Kris's Research Notes

August 26, 2011

Droplet Formation, Again

Filed under: GaAs Simulations — Kris Reyes @ 5:41 pm

In this note, we re-examine droplet formation under the new model. We describe the effect of energy parameters, and obtain a set of parameters which give the correct droplet density.

We consider droplet formation on a domain of width 1024 atoms. Ga is deposited at a rate of 0.1 monolayers/second for 35 seconds at 200 C, then anneal without any flux for 60 seconds. In experiments, at these growth conditions, we expect 5-10 droplets to form, each about 15 nm (about 60 atoms). However, in experiments, the initial substrate is As terminated, whereas in our simulations we used an initially Ga terminated substrate. This should result in more Ga mass in droplets, but should not affect the number of droplets formed.

We vary energy parameters as:

\gamma_{GG}, \gamma^\prime_{GG} \in \left\{0.200, 0.225, 0.250, 0.275, 0.300\right\};

\gamma_{HH} \in \left\{-0.6, -0.7, -0.8, -0.9, -1.0\right\};

\lambda_D \in \left\{0.6, 0.7, 0.8, 0.9, 1.0\right\};

For each set of parameters, we run 16 independent trials, resulting in 10,000 trials total!

We measure droplet counts and widths. Here is a plot of counts vs. width:

Each point corresponds to a fixed value of the tuple (\gamma_{GG}, \gamma^\prime_{GG}, \gamma_{HH}, \lambda_D). We see that there is a small set of tuples that agree with experiments (i.e. droplet count \geq 5 droplets, droplet width ~ 60 atoms). From now on, we only consider this set of parameters.

We discover \gamma_{GG} = 0.30 eV for all such tuples. Here is a plot of \gamma^\prime_{GG} vs. droplet counts:

Here is \gamma^\prime_{GG} vs. droplet width:

Larger \gamma^\prime_{NN} lead to more, but not necessarily smaller droplets.

Here is \gamma_{HH} vs. droplet counts:

It appears that all curves attain a maximum number of droplets around \gamma_{HH} = 0.7 eV.

Finally, here is \lambda_D vs. droplet counts:

There does not appear to be any dependence on \lambda_D.

Simulation Results

We fix \gamma_{GG} = \gamma^\prime_{GG} = 0.30. The simulations are performed according to the following experimental procedure:

  1. Deposit Ga at a rate of 0.1 monolayers/second for 35 seconds at 200C;
  2. Anneal for 60 seconds without any flux;
  3. Deposit As at a rate of 1 monolayer/second for 10 seconds;
  4. Increase the temperature to 350C for 5 minutes while maintaining As flux.

The Ga deposited in step 1 is colored purple. The As deposited in step 3 is colored light blue, while the As deposited in step 4 is colored dark blue.

Here is the simulation results for \gamma_{HH} = 0.60 eV and \lambda_D \in \left\{ 0.3, 0.4, ... , 1.0\right\}.

Similarly, here are the simulation results for \gamma_{HH} = 0.70 eV and varying \lambda_D:

Lastly, here is \gamma_{HH} = 0.80 eV:

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