Kris's Research Notes

May 31, 2011

Substrate Growth without Extended Species

Filed under: GaAs Simulations — Kris Reyes @ 8:58 pm

This is a follow up of this post. In that post, we were able to grow droplets without using the notion of extended species. In this post, we examine substrate growth without extended species.

With respect to substrate growth, we had used extended species to differentiate between different scenarios which had the same number of Ga-As bonds. Consider three cases: 1) adatom hopping, (2) an atom breaking off from a step-edge and (3) an atom breaking off from a completed layer:

All three events break two Ga-As bonds, and yet we would expect that the three events would occur at different rates. We addressed this by stating that the Ga-As bonds in each of the three cases were different. Specifically, for the first case we break two Ga(2)-As(3) bonds, in the second case we break a Ga(2)-As(4) and a Ga(2)-As(3) bond and in the last case we break two Ga(2)-As(4) bonds. Since we always used the general rule:

\displaystyle \gamma(Ga(2), As(3)) \geq \gamma(Ga(2), As(4)),

each case is has a higher barrier than the previous. Specifically, we had set \gamma(Ga(2), As(3)) = 0.3 eV, \gamma(Ga(2), As(4)) = 0.6 eV. Therefore, case 1 had a barrier of 0.6 eV, case 2 had a barrier of 0.9 eV and case 3 had a barrier of 1.2 eV.

Observe that each case differs from its previous case by one Ga-Ga next-nearest bond strength. Therefore, we can alternatively distinguish between these three cases if we set this bond strength \gamma^\prime_{GG} = 0.3 eV instead of using extended species.

I tried to grow GaAs without extended species. I fixed \gamma_{AA} = 0.1 eV, \gamma_{GG} = 0.3 eV. I also fixed the desorption potential of As, \mu_{As} = 0.35 eV. I varied the other energy parameters as:

\displaystyle \gamma_{GA} \in \left\{0.5, 0.6, \hdots, 1.0\right\} eV,

\displaystyle \gamma^\prime_{GG} = \gamma^\prime_{AA} \in \left\{ 0.1, 0.2, 0.3 \right\} eV.

I grew GaAs with flux R_{Ga} = 0.58 monolayers/second and R_{As} = 2.32 monolayers/second (a ratio of 4:1 As to Ga). The temperature was 700K. I deposited material for 10 seconds.

Here are the results for different values of \gamma_{GA} and \gamma^\prime_{GG}=\gamma^\prime_{AA} =: \gamma^\prime:

\gamma_{GA} \backslash \gamma^\prime 0.1 eV 0.2 eV 0.3 eV
0.5eV movie movie movie
0.6eV movie movie movie
0.7eV movie movie movie
0.8eV movie movie movie
0.9eV movie movie movie
1.0eV movie movie movie

For each set of parameters, I also ran the identical simulation as in the previous post, droplet formation without extended species. Here are the results:

We see that there there is indeed step flow case in the case \gamma_{GA} = 0.6 eV, \gamma^\prime = 0.2 eV for example. There are other cases where the growth is somewhat rougher, but this may be due to the low temperature. I am currently running similar simulations at a temperature T = 800 K.

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