# Kris's Research Notes

## February 7, 2011

### Model Parameters — Part 3.

Filed under: GaAs Simulations — Kris Reyes @ 8:03 am

This is a follow-up to this post.

Recall in the previous post, we noted for the low temperature/high As over pressure regime, we observed excess As. We noted at the end that this could be addressed by either lowering the $As-As$ bond strength or introducing a sufficiently small desorption potential for $As(0)$ which would effectively disallow excess As.

## Lowering As-As bond strength

I first lowered the As-As bond strength. This has the advantage of not introducing an extra parameter $\mu_{As(0)}$, but requires more computation-time as now As diffusing on excess As will take up significantly more MC steps.

In this run, we set all $As-As$ bond strengths to 0.05 eV. The $\gamma_{i,j} = \gamma(Ga(i), As(j))$ bond strengths are

$(\gamma_{i,j}) = \begin{pmatrix} 0.19 & 0.19 & 0.19 & 0.19 \\ 0.19 & 0.19 & 0.19 & 0.95 \\ 0.19 & 0.19 & 0.95 & 0.95 \\ 0.19 & 0.95 & 0.95 & 0.95 \end{pmatrix}$ eV.

All $Ga-Ga$ bond strengths were set to 0.25 eV, except for $\gamma(Ga(0), Ga(0)) = 0.30 eV$. The exchange coefficient was set at 0.3.

I varied temperature $T$ as

$T \in \left\{714, 769, 833, 900\right\},$ K

and $r_{\downarrow As}$ as:

$r_{\downarrow As} \in \left\{1, 2, 4, 6, 8, 10\right\},$ monolayers/second

and fixed $r_{\downarrow Ga} = 1$ monolayers/second. I varied $\mu_{As}$:

$\mu_{As} \in \left\{0.4, 0.5, 0.6, 0.7\right\},$ eV.

The experiments were done on a lattice of width 4092 atoms. To calculate the surface concentration, I averaged over the last 10 of 1000 frames. For each frame, I counted how many atoms of each species were exposed to vacuum.

Here are the phase diagrams (organized with increasing $\mu_{As}$) along with Denis’s experimental data:

We see that this doesn’t provide a good match to experiments and a large $\mu_{As}$ favors a more As-terminated surface in addition to making the surface reconstruction less dependent on temperature.

Here are some frames for reference. Consider the $\mu_{As} = 0.4 eV, T = 833 K$ case. According to our phase diagram, the transition from a $Ga$-terminated surface to a $As$ terminated one occurs around $r = \frac{r_{As}}{r_{Ga}} = 4$ in our simulations. Here are sample frames for $r = 1, 2, 4$ and $6$ for this case:

We see that for Ga droplets occur for the low ratio cases, while at $r=4$, the surface has both As and Ga atoms. At $r = 6$, we have a purely As-terminated surface.

As another example, in the $\mu_{As} = 0.5 eV, T = 900 K$ case, the transition occurs between $r = 3$ and $r = 4$. Here are sample frames for $r = 2, 4, 6$:

We see the $r = 2$ case still contains droplets while when $r = 4, 6$ we get a mostly As-terminated surface, which again agrees with the phase diagram.

## Setting As(0) desorption potential low

Now we set $As-As$ bonds back to 0.10 eV and create a new desorption potential for As(0) atoms — that is atoms only attached to other As atoms. If set sufficiently low, this effectively prevents excess As from occurring. I fix $\mu_{As(0)} = 0.01$ eV, a nominally small value, in order to achieve this. Apart from this, I repeat the same experiment as above, varying $\mu_{As}, T$ and $r$.

Here are the phase diagrams for $\mu_{As} = 0.4, 0.5, 0.6$ and $0.7$ eV, respectively:

This also doesn’t produce a good fit to experimental data. While increasing the desorption potential seems to make the shape of the plot agree more qualitatively with experiments, the simulations produce consistently Ga-terminated surfaces.

To confirm again that these contour plots agree with what we see in the movies, here is the $\mu=0.6, T = 714 K$. According to the phase diagram, we should see a gradual change from a Ga to an As-terminated surface as we vary $r$:

The progression of the phase diagrams above may suggest increasing $\mu_{As}$ to a larger value. But even at $\mu_{As} = 1.0 eV$, the surface is still Ga-terminated when $T = 833 K, r = 2$ — which is incorrect:

To confirm we do not get excess As, here is the $\mu_{As} = 0.6, T = 573, r = 80$ case:

Indeed, we do not have As droplets. This run took 143 seconds, which is much faster than the method above.

## Conclusion

Recall: we started our investigation trying to produce the correct transition for the $T=833K$ case between $r = 1$ and $2$, while disallowing excess As. We have seen in the previous post, if $As-As$ bond strength was set to 0.10 eV, we got excess As for as low as $\mu_{As} = 0.40$ eV but we needed (according to our model) a potential of at least $\mu_{As} = 0.5$ eV to produce the correct transition at $T=833K$. We addressed this in two ways. First we lowered the $As-As$ bond strength to 0.05 eV. This produced surfaces that where Ga-terminated, but we could attempt to fix this by increasing $\mu_{As}$. This, however, doesn’t preserve the temperature dependence of the phase diagram, as illustrated in the extreme by the $\mu_{As} = 0.7$ eV case. Then we tried explicitly disallowing excess $As$ by introducing a desorption potential $\mu_{As(0)}$ for those As atoms on top of other As atoms. While this produced more qualitatively accurate phase diagrams, we could not get phase change in the correct spots. The simulations always favored more Ga-terminated surfaces.