Effect of concentration fluctuations on material properties of disordered alloys

Alloying compound $AX$ with another compound $BX$ is widely used to tune material properties. For disordered alloys, due to the lack of periodicity, it has been challenging to calculate and study their material properties. The Special quasi-random structure (SQS) method has been developed and widely used to treat this issue by matching averaged atomic correlation functions to those of ideal random alloys, enabling accurate predictions of macroscopic material properties such as total energy and volume. However, in $A_xB_{1-x}$ alloys, statistically allowed local concentration fluctuations can give rise to defect-like minority configurations, such as bulk-like $AX$ or $BX$ regions in the extreme, which could strongly affect calculation of some of the material properties such as semiconductor bandgap, if it is not defined properly, leading to significant discrepancies between theory and experiment. In this work, taking the bandgap as an example, we demonstrate that the calculated alloy bandgap can be significantly underestimated in standard SQS calculations when the SQS cell size is increased to improve the structural model and the bandgap is defined conventionally as the energy difference between the lowest unoccupied state and the highest occupied state, because the rare event motifs can lead to wavefunction localization and become the dominant factor in determining the “bandgap”, contrary to experiment. To be consistent with the experiment, we show that the bandgap of the alloy should be extracted from the majority configurations using a density-of-states fitting (DOSF) method. This DOSF approach resolves the long-standing issue of calculating the electronic structure of disordered semiconductor alloys. Similar approaches should also be developed to treat material properties that depend on localized alloy wavefunctions.