Kris's Research Notes

October 19, 2010

Droplet Crystallization – Part 3

Filed under: GaAs Simulations — Kris Reyes @ 11:32 pm

This is a follow up of this post. We had observed that, in the movies, once an $As$ atom came close to the droplet/crystal interface, the crystal surface became unstable. By unstable, we mean that the $As$ atoms on the surface of the crystal would start diffusing rapidly into the droplet — causing the droplet to etch into the crystal. We had concluded that this must have been  a bug. It was indeed is a bug, one that involves next nearest neighbor swapping.

We want next-nearest neighbor swapping in general. For example, consider one atom diffusing on the surface of the crystal:

Without next-nearest neighbor swapping, the atom would have to do three swaps with nearest neighbors in order to move one position to the right. This involves breaking several bonds. This probably doesn’t happen in real life.

Having next-nearest neighbor swaps contributes to the bug. Consider the following situation where a $As$ atom (green) diffuses through a $Ga$ droplet and approaches the droplet/crystal interface:

Consider the darker $Ga^{(1)}$ atom (recall $Ga^{(1)}$ means the Gallium atom has one Arsenic neighbor). The diffusion coefficient assigned to the indicated swap, $\alpha( Ga^{(1)}, As^{(4)}) = \epsilon$ is small. This is how the surface becomes unstable.

To fix this, we assign a separate diffusion coefficient for nearest neighbor swaps and next-nearest neighbor swaps. Then we assign (for now) all next-nearest neighbor swaps  to $\infty$. Here is a movie if we set $\epsilon = 0.11$. The temperature was set at $T=498 K$, $\mu_{As} = 0.35.$ We deposit Arsenic at the rate of $r_{\downarrow As} = 1$ monolayer/second for 15 seconds. (Here the Gallium droplet is blue, deposited Arsenic is purple, Gallium and Arsenic in the crystal are red and green, respectively):

Note, there is no crystal nucleation within the droplet, not even at the droplet/crystal interface (and hence, the “hills” of $GaAs$ form away from the droplet). This is easy to explain. Consider the case where an $As$ atom has diffused to the droplet/crystal interface:

To the atom, it is surrounded by Gallium atoms, and hence it is in an identical situation to diffusing in the droplet. In other word, the $As$ atom does not know it is at the droplet/crystal interface, it only knows about its nearest neighbors. Therefore, it is likely to swap with either of the two Gallium neighbors above it.

We can attempt to address this by increasing the $Ga^{(2)}-As^{(4)}$ and $Ga^{(3)}-As^{(4)}$ bonds strengths. We can make them both 1.0 eV (the same as $Ga^{(4)}-As^{(4)}$). Here are movies where I vary $\epsilon \in \left\{ 0.11, \hdots, 0.20\right\}$ (organized so that $\epsilon$ is increasing from left to right, top to bottom). I simulated 10 seconds for this run:

I believe these trials show that $GaAs$ is nucleating within the droplet. Compare the distribution of $As$ within the droplet in the previous case (before we adjusted the bond strengths) to the $As$ distribution in these movies. Before, the $As$ seemed to be uniformly distributed within the droplet, whereas in these movies, the $As$ is concentrated in the bottom.

Next, I simulate a scenario where we anneal for 10 seconds prior to any $As$ depositions. This will allow the droplet to come to its equilibrium shape (with respect to our simulations). I then deposited $As$ for 10 additional seconds. Here is the case where $\epsilon = 0.15$:

Here are is a run where the droplet size is increased (with and without annealing):

Note, we do not get the distribution of $GaAs$ crystal inside the droplet that we expected in this post. That is, we had previously calculated that there should be more $As$ atoms diffusing to the edges of the droplet than in the middle, and we don’t see this in the simulations.

To see why this happens, we slow down the movie. Here is one second of simulation time, sampled every 0.01 seconds.

We see that the $As$ atoms on the droplet/crystal interface still diffuse readily on that interface. This would explain why we see a uniform distribution of $GaAs$ nucleating at the inteface.  In fact, this may not be a bad thing (but I really don’t know).