Study of percolation and modeling of the order-disorder transition for zincblende-diamond structures: Percolation and the existence of a unique band of events

In this paper, the dependence of the crystallographic direction in the critical concentration of IV-type atoms for the zincblende-diamond (order-disorder) transition in (III-V)-IV semiconductor alloys were found for the (001), (110), and (111) growth directions by using Monte Carlo simulations. Intervals for the concentration values were determined by simulation, generating a band that is consistent with experimental data. Selecting the average value of this band produces good agreement with previous experimental results. It was also found that the relationship between order parameter and concentration does not have unique values and that there exists a band of events. The existence of this band can explain the scatter in the experimental data reported in x-ray, Raman, and optical anisotropy. It was found that the site percolation threshold is independent of the crystallographic direction of growth and converges to a single concentration value x ≈ 0.437.