# Kris's Research Notes

## February 22, 2012

### How Ga-As and Ga-Ga bonds affect Roughness and Wicking. Also, nanowires.

Filed under: GaAs Simulations — Kris Reyes @ 1:10 am

Recall previously we had considered increasing the Ga-As bond strength $\gamma_{GA}$ and decreasing the Ga-Ga bond strength $\gamma_{GG}$. Doing so would increase the difference in the local energies between a solid, crystalline and liquid neighborhoods. With our old energies ($\gamma_{GA} = 0.5$eV, $\gamma_{GG} = 0.3$eV), the difference in local energies between solid and liquid neighborhoods is = 0.8 eV. Setting $\gamma_{GA} = 0.7$eV and $\gamma_{GG} = 0.24$eV, this difference becomes 1.84 eV. In this note, we examine the effect of changing these parameters on simulation results.

The new energies affect the simulations in two main ways. First, an increase in $\gamma_{GA}$ results in a roughening of the surface due to a stronger persistence of GaAs nuclei on the surface. Second, the smaller $\gamma_{GG}$ value suggests that a Ga atom in the liquid is more likely to leave and nucleate away from the droplet, i.e. the rate of the wicking process (detailed here) is increased.

For example, consider the crystallization of a liquid droplet at 623K via an As flux of 1.00 ML/sec. We consider the simulation results using the old and new energies. Here are the surfaces away from the liquid droplet under both the old and new energies:

 $\gamma_{GA} = 0.5$eV, $\gamma_{GG} = 0.30$eV $\gamma_{GA} = 0.7$eV, $\gamma_{GG} = 0.24$eV

Indeed, the surface is much rougher for the large $\gamma_{GA}$ case. If we examine the neighborhood near the liquid droplet after crystallization has occurred, we observe a significant morphological difference between the two cases:

 $\gamma_{GA} = 0.5$eV, $\gamma_{GG} = 0.30$eV $\gamma_{GA} = 0.7$eV, $\gamma_{GG} = 0.24$eV

In the former case, the rate of the wicking process essentially occurs on the same order as the rates for the other processes. In the former case, the wicking rate is on a different order, and hence hardly any crystallization occurs at the site of the liquid droplet.

We may measure how sensitive the resulting morphology is to both $\gamma_{GA}$ and $\gamma_{GG}$ by crystallizing a liquid droplet for various choices of energies. For example, we vary $\gamma_{GA}$ between 0.35 eV to 0.7 eV, fixing $\gamma_{GG} = 0.24$ eV.

 $\gamma_{GA} = 0.7$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.6$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.50$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.40$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.30$ eV, $\gamma_{GG} = 0.24$ eV,full frame

We see that for all but the lowest value of $\gamma_{GA} = 0.30$ eV, a hole forms. Something completely different happens in the $\gamma_{GA} = 0.30$ eV case: a nanoring begins to grow. To examine, this, we consider the refine our search, varying $\gamma_{GA}$ between 0.30 eV to 0.40 eV.

 $\gamma_{GA} = 0.40$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.39$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.38$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.37$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.36$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.35$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.34$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.33$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.32$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.31$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.30$ eV, $\gamma_{GG} = 0.24$ eV,full frame

We see that around $\gamma_{GA} = 0.34$ eV, the system switches from material preferentially leaving the droplet site to preferentially entering the site. That is, the wicking mechanism is effectively turned off (and possibly reversed) for low $\gamma_{GA}$. This may suggests a convection term is relevant when modeling the wicking process. Of course, this is not enough to explain nanowires — in place crystallization can also occur if wicking is not present. Indeed, there appears to be some sort of phase segregation driving the nanowire formation.

We also may fix $\gamma_{GA} = 0.5$ ev and vary $\gamma_{GG}$ between 0.24 eV and 0.30 eV.

 $\gamma_{GA} = 0.50$ eV, $\gamma_{GG} = 0.24$ eV,full frame $\gamma_{GA} = 0.50$ eV, $\gamma_{GG} = 0.26$ eV,full frame $\gamma_{GA} = 0.50$ eV, $\gamma_{GG} = 0.28$ eV,full frame $\gamma_{GA} = 0.50$ eV, $\gamma_{GG} = 0.30$ eV,full frame