# Kris's Research Notes

## June 8, 2011

### Hill Formation

Filed under: GaAs Simulations — Kris Reyes @ 9:01 pm

During our meeting, we had discussed the a potential mechanism for hill formation. The idea was that in the presence of nearby As atoms (for example, newly deposited As atoms during crystallization) the Ga atoms in the liquid Ga droplet would move to them in order to form energetically favorable Ga-As bonds. In this post, we examine results from experiments that show this is indeed the case and how hills can form as a result.

Atomistically, the process is illustrated as follows:

When As atoms are nearby liquid Ga, the atoms in the Ga droplet move to occupy the positions above exposed As. As more As is deposited on top of these newly positioned Ga atoms, the process repeats as the remaining Ga atoms move to occupy those favorable positions. The diffusion rates for Ga on top of Ga and Ga on top of As should control the shape, position and size of the nucleating GaAs hills, and in this post we examine the effect of these parameters.

Globally, this mechanism serves to “wick” Ga liquid away from the droplet when As is present nearby:

That is, Ga atoms in the liquid droplet will tend to wet an As terminated surface, depleting the droplet in the process. Again, controlling how fast this occurs will affect the geometry of the resulting hills.

## Results

To show that this wicking mechanism does occur in our simulations, we consider an etched droplet within both a Ga-terminated substrate and an As-terminated one. We expect the liquid Ga to wet the As-terminated substrate, thus depleting the droplet. In the Ga-terminated case, the droplet should more-or-less stay in place. The energy parameters were set at $\gamma_{GG} = 0.3$ eV, $\gamma_{GA} = 0.6$ eV, $\gamma_{AA} = 0.10$ eV, $\gamma^\prime_{GG} = \gamma^\prime_{AA} = 0.20$ eV, and $\gamma^\prime_{HH} = -0.7$ eV. The temperature was set at T=593K and I simulated 10 seconds.

Here is the result for the As-terminated surface:

Note while the Ga atoms in the liquid droplet do indeed wet the As-terminated surface, we also get As surface atoms diffusing into the droplet.

Here is the result for the Ga-terminated surface:

The droplet behaves as expected.

Now consider the crystallization of the etched droplet via an As flux of 1 monolayer/second for ten seconds. With a constant supply of As atoms, the droplet should be depleted as it reacts with the incoming As atoms to form GaAs:

Indeed, the presence of As effectively wicks Ga atoms away from the liquid droplet, but it does so too quickly. That is, instead of forming hills, the Ga atoms were able to diffuse at a sufficient rate to form GaAs layers.

## Effect of $\gamma_{GA}, \gamma_{GG}$ and $\gamma^\prime{HH}$

As we have seen above, the As atoms deposited during crystallization wicks Ga atoms from the liquid Ga droplet, which was our proposed mechanism for hill formation. However we do not see GaAs hills, but rather flat (albeit rough) layers of GaAs. This suggests that certain diffusion rates are too large. In this section, we consider the effect of $\gamma{GA}$ (which determines how fast Ga diffuses on top of As), $\gamma_{GG}$ (which determines how fast Ga diffuses on top of other Ga) and $\gamma^\prime_{HH}$ (which measures how fast do exchanges occur within the droplet).

First, we vary $\gamma^\prime_{HH} \in \left\{-0.4, -0.5, ... , -0.9\right\}$ eV. This should control how fast exchanges within the droplet occur. If too small in absolute value, then the barrier for exchange is small and hence the droplet will tend to crystallize in place.

### $\gamma^\prime_{HH} = -0.9$ eV

Indeed, we see that for $|\gamma^\prime_{HH}|$ small the droplet does crystallize in place while for large values the droplet is wicked out by the deposited As atoms.

Fixing $\gamma^\prime_{HH} = -0.7$ eV again, we now vary $\gamma_{GA} \in \left\{0.5, ... , 1.0\right\}$ eV.

### $\gamma_{GA} = 1.0$ eV

Apart from the roughening of the surface, there is no effect of $\gamma_{GA}$ on the wicking mechanism. However, we note for higher $\gamma_{GA}$ energies, we see more nucleation in the initial droplet region, which suggests that there was nucleation within the droplet instead of at its boundaries. This is apparent when we consider e.g. $\gamma_{GG} = 0.40, \gamma^\prime_{HH} = -0.90$. Here is a comparison in that case between $\gamma_{GA} = 0.50$ eV (which incidentally is an example of good hill formation) and $\gamma_{GA} = 1.0$ eV:

### $\gamma_{GA} = 1.0$eV

In the latter case, we clearly see nucleation within the droplet.

As indicated above, perhaps the parameter most responsible for controlling the diffusiveness of the hills (in the extreme case, flat layers) is $\gamma_{GG}$. Here we vary $\gamma_{GG} \in \left\{0.25, 0.30, 0.35, 0.40\right\}$ eV and fix $\gamma_{GA} = 0.60$ eV, $\gamma^\prime_{HH} = -0.70$ eV.

### $\gamma_{GG} = 0.40$eV

Here we see $\gamma_{GG}$ quite effectively controls the width of the hills.

## Parameters that produce hills

Here are other choices of parameters $(\gamma_{GG}, \gamma_{GA}, \gamma^\prime_{HH})$ that result in hill growth.