Results

From normal Monte Carlo method, we can find that As-rich acts quite differently compared to Ga-rich surface. Ga atoms are much more active than As atom. We can see from below:At 3000k, After 60000 runs, As atoms mostly stay at the original position, while Ga atoms moves a lot.

Note for all the graph: Blue sphere is the As atom while the read sphere is the Ga atom. Different size indicates different layers, the larger the topper. In the normal-view, the paper plane is (001).

Below is the As-riched surface, left is the side-view.

Below is the Ga-riched surface, left is the side-view. You can also see that almost all the Ga aotms move the center of the square of the As atoms of the next layer.

Why the two atoms acts so differently, we can get the answer from the potential contour. As potential contour on the left and Ga on the right.

Ga atom can almost freely move without any potential change while As faces big potential difference.

Note: The potential is only One atom on the layer of the other kind of atom. The size of the square is one side of a unit cell.

Below is the potential curve while running.

Since I have pointed out that Ga atoms prefer to move to the center of the square of the 4 As atoms of the next layer, so I can faster the process by ONLY allowing the Ga atoms to move between the centers. In another words, I use a lattice model. I must thank Xuemin Gu for this. It is his suggestion. Below is a larger size(8*8), and we can see the reconstruction pattern. Left is the original postion, right is the final position.

We can see more clearly below: