Kris's Research Notes

November 19, 2010

Droplet Size Experiments

Filed under: GaAs Simulations — Kris Reyes @ 4:18 am

In this post we discuss Ga droplet formation as a function of model parameters \gamma_{droplet} = \gamma(G0, G0), \gamma_{surface} = \gamma(G2, A4) and physical parameters T, r_{\downarrow Ga} and d, the amount of Gallium deposited (monolayers). (more…)

November 15, 2010

Rereading Krug

Filed under: Stat. Mech for SOS Model — Kris Reyes @ 8:54 am

I am currently rereading J. Krug’s paper “Atom Mobility for the Solid-on-Solid Model.” I think I understand more of it than last time, so I will now attempt to discuss the continuum limit for the evolution of a height profile. (more…)

November 4, 2010

GaAs Crystal Growth: Phase Diagram pt. 2

Filed under: GaAs Simulations — Kris Reyes @ 7:03 pm

This is a follow-up of this post.

I was worried that the asymmetry between the surface Gallium bond strength \gamma(Ga(2), As(4))  (which was set 0.7 eV in the previous post) and the surface Arsenic bond strength \gamma(Ga(4), As(2)) (which I varied between 0.85 eV and 0.95 eV). In these trials, I made these two bond strengths more symmetric. Specifically, I fixed \gamma(Ga(2), As(4)) = 0.95 eV, and I varied \gamma(Ga(4), A(s2)) \in \left\{0.85, 0.95\right\} eV. I also varied Gallium flux r_{\downarrow Ga} \in \left\{ 1, 5 \right\} monolayers/second. Here are the four resulting contour plots. (Note the horizontal label is incorrect. It should read r_{\downarrow As}/r_{\downarrow Ga}.) (more…)

November 3, 2010

GaAs Crystal Growth: Phase Diagram

Filed under: GaAs Simulations — Kris Reyes @ 10:53 pm

Recall we wished to examine how a GaAs crystal is terminated as a function of deposition rates r_{\downarrow Ga}, r_{\downarrow As} (measured in monolayers per second) and temperature T (measured in degrees Kelvin). Specifically, we wish to determine the proportion of  Gallium surface atoms (defined to be Gallium atoms exposed to vacuum) to surface atoms in general. In the following trials, we vary temperature

T \in \left\{ 400, 417, 435, 455, 476, 500, 526, 555, 588, 625, 666, 714, 769, 833, 909, 1000 \right\}

and deposition ratio \rho = r_{\downarrow As}/r_{\downarrow Ga}

\rho \in \left\{ 0.1, 0.2, 0.4 ,0.6, 0.8, 1, 2, 4, 6, 8, 10, 20 , 40, 60 , 80, 100 \right\}.

The energy \gamma(Ga(4), As(2) is the relevant bond strength for an Arsenic atom on the surface of the crystal, and I vary this as well. The surface Gallium bond strength \gamma(Ga(2), As(4)) was fixed at 0.7 eV, which was left over from the droplet experiments (in a later post, I will change this to a more symmetric case). (more…)