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.

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1 Comment »

  1. […] is a follow up of this post. We had observed that, in the movies, once an atom came close to the droplet/crystal interface, […]

    Pingback by Droplet Crystallization – Part 3 « Kris's Research Notes — October 19, 2010 @ 11:32 pm


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