Kris's Research Notes

April 24, 2012

Morphological Phase Diagrams

Filed under: GaAs Simulations — Kris Reyes @ 9:02 am

In this note, we present three morphological phase diagrams illustrating the presence of (1) nanorings, (2) liquid cores and (3) nucleation. The experimental procedure is altered to omit the last annealing step, in order to simplify the discussion. We also consider higher temperatures and lower As flux than before.

Recall the standard droplet crystallization procedure we had used in previous posts:

  1. Deposit Ga at a rate of 0.1 monolayers/second at a temperature T until 4.0 monolayers are deposited;
  2. Anneal for 60 seconds without depositing any material;
  3. Deposit As at a rate of F_{As} monolayers/second for 60 seconds;
  4. Increase the temperature to T_{f} > T, maintaining the same As flux as in step 3.

We had concluded that the last annealing step at the higher temperature T_f confounded the analysis of the morphological dependence on T, F_{As}. In this note, we present results of simulation runs where we omit this step. We also consider a larger temperature range:

T \in \left[150, 400\right] C,

and a larger As flux range

F_{As} \in \left[0.01, 1\right] monolayers/second.

Raw data may be found here.

Nanoring Formation

Here is the phase diagram of compact vs. noncompact structures as a function of T, F_{As}:

Liquid Cores

To measure liquid cores, we count the number of liquid Ga atoms in the final configuration of a simulation.Here are the contours of this count:

We observe the general trend for lower liquid Ga in the high temperature, low As flux. There are a few exceptions to this, including the extreme low As flux/ high temperature regime as well as in the (T, F_{As}) = (350, 0.1) case. Examining the low As flux/ high temperature cases, we see that the simulations did not crystallize the droplet in the allotted time (3600 seconds). For example, here is the results when F_{As} = 0.02 monolayers/second:

Hence, we should not consider such invalid cases. When (T, F_{As}) = (350, 0.1), we have:

Here we see that the droplet has etched into the substrate. This may be an atypical case — so I am re-running several simulations in the high temperature regime to see how often this happens. Ignoring these pathological cases, we obtain the following phase diagram:

Nucleation

To measure the amount of nucleation, we count the number of anti-site defects in an atom configuration. Here is the phase diagram:

We see that anti-sites do not occur except for the low temperature/high AS flux case.

Summary

Here are the simulation results presented in one phase diagram:

The dotted black line indicates the set of parameter space we had considered in previous posts. It is important to note that these linear boundaries are fitted to simulation data, and hence serve only as an approximate phase diagram. For example, the boundaries predict a region where nucleation occurs, but no liquid cores are observed. However, this is not actually observed in the simulations.

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