Kris's Research Notes

October 1, 2010

Some Movies of Crystal Growth

Filed under: GaAs Simulations — Kris Reyes @ 4:02 pm

In this run, I changed the prefactor \Omega in the swapping rates of two atoms A, B:

r_{swap}(A, B) = \Omega e^{-\beta \Delta E_{A,B}},

where \Delta E_{A,B} is the (neighborhood-specific) some measure of the change in energy when swapping atoms A and B. Before it was set at 10^{13}, and I lowered it to 10^9. This has the effect to scaling back the swapping rates and desorption while holding deposition rates constant. This has essentially the same effects of scaling up the deposition rates, but allows us to work with deposition rates that are not as crazy as e.g. 10000 monolayers per second. It also is the one which we haven’t really calculated the exact values for, whereas we had calculated (or know) to some degree the other parameters — except for desorption potential.

I changed the width to 1024 atoms. It was 256 atoms previously.

I also changed bonds between “extended types” slightly. Recall an extended type for an atom encodes in some way the local neighborhood and species of that atom. We had defined 6 types of atoms, which depend on the number of different-species neighbors an atom had:

  • Ga^{(0)} has zero As neighbors;
  • Ga^{(1)} has one, two or three As neighbors;
  • Ga^{(2)} has four As neighbors;

and similarly for As^{(0)}, As^{(1)}, As^{(2)}. The pairwise bond strengths (in eV) are now:

Ga^{(0)} Ga^{(1)} Ga^{(2)} As^{(0)} As^{(1)} As^{(2)}
Ga^{(0)} 0.3 0.25
Ga^{(1)} 0.25 0.25 0.25 0.95
Ga^{(2)} 0.95 1.0
As^{(0)} 0.05 0.05
As^{(1)} 0.25 0.95 0.05 0.05
As^{(2)} 0.95 1.0

The desorption potential for As was set at \mu_{As} = 0.35 eV and \mu_{Ga} = \infty. The deposition rate of Ga was set at r_{\downarrow Ga} = 2 monolayers/sec. I varied the deposition rate for As

r_{\downarrow As} \in \left\{2, 4, 6, \hdots, 20\right\} monolayers/sec.

I also varied the temperature

T \in \left\{ 600, 700, 800, 900, 1000\right\} K.

I ran each trial for a simulation time of 10 seconds. The following table has are links to the movie files. (Note: The horizontal/vertical aspect ratio is almost 1:1 and so because of the width of the crystal, the images are quite long in the horizontal direction. Also note that if you open these in Firefox, you may have to “unzoom” the image by clicking on it, since Firefox tries to fit the entire image into your browser window.)

T \ r_{\downarrow As} 2 4 6 8 10 12 14 16 18 20
600 movie movie movie movie movie movie movie movie movie movie
700 movie movie movie movie movie movie movie movie movie movie
800 movie movie movie movie movie movie movie movie movie movie
900 movie movie movie movie movie movie movie movie movie movie
1000 movie movie movie movie movie movie movie movie movie movie

For each temperature, and Arsenic deposition rate, we can calculate the average (over time) surface Ga concentration, where we count an atom as a surface atom if in contact with the vacuum. For a fixed temperature, we may plot this average as a function of Arsenic deposition rate, and compare the different plots as we vary temperature.This is what the following graph shows. The temperatures T = 600, 700, 800, 900, 1000 correspond to the red, green blue, black and magenta plots, respectively.

We may further increase r_{\downarrow As} for the T= 1000 case if we wanted to see how the plot behaves. Here I plotted the average surface Ga concentration, adding r_{\downarrow As} \in \left\{30, 40, 50\right\}. Here is the plot:

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2 Comments »

  1. […] Filed under: Uncategorized — Kris Reyes @ 1:44 pm I repeated the experiment in this post, but I set . This means it is easier for atoms to […]

    Pingback by Crystal Growth Again « Kris's Research Notes — October 6, 2010 @ 1:44 pm

  2. […] extended species definitions are the same as the ones detailed in this post. The pairwise energies are also the same, except I changed the bond strength to 0.28 eV (I thought […]

    Pingback by Ga Droplet crystallization « Kris's Research Notes — October 8, 2010 @ 2:41 pm


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