Kris's Research Notes

June 21, 2011

Barriers Inside Ga Liquid

Filed under: GaAs Simulations — Kris Reyes @ 10:30 pm

We had previously discussed treating the process of an As atom diffusing inside Ga liquid as a separate process, which did not necessarily involve bond-counting to determine energy barriers for such events. In order to do this, we introduce barriers for these events. In this note, we discuss these barriers, their associated rates and how we determine when an atom in Ga liquid.

Liquid Neighborhood

In order to apply the appropriate barriers, it is necessary to determine whether two exchanging atoms A, B are within liquid Ga. To do this, we simply count the number of Ga and As atom within a small neighborhood N_s(A), N_s(B) about each atom. If the number of As atoms is smaller than some threshold n_{\ell}, we declare such a neighborhood within liquid Ga and assign special barriers for the exchange. For efficiency reasons, we require

\displaystyle N_s(A) \cup N_s(B) \subseteq H(A), H(B),

where H(A) is the neighborhood about atom A used to index the rate cache hashtable. (Recall, the rate cache stores precomputed rates as a function H(A) so that any two atoms A,B such that H(A) = H(B) will have the identical rates for all events.) As of this post, n_{\ell} = 1.

Moreover, we must make the distinction for atom exchanges at the droplet/vacuum interfaces and exchanges in the droplet proper. This is done by examining whether either of the exchanging atoms are exposed to vacuum, i.e. if the atom has a vacuum neighbor or next-nearest neighbor. In summary, we have two additional barriers \lambda_{S}, \lambda_{D} that correspond to the energies for an atom-atom exchange on the surface of a liquid Ga droplet and in the droplet proper, respectively.

Liquid barriers are used for atom-atom exchanges only when both atoms are in a liquid neighborhood. In this case, if either atom is exposed to vacuum, the barrier for exchanges is \lambda_S, otherwise it is \lambda_D. For now, we set \lambda_S = 2 \gamma_{GA} + \epsilon, slightly larger than the barrier for As diffusion on the droplet. The parameter \epsilon serves as a small surface-tension penalty for an As atom to break into the droplet from its surface. The barrier \lambda_D is a free parameter.

The effect of \lambda_D

In this section, we fix parameters \gamma_{GG} = 0.4 eV, \gamma_{GA} = 0.6 eV, \gamma_{HH} = -0.7 eV and vary \lambda_D \in \left\{ 0.3, 0.4, ... 1.0\right\}. In the simulation, a Ga droplet is crystallized at 475K with an As flux r_{As} = 1 monolayer/second for 10 seconds. We expect for small \lambda_D, As diffusion inside the droplet to be quick and that the droplet should crystallize in-place. In the larger \lambda_D cases, GaAs should crystallize in and near the surface of the droplet.

\lambda_D = 0.3eV

\lambda_D = 0.4eV

\lambda_D = 0.5eV

\lambda_D = 0.6eV

\lambda_D = 0.7eV

\lambda_D = 0.8eV

\lambda_D = 0.9eV

\lambda_D = 1.0eV

Indeed, we see for the low \lambda_D case, nucleation occurs on the side and at the bottom of the droplet. For larger \lambda_D, we do not observe nucleation at the bottom. Rather, in these cases, GaAs nucleates near the surface. The different regions of GaAs at the surface indicate areas where nucleation occured.

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