# Kris's Research Notes

## January 31, 2011

### Droplet Experiments — Effect of Droplet Etching

Filed under: GaAs Simulations — Kris Reyes @ 5:32 pm

The previous droplet experiments did not allow for droplet etching, which we model as instability at the droplet/substrate interface. In these set of runs, we turn it back on. We focus the idea of a critical thickness — the amount of deposited Gallium where droplets start to occur.

Recall how we model droplet etching. At a $Ga$ droplet / $GaAs$ substrate interface, we introduce instability by allowing $Ga$ atoms on this interface to more readily exchange with any of neighboring $As$ atoms. We define a $Ga$ atom on this interface as an atom of type $Ga(2, 2)$, which means it has exactly two $Ga$ neighbors (from the droplet) and two $As$ neighbors (from the crystal). The rate of exchanging a $Ga(2,2)$ and any $As$ atom is given by

$r_{Ga(2,2), As} = \Omega e^{ -\beta \epsilon (E_{Ga} + E_{As}) },$

where $E_{Ga}, E_{As}$ is the local energy of the $Ga(2,2), As$ atom, respectively and $\epsilon$ is a small parameter. We also give an $As$ atom diffusing through the droplet (i.e. the exchange of $As(4,0), Ga(3,1)$ atoms) a similar rate.

In these experiments we vary $\epsilon$, the amount of $Ga$ deposited $D$ and temperature $T$. We fix $Ga, As$ flux to be 0.1 and 0.01 monolayers/second, respectively.

## $\epsilon = 0.20$

In the first set of trials, we set $\epsilon = 0.20$, which is relatively small and hence allows for more significant droplet etching. We vary

$D \in \left\{2.0, 2.5, 3.0, 3.5, 4.0\right\}$ monolayers,

and

$T \in \left\{400, 425, \hdots 600 \right\}$ K.

Final frames for these runs are located here. Here is a plot of droplet width vs. $D$ as calculated via thresholding:

Here is droplet width vs. $D$ as calculated with the autocorrelation function:

## $\epsilon = 0.3$

Final frames for these runs are located here. Here we set $\latex \epsilon 0.30$, which reduces the amount of droplet etching. Here is the plot of droplet width vs thickness, as calculated by thresholding:

and via autocorrelation: