Kris's Research Notes

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.

We follow the experimental procedure outlined here. All simulations were performed on a domain of width 1024 atoms (about 292 nm). Droplet statistics were calculated by examining the final atom configuration of each trial. Droplet widths were calculated using the autocorrelation of the resulting height profile and with a simple thresholding scheme. Thresholding was done by ignoring those atoms below a specified threshold height above the minimum height of the configuration, as illustrated below:

\theta series (T = 456K)

We varied \theta in:

\displaystyle \theta = \left\{2.7, 2.9, 3.7, 4.2, 4.7\right\} monolayers of Ga.

Temperature was fixed at T = 456K. Statistics were obtained by ensemble averaging 128 independent trials, and are summarized below:

\theta # Droplets Width – Thresholding (#atoms) Width – Autocorrelation (#atoms)
2.7 8.5234 32.4204 29.7435
2.9 8.6250 35.2875 30.4465
3.7 8.3672 54.2442 32.8690
4.2 7.7891 69.3675 34.9988
4.7 7.3047 84.8789 35.9573

Here are plots of the data along with our experimental results:

Droplet Width (nm) vs Thickness

Linear Density (#/μm) vs. Thickness

Temperature Series \theta = 2.9 ML

Here, we vary temperature T \in \left\{456, 464, 723\right\}K and fix \theta 2.9 monolayers Ga. Simulation statistics was obtained by ensemble averaging 128 independent trials.

T(K) # Droplets Width – Thresholding (#atoms) Width – Autocorrelation (#atoms)
456 8.5625 35.4258 31.1199
464 8.1667 35.2945 31.1053
472 8.3402 34.1838 29.5492

Here is the data plotted with experimental results:

Droplet Width (nm) vs. Temperature (°C)

Linear Density (#/μm) vs. Temperature (°C)

We observe that simulation results are essentially constant while there is a clear trend in experimental data. This is readily explained by the fact that in our simulations, low temperatures yield rough surfaces (exacerbated by the fact that simulation results in 1+1 dimension are often rougher than 2+1). Hence, there is a significant amount of noise in simulation data. This can be addressed by both increasing the amount of Ga deposited (yielding larger droplets and hence delineating surface roughness from genuine droplets) and increasing temperature (making the surface smoother).

Indeed, if we consider \theta = 3.5 monolayers Ga and a larger for temperature (including higher temperature cases) we get similar trends to the data. For example, if we consider temperature in

\displaystyle T \in \left\{ 450, 470, 490, 510, ..., 590 \right\} K,

and fix \theta = 3.5 monolayer Ga, we obtain the following plots:

Droplet Width (nm) vs. Temperature (°C)

Linear Density (#/μm) vs. Temperature (°C)

It appears that simulation data is too noisy for cases T < 220^\circC, but correct qualitative trends appear past this point.

N.B. For these trials, statistics were obtained from 16 independent trials for each choice of T.

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