Kris's Research Notes

September 6, 2011

Droplet Formation and Crystallization

Filed under: GaAs Simulations — Kris Reyes @ 11:51 am

We simulate droplet formation and crystallization at various energy parameters and temperatures.

Recall we had previously determined a set of parameters which yield step flow growth of GaAs in the temperature range $[700, 925]K$ and a reasonable number of droplets (five or more) formed at 473K. In this note, we consider droplet growth and crystallization at 473, 523 and 573K. As before, we vary $\gamma_{GG}, \gamma_{HH}$ and $\lambda_D$. Specifically:

$\gamma_{GG} \in \left\{0.28, 0.29, 0.30\right\}$,

$\gamma_{HH} \in \left\{-0.5, -0.6, ..., -1.0\right\}$,

$\lambda_D \in \left\{0.3, 0.4, ..., 1.0 \right\}$.

The initial configuration was a 1024×64 As-terminated substrate of GaAs. We simulate the following experimental procedure:

1. Deposit Ga at a rate of 0.1 monolayers/sec at $T = 473, 523, 573$K until 3.5 monolayers has been deposited.
2. Anneal with no flux for 60 seconds at temperature $T$.
3. Deposit As (light blue in the simulations) at a rate of 0.1 monolayers/sec for 60 seconds at temperature $T$.
4. Increase temperature to 625K while maintaining the above As flux (dark blue) for 5 minutes.

Here is the result for $\gamma_{GG} = 0.3$ eV, $\gamma_{HH} = -0.70$ eV and $\lambda_D = 0.70$ eV:

We observe that for the $T = 473$K case, we see explicit GaAs nanodots. We also see a large incorporation of As deposited during the last phase (high temperature) of the experiment. Here is the configuration of this trial after the third phase — droplets crystallized at 473K before the temperature is increased:

We see that before the temperature is increased, the crystallized droplets have small liquid Ga core. When the temperature is increased, this liquid core quickly escapes from the GaAs shell, and fully crystallize droplets are allowed to form. Here is the configuration 0.4 seconds after the temperature is increased:

The newly exposed Ga reacts with the deposited As, hence the high concentration of dark blue As atoms at the surface.

We do not observe this in the higher temperature cases. There still is a small Ga liquid core in the T=523 case. Perhaps the GaAs core is to thick for the Ga to escape. In this case, we observe the transition from nanodrops to nanorings. This transition has completely occurred in the T=573 case where we see explicitly nanoring formation.

Here is the Ga surface concentration phase diagram for the above choice of parameters:

There are more parameters which exhibit the above behavior — nanodots at 473K, nanorings at 573K and a transition state at 523K. For example, here is $\gamma_{GG} = 0.30$ eV, $\gamma_{HH} = -0.80$ eV, and $\gamma \lambda_D = -0.80$ eV:

This example also seems to exhibit a double nanoring in the T=573 case.

These simulations seem to agree with experiments at lower experimental temperatures different temperatures. That is, the nanorings observed at T=573K in our simulations tend to agree (in size) with the experiments at T=523K. For example, in experiments, nanorings of diameter on the order of 100 to 150 atoms were observed at 523K, whereas in our simulations, we get such nanorings at 573K. Hence for parameter values $\gamma_{GG} \approx 0.3$, $\gamma_{HH} \approx -0.7$, $\lambda_D \approx -0.7$ eV, we get good qualitative agreement with experiments in both substrate growth and droplet formation/crystallization.