# Kris's Research Notes

## August 16, 2011

### Nanowire Simulations

Filed under: GaAs Simulations — Kris Reyes @ 7:34 pm

In this note, we present KMC simulations of VLS nanowire growth and examine the effect of several parameters on nanowire growth.

We consider a two species $(A, B)$ system where a $B$ liquid droplet is on an $A$-substrate and is exposed to $A$ vapor:

The relevant parameters are the bonding energies $\gamma_{AA}, \gamma_{AB}, \gamma_{BB}$, the penalty for atom-atom exchanges $\gamma_{HH}$ and the barrier for diffusion inside the liquid droplet $\lambda_D$. We fix $\gamma_{BB} = 0.5$ eV and consider the effects of varying the other parameters. All simulations start with a substrate of $A$ atoms and a hemispherical liquid $B$ droplet of width 16 atoms. We deposit $A$ atoms at a rate of 0.1 monolayers/second for 300 seconds at a temperature of 700K. In the simulations $B$ is colored red, substrate $A$ atoms are green and deposited $A$ atoms are blue.

The base case is $(\gamma_{AA}, \gamma_{AB}, \gamma_{HH}, \lambda_D) = (0.4, 0.2, -1.1, 0.6)$. Here is the result:

This result is fairly robust. Here is the result of averaging the result of 64 independent trials with the above parameters:

Of the 64 trials, there were three trials which deviated from the above picture significantly. In all three cases, we see that crystallization of species $A$ at the sides of the droplet occurred fast enough to surround the droplet. This alters the geometry of the droplet and hence the growth mode of the nanowire. Here is one example where this occurs early in the nanowire formation:

Here is an example where this occurs late in nanowire formation:

I believe this is an artifact of the simulations. Recall when we performed the GaAs simulations, we considered an Ga atom to be part of a GaAs crystal if there was a significant amount As in its local neighborhood. In the nanowire case, because of the small size of the droplet, it appears that when crystallization occurs fast enough to crystallize both sides (which is a rare event for these parameters), then the $B$ atoms become crystalline. Any exchanges between such $B$ atoms and surrounding $A$ atoms are then dictated via bond counting rather than the liquid barrier $\lambda_D$.

### Effect of $\gamma_{AA}$

First, we vary $\gamma_{AA} \in \left\{0.4, 0.5, 0.6\right\}$ and hold other parameters constant.

### Effect of $\gamma_{AB}$

We vary $\gamma_{AB} \in \left\{ 0.05, 0.10, 0.2\right\}$ and hold other parameters constant.

We see that for weaker $\gamma_{AB}$, the $B$ liquid droplet splits, forming two thinner nanowires with a common trunk. We also note that the weaker $\gamma_{AB}$, the earlier the split is likely to occur. Compare the size of the trunk at the time of the split for $\gamma_{AB} = 0.05$ eV with the case $\gamma_{AB} = 0.1$ eV.

### Effect of $\gamma_{HH}$

Now we vary $\gamma_{HH} \in \left\{ -1.0, -1.1, -1.2\right\}$ while hold the other parameters constant. Recall, $\gamma_{HH}$ dictates how fast atom-atom exchanges occur at the droplet/solid interface. The larger it is in absolute value, the more difficult such exchanges are.

### Effect of $\lambda_D$

Here we consider varying $\lambda_D \in \left\{ 0.5, 0.6, 0.7\right\}$ while holding the other parameters constant.

There does not appear to be any effect.

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