# Kris's Research Notes

## January 31, 2011

### Droplet Experiments — Effect of Droplet Bonds

Filed under: GaAs Simulations — Kris Reyes @ 6:00 pm

In previous experiments, we did not observe a critical thickness. I wanted to see how the bonding energy within a droplet (i.e $G0-G0$ bond strength) affected this. So I ran some trials with lower intra-droplet bonding energies, which means the droplets would wet the surface more readily. Here I fixed $\epsilon = 0.20, T = 500K, r_{\downarrow Ga} = 0.1$ monolayers/second, $r_{\downarrow As} = 0.01$ monolayers/second. I varied $\gamma(G0, G0) \in \left\{0.26, 0.25\right\}$ eV. Recall all other $Ga-Ga$ bonds are fixed at $0.25$ eV.

Note: While debugging and trying different parameters, I changed the pairwise $G(i)-A(j)$ bond strengths slightly to minimize the number of parameters and hence simplify the model. The old energies $G(i)-A(j)$ were given as the $(i,j)$-th entry of the matrix:

$\begin{pmatrix} \gamma_\epsilon(1) & \gamma_\epsilon(2) & \gamma_\epsilon(3) & 0.05 \\ 0.05 & 0.25 & 0.95 & 0.95 & \\ 0.05 & 0.25 & 0.95 & 0.95 \\ 0.05 & 0.30 & 0.95 & 1.00 \end{pmatrix}$,

where $\gamma_\epsilon (i)$ is determined to encourage diffusion of an $As$ atom through a droplet rather than on its surface (see this post). The new energies simplify this by setting all $Ga-As$ bonds to 0.19 eV except for those in the substrate and for $Ga$ atoms on the surface of the substrate:

$\begin{pmatrix} 0.19 & 0.19 & 0.19 & 0.19 \\ 0.19 & 0.19 & 0.19 & 0.95 \\ 0.19 & 0.19 & 0.95 & 0.95 \\ 0.19 & 0.19 & 0.95 & 0.95 \end{pmatrix}$,

This matches numbers previously calculated by Denis as taken from the literature. Diffusion through the droplet is still achieved by picking a sufficiently small diffusion coefficient.

Movies for these runs are located here. Final frames are here.

Here is droplet width as a function of thickness (thresholding):

and via autocorrelation:

We notice the different behavior between the two ways of measuring width. This is readily explained. When droplets start to etch the surface, they create roughness and differences in height. When they try to wet the surface, they create large regions that the thresholding scheme believes to be droplets:

This may be somewhat physical, as when the droplets are crystallized, the indicated region would appear to be a large droplet.

Here is droplet width vs $G0-G0$ bond strength (thresholding):

and again via autocorrelation:

Here is droplet width vs $\epsilon$. Thresholding:
We see that, as before, lower $\epsilon$ leads to rougher surfaces which yields larger apparent droplets as described above.

Here is the same data obtained from autocorrelation:

The effect of the droplet etching is masked here and so we do not see large droplet size. In fact, there is very little structure in the plot.

Perhaps it’s useful to look at sample autocorrelation functions. Here are autocorrelation functions for $\epsilon = 0.15, \gamma(G0,G0) = 0.26$ eV as we vary thickness:

We see that the two methods consistently do not match. Now consider the effect of increasing $\epsilon$ (fixing $\gamma(G0,G0) = 0.26$ eV, $D = 4.0$ mL):

The two methods converge as $\epsilon$ increases.