Direct enumeration of alloy configurations for semiconductor electronic structure properties*

We present an approach to directly enumerating the electronic structure of all possible zincblende-based alloy configurations whose unit cell contains up to a specified number of atoms. This method allows us to map the space of bandgaps and effective masses versus alloy composition and atomic configuration. We demonstrate for GaInP alloys that a large range of bandgaps and masses are available for a given composition. By decomposing the space of possible atomic configurations into categories based on superlattice structure, we can identify trends in bandgap extrema. For example, bandgap maxima typically occur in [0 h k] superlattices where h is not equal to k, and minima typically occur in [1 1 1] superlattices. We focus on dilute alloys where the minority composition is below 10 percent. The empirical pseudo potential method (EPM) and folded spectrum method are used to solve the single particle Schr\"{o}dinger equation. The results from the EPM are compared with first- principle calculations.