Alloy composition fluctuations and percolation in semiconductor alloy quantum wells

Fluctuations in local alloy composition on small length scales may have a significant effect on device performance, particularly when there is a large disparity in the properties such as atomic size of the constituent alloy components. In particular, a random alloy is subject to a percolation threshold, above which an infinitely connected network of the minority alloy component exists. While these percolation thresholds are well known for ideal 2D and 3D lattices, they are unknown for the intermediary "2.5D" case, appropriate for quantum well structures. This letter presents calculations of the percolation threshold for 2.5D quantum well-like hexagonal, diamond/silicon and body-centred cubic lattices that are directly relevant to many semiconductor alloys, and enables further experimental inquiry into the effect of percolation on the properties of semiconductor alloys.