Undoing band anticrossing in highly mismatched alloys by atom arrangement

The electronic structures of three highly mismatched alloys (HMAs)—GeC(Sn), Ga(In)NAs, and BGa(In)As—were studied using density functional theory with HSE06 hybrid functionals, with an emphasis on the local environment near the mismatched, highly electronegative atom (B, C, and N). These alloys are known for their counterintuitive reduction in the bandgap when adding the smaller atom, due to a band anticrossing (BAC) or splitting of the conduction band. Surprisingly, the existence of band splitting was found to be completely unrelated to the local displacement of the lattice ions near the mismatched atom. Furthermore, in BGaAs, the reduction in the bandgap due to BAC was weaker than the increase due to the lattice constant, which has not been observed among other HMAs but may explain differences among experimental reports. While local distortion in GeC and GaNAs was not the cause for BAC, it was found to enhance the bandgap reduction due to BAC. This work also found that mere contrast in electronegativity between neighboring atoms does not induce BAC. In fact, surrounding the electronegative atom with elements of even smaller electronegativity than the host (e.g., Sn or In) consistently decreased or even eliminated BAC. For a fixed composition, moving Sn toward C and In toward either N or B was always energetically favorable and increased the bandgap, consistent with experimental annealing results. Such rearrangement also delocalized the conduction band wavefunctions near the mismatched atom to resemble the original host states in unperturbed Ge or GaAs, causing the BAC to progressively weaken. These collective results were consistent whether the mismatched atom was a cation (N), anion (B), or fully covalent (C), varying only with the magnitude of its electronegativity, with B having the least effect. The effects can be explained by charge screening of the mismatched atom's deep electrostatic potential. Together, these results help explain differences in the bandgap and other properties reported for HMAs from different groups and provide insight into the creation of materials with designer properties.