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.

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1 Comment »

  1. […] Droplet Size Experiments — Deposited Gallium Histogram Filed under: GaAs Simulations — Kris Reyes @ 5:25 pm This is a follow-up to this post. […]

    Pingback by Droplet Size Experiments — Deposited Gallium Histogram « Kris's Research Notes — December 16, 2010 @ 5:25 pm


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