Cluster expansion based configurational averaging approach to bandgaps of semiconductor alloys

Configurationally disordered semiconducting materials including semiconductor alloys [e.g., (GaN)_1-x(ZnO)_x] and stoichiometric materials with fractional occupation (e.g., LaTiO₂N) have attracted a lot of interest recently in search for efficient visible light photo-catalysts. First-principles modeling of such materials poses great challenges due to the difficulty in treating the configurational disorder efficiently. In this work, a configurational averaging approach based on the cluster expansion technique has been exploited to describe bandgaps of ordered, partially disordered (with short-range order), and fully disordered phases of semiconductor alloys on the same footing. We take three semiconductor alloys [Cd_1-xZn_xS, ZnO_1-xS_x, and (GaN)_1-x(ZnO)_x] as model systems and clearly demonstrate that semiconductor alloys can have a system-dependent short-range order that has significant effects on their electronic properties.