will post the autocorrelation and histograms in later posts.

## Droplet Size vs. $r_{\downarrow Ga}$

Here are plots of droplet width as a function of $r_{\downarrow Ga}$, computed with both the autocorrelation function and histogram. The different curves in the plot correspond to different temperatures.

Droplet Width vs Ga Flux -- computed from autocorrelation

Here is the same plot, but calculated from the histogram:

Droplet Width vs. Ga Flux -- computed from histogram

Note that the two plots are similar, except the histogram measures a smaller droplet width than the autocorrelation function. We also see that the droplet width decreases with increasing Gallium flux. Lastly, we also observe that droplet width increases with increasing temperature, and that the increase is somewhat linear. We shall observe this more directly later when droplet width is plotted against temperature.

Here is the droplet height vs. Ga Flux, which we have computed from the histogram.

Droplet Height vs. Ga Flux

Here is the plot of droplet mass vs. Ga Flux.

Droplet Mass vs. Ga Flux

As with droplet width, mass and height decreases with increasing flux, and increases with increasing temperature. The shape of the curves is similar to droplet width. This suggests that droplet mass is linear with respect to droplet width.

Lastly we have mean number of droplets vs. Ga Flux

Number of Droplets vs. Ga Flux

## Droplet Size vs. Temperature

Here we plot the same information as a function of temperature. First is droplet width calculated from the autocorrelation function.

Droplet Width vs. Temperature -- computed from autocorrelation

Here’s  droplet width computed from the histogram.

Droplet Width vs. Temperature -- computed from histogram

Again, we see the two plots are similar, except the histograms predict smaller droplet widths. Both plots suggest droplet width is linear in temperature.

Droplet height vs. temperature:

Droplet Height vs. Temperature

Droplet mass as a function of temperature:

Droplet Mass vs. Temperature

Once more, the similarity between the curves in this plot and the curves in droplet width vs. temperature suggest mass, height and width are linearly related.

Finally mean number of droplets vs. temperature:

Mean Number of Droplets vs. Temperature

## 4 Comments »

1. […] Simulations — Kris Reyes @ 5:53 pm Here are the autocorrelation functions described in this post. The rows correspond to temperature, increasing from 450K to 600K. The columns correspond to […]

Pingback by Droplet Size Experiments — Part 3. Autocorrelations « Kris's Research Notes — December 2, 2010 @ 5:53 pm

2. […] Kris Reyes @ 6:07 pm Here are histograms of droplet width, height and mass described in this post. Each row correspond to a fixed pair and the columns correspond to width, height and mass, […]

Pingback by Droplet Size Experiments — Part 4. Droplet Size Histograms « Kris's Research Notes — December 2, 2010 @ 6:07 pm

3. […] are sample profiles for each trial described in this post. For each pair, we ran 16 trials. Here are sample final height profiles (truncated to 256 atoms) […]

Pingback by Droplet Size Experiments — Part 5. Sample Profiles « Kris's Research Notes — December 2, 2010 @ 6:14 pm

4. […] is a follow up to this post. Here we repeat the droplet size experiments, but include lower temperatures. We also consider […]

Pingback by Droplet Size Experiments — Part 6. Low Temperature and Arrhenius Plots « Kris's Research Notes — December 10, 2010 @ 2:38 am