Origin of the failed ensemble average rule for the band gaps of disordered nonisovalent semiconductor alloys

Recent calculations show that the band gaps of the nonisovalent random alloys such as Zn0.5Sn0.5P are much smaller than those of their ordered phases; that is, the band gap of the random alloy is not the ensemble averaged value of the ordered structures, in contrast to the trend observed in most isovalent semiconductor alloys and predicted by the cluster expansion theory. We show that this abnormal behavior is caused by the strong wave-function localization of the band-edge states in the nonisovalent alloys. Moreover, we show that although the disordered phase of the isovalent alloys is similar to the random phase, for the nonisovalent alloy, the disordered phase deviates significantly from the random phase and the fully random phase is not achievable under the equilibrium growth conditions.