# Kris's Research Notes

## December 10, 2010

### Droplet Size Experiments — Part 6. Low Temperature and Arrhenius Plots

Filed under: GaAs Simulations — Kris Reyes @ 2:38 am

This is a follow up to this post. Here we repeat the droplet size experiments, but include lower temperatures. We also consider different intra-droplet bonding energies and present Arrhenius plots of droplet size with respect to inverse temperature.

Specifically, we now consider the experiments where parameters range as:

$\gamma = \gamma(G0,G0) \in \left\{ 0.29, 0.30, 0.35, 0.40\right\} eV,$

$T \in \left\{ 350, 375, 400, \hdots, 575, 600\right\} K$,

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

For each triple $(\gamma, T, r_{\downarrow Ga})$, we perform 16 trials, where 4.0 monolayers of $Ga$ are deposited, after which we anneal the system for 30 seconds. We then measure droplet width, height and mass, and the number of droplets. The 16 trials yield a histogram for each statistic as well as an averaged autocorrelation function for the height profile of the system.

Here are the plots of these statistics as functions of specific parameters:

## Varying $\gamma$

Here are plots where $\gamma$ varies while the other two parameters $(T, r_{\downarrow Ga})$ are fixed.  Here is the average droplet width, as given by the histogram (left), and autocorrelation function (where it interesects $\frac{1}{e}$, right). Each curve in the plots correspond to a fixed $( T, r_{\downarrow Ga})$ pair.

The two plots are in qualitative agreement. There is a downward trend as intra-droplet bond strengths increase. Consider the case $(T, r_{\downarrow Ga}) = (525, 0.25)$ — the green line with open circles. Here are the simulations (on a truncated lattice of width 1024 atoms) as we vary $\gamma$:

 $\gamma (eV)$ $0.29$ $0.30$ $0.35$ $0.40$ movie movie movie movie

We note that that as the intra-droplet strength increases, the shape of the islands become more triangular.

Here are plots of height and mass of droplets as a function of $\gamma$:

There seems to be two types of behavior within each plot. For example, in the mass vs. bond strength plot, there are some curves which increase mass between $\gamma = 0.29 eV$ and $0.30 eV$, while other curves decrease between these two energies. Here are simulations for two curves. First is the curve with fixed parameters $(T, r_{\downarrow Ga}) = (600, 0.1)$ — the green dash-dot line — which increases between the two energies. Second has fixed parameters $(0.2, 600)$ — the blue dashed line with open circles — which is monotone decreasing.

 $(T, r_{\downarrow Ga}) \backslash \gamma (eV)$ 0.29 0.30 0.35 0.40 $(600, 0.1)$ movie movie movie movie $(600, 0.2)$ movie movie movie movie

Finally, here is number of droplets vs bonding energy:

The typical trend is an increase in number of droplets as bonding-energy increases. There are a few pathological cases where the number of droplets decrease — the $(350, 0.4)$ is most exaggerated. Here are the simulations for this case:

 $(T, r_{\downarrow Ga}) \backslash \gamma (eV)$ 0.29 0.30 0.35 0.40 $(350, 0.4)$ movie movie movie movie

In fact, droplets don’t actually form — the Gallium wets the surface completely. The behavior is similar for most of the low-temperature runs.

## Varying $r_{\downarrow Ga}$

Here are the plots of droplet width, height and mass, as calculated from the histograms. Each curve corresponds to a fixed $(\gamma, T)$ pair.

We see there is a general trend for smaller droplets as Ga flux increases.

Here is number of droplets as a function of flux.

Again, we note the low temperature cases are pathological.

## Varying $T$ and Arrhenius Plots

Here are Arrhenius plots of droplet statistics vs. inverse temperature. First are width, height and mass:

Here is the plot for the number of droplets vs. inverse temperature:

This follows the behavior we discussed last time: The plots are linear in the high temperature regime and approaches a constant value for lower temperatures.