# Kris's Research Notes

## October 15, 2010

### Droplet Crystallization Part 2

Filed under: GaAs Simulations — Kris Reyes @ 6:48 pm

Recall in the previous post, we simulated $Ga$ droplet crystallization. In the simulation, we formed $Ga$ droplets, and then turned on a flux of $As$. The droplets immediately formed shells of $GaAs$, which we do not observe in experiments. We had concluded in the previous meeting that it would be interesting to see what happens if we allow $As$ atoms to diffuse through the $Ga$ droplet at a fast rate.

First, I refined the notions of “extended species”. We define the extended species $Ga^{(i)}$ to be a $Ga$ has exactly $i$ neighbors of type $As$, and similarly for $As^{(i)}$. In fact, the code has been modified to handle species of the form $Ga^n$, where $n = (n_V, n_{Ga}, n_{As})$ is a vector of counts, e.g. $n_{Ga}$ is the number of Gallium neighbors. But as a first step, we forget about the other counts besides $n_{As}$ so that, for example $Ga^{(2,1,1)}$ is more or less identical to  $Ga^{(1,2,1)}$. That is, we obtain the extended type definition above from this more general setting. For now, I used the same bonding energies after we map to the coarser definitions for extended type.

Next, we define the swapping rate of two atoms $A, B$ as

$r_{swap}(A, B) = \Omega \exp\left[ \alpha(A, B) ( E(A) + E(B) )\right].$

where as before $\Omega$ is a constant prefactor, $E(A), E(B)$ are the local energies of $A$ and $B$, respectively. The diffusion coefficient $\alpha(A, B)$, is given by:

• $\alpha(A,B) = 1$ if one, but not both of the atoms is a vacuum (surface diffusion);
• $\alpha(A,B) = \epsilon$ if one of the atoms is $Ga^{(1)}$ and the other is $As$ (fast diffusion through droplet);
• $\alpha(A,B) = \infty$ otherwise.

I varied $\epsilon \in \left\{0.5, 0.8, \hdots, 0.15, 1 \right\}$. I started with a hemispherical droplet of radius 32 lattice sites. I fixed $T = 498, \mu_{As} = 0.35$. I used deposition rates $r_{\downarrow As} = 1$ monolayer/second. and $r_{\downarrow Ga} = 0$. For each $\epsilon$ I ran two trials. First I simulated 0.1 seconds, measuring the configuration every 0.001 seconds.  Second I simulated 5 seconds measuring every 0.05 seconds.

Here are the movies, with each row corresponding to $\epsilon$.