# 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.

## April 26, 2012

### Mullins Sekerka Instability and Liquid Cores

Filed under: GaAs Simulations — Kris Reyes @ 10:55 pm

In this note, we model the formation of liquid cores during droplet crystallization as a Mullins Sekerka instability. We then compare the theoretical critical curve for the instability with simulation results.

### A Mullins-Sekerka Instability for Crystallization

Filed under: GaAs Simulations — Kris Reyes @ 9:05 am

In this note, we show how the deposition of As into liquid Ga exhibits a Mullins-Sekerka instability.

## April 24, 2012

### Morphological Phase Diagrams

Filed under: GaAs Simulations — Kris Reyes @ 9:02 am

In this note, we present three morphological phase diagrams illustrating the presence of (1) nanorings, (2) liquid cores and (3) nucleation. The experimental procedure is altered to omit the last annealing step, in order to simplify the discussion. We also consider higher temperatures and lower As flux than before.

## April 10, 2012

### Nucleation Regime. Part 2

Filed under: GaAs Simulations — Kris Reyes @ 11:41 pm

This note is a follow-up to this post. In that note, we developed an expression for when nucleation is possible by expressing the rate of change in concentration $c_r$ as the net effect of atoms impinging upon the nucleus (given by an As flux and Laplace’s equation) and atoms leaving the nucleus (given by the Gibbs-Thomson relation). In this note, we discuss the problems with the discussion in that post and describe alternative models for surface nucleation.

## March 21, 2012

### Nucleation Regime

Filed under: GaAs Simulations — Kris Reyes @ 6:58 pm

In this note we discuss the nucleation process, one of the three key processes involved in droplet epitaxy. We derive an expression for the critical nucleus radius and compare it with the size of a liquid droplet at fixed growth conditions. We shall see that this defines a regime in which nucleation is impossible in equilibrium. This regime agrees well with the morphological phase diagram obtained through simulations.

## March 12, 2012

### 2+1 GaAs Simulations

Filed under: GaAs Simulations — Kris Reyes @ 4:21 pm

Our KMC code can be easily extended to 2+1 dimensions by altering the underlying lattice to include a z-component. In this note, I describe how this change was made and present interesting simulation results from a brief set of runs with the 2+1 system. While the parameters used have not been tuned to experimental evidence, we see that the simulations are able to capture a wide range of phenomena that depend on both energy and experimental parameters. This can serve as a starting point for future work.

## 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.

## February 15, 2012

### Bulk Diffusion and Liquid Cores

Filed under: GaAs Simulations — Kris Reyes @ 6:27 pm

Recall, we had discovered that antisite defects in GaAs diffused through the crystal quite quickly. In this note, we discuss a bulk diffusion barrier that addresses this problem.

## November 15, 2011

### Some Droplet Statistics

Filed under: GaAs Simulations — Kris Reyes @ 5:50 am

In this note, we examine droplet width and linear density as a function of temperature $T$ and the amount of Ga deposited $\theta$.

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