The effects of unit cell size on the bandgap range in the direct enumeration study of AlxGayIn1−x−yP alloys

Direct enumeration method is an efficient way for scanning alloy properties by computing all possible configurations. This method thoroughly covers all possible configurations without bias and provides an informative trend of alloy properties on ordering patterns. In an actual study, the number of possible configurations increases rapidly with the size of the unit cell and usually a reasonable size that give a sufficiently large number of configurations are chosen. In this work, the convergence of the bandgap range with respect to the unit cell size of AlGaInP alloy is studied up to 8 cation atoms per unit cell. It is found that the bandgap range already converges to within 0.1 eV when the unit cell size is 4 cation atoms. Interestingly, we also found that the lowest bandgap value of GaInP alloy is achieved already in a small cell (2 cations in the unit cell). The cause for this special small bandgap case is discussed.