Kris's Research Notes

July 13, 2012

Crystallization on Grooved Substrates

Filed under: GaAs Simulations, KMC — Kris Reyes @ 3:01 am

In this note, we consider liquid Ga droplet formation and crystallization by As on a substrate with a triangular groove. We study the effect of substrate species by considering first a GaAs substrate and second a substrate composed of a third species (nominally Si). In the latter case, nucleation at the liquid/solid interface is not preferred leading to increased surface nucleation as well as a different geometry of the crystallization front.

GaAs Substrate

All simulations are done on a domain 256 atoms wide. A triangular pit with side length 64 atoms was removed. Ga atoms were deposited at a rate of 0.1 ML/sec until 6.0 monolayers of Ga was deposited. The system was then annealed in the absence of any deposition for 60 seconds. Lastly, an As flux was introduced at a deposition rate F_{As} ML/sec, where

\displaystyle F_{As} \in \left\{0.05, 0.1, 0.2, 0.4\right\} ML/sec.

The temperature T was also varied:

\displaystyle T \in \left\{473, 523, 573, 623 \right\} K.

Here are the results arranged in rows by constant F_{As} and in columns by constant T:

[Recall our coloring scheme: Red = Ga atoms in substrate, Green = As atoms in substrate, Purple = Ga atoms deposited, Blue = As atoms deposited.]

The simulations behave as expected with respect to deposition rate and temperature. In the low temperature case, we have nucleation of several smaller droplets, though it is interesting that there seems to be a preference to nucleate near or in the pit. In the low temperature/high As flux regime, we observe liquid cores. In the high temperature, low As flux, the system appears to try to form flat GaAs layers, filling in the pit.

Si Substrate

We performed simulations identical to above, except that the substrate was changed to a third species, which we identify nominally as Si. The nearest neighbor bonding energies were specified as:

\displaystyle \gamma(Ga, Ga) = 0.30 eV

\displaystyle \gamma(As, As) = 0.10 eV

\displaystyle \gamma(Ga, As) = 0.50 eV

\displaystyle \gamma(Ga, Si) = 0.25 eV

\displaystyle \gamma(As, Si) = 0.25 eV

and next-nearest neighbor bonding energies:

\displaystyle \gamma_{nn}(Ga, Ga) = 0.30 eV

\displaystyle \gamma_{nn}(As, As) = 0.10 eV

\displaystyle \gamma_{nn}(Ga, Si) = 0.25 eV

\displaystyle \gamma_{nn}(As, Si) = 0.25 eV

so that the next-nearest neighbor bonding energies are identical to the nearest neighbor bonding energies for all but the Ga-As bond case. Large bonding energies between Si atoms were used in order to ensure that the Si atoms remain fixed and don’t participate in the simulations.

\displaystyle \gamma(Si, Si) = 1.50 eV,

\displaystyle \gamma_{nn}(Si, Si) = 1.50 eV

Here are the results (Si atoms are colored gray):

We observe the presence of channels of liquid Ga at the liquid/solid interface in several of the simulations:

This suggest that nucleation at this interface is not preferred. Suppose GaAs seed nucleates at the interface:

If we compare the local energy about an As atom in this configuration with the energy about an As atom in a completely GaAs neighborhood, we see that the former has a higher bonding energy:

On the interface, an As atom in a nucleating cluster has local energy

\displaystyle 3\gamma(Ga, As) + 2\gamma_{nn}(As, As) + 2\gamma(As, Si) + \gamma_{nn}(As, Si) = 2.45 eV

while the As atom in a GaAs neighborhood has local energy

\displaystyle 4\gamma(Ga, As) + 4\gamma_{nn}(As, As) = 2.40 eV,

and so for the energies selected, it is more energetically favorable for an As atom to reside on the interface than in a GaAs neighborhood. Similar calculations may be performed on slightly different neighborhoods from the ones considered above yielding the same conclusion. This is counter to the results above, which suggests there is an implicit nucleation barrier at the liquid/solid interface.

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