However, random substitutional alloys lack formal translational symmetry and therefore, cannot be described by the standard bandstructure E( k) dispersion. We use the effective band structure (EBS), proposed by Popescu and Zunger, to interpret the conduction band electronic structure of the alloys. The computational details of EBS calculations are provided in the Methods (Section 4.4). The EBS is obtained by unfolding the SQS supercell bands to the primitive cell Brillouin zone using spectral decomposition. The resulting EBS reveals the extent to which the band characteristics are preserved or lost. Band convergence can be determined by examining the EBS. In addition, the linewidth or band broadening at each E( k) is reflective of the electronic carrier lifetimes due to alloy scattering; the larger the band broadening (more "smeared" bands), the shorter the carrier lifetimes.