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:

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