Fingerprints of CuPt ordering in III-V semiconductor alloys: Valence-band splittings, band-gap reduction, and x-ray structure factors

Spontaneous CuPt ordering induces a band-gap reduction E₆ relative to the random alloy, a crystal field splitting ₂₅ at valence-band maximum, as well as an increase of spin-orbit splitting ₒ₎. We calculate these quantities for AlₗIn₁-ₗP, AlₗIn₁-ₗAs, GaₗIn₁-ₗP, and GaₗIn₁-ₗAs using the local density approximation (LDA), as well as the more reliable LDA-corrected formalism. We further provide these values and the valence-band splittings E₁₂ (between {}₄, ₅ₕ and {}₆ₕ^ (1) ) and E₁₃ (between {}₄, ₅ₕ and {}₆ₕ^ (2) ) for these materials as a function of the degree of long range order. In the absence of an independent measurement of, experiment is currently able to deduce only the ratio E₆/₂₅. Our LDA-corrected results for this quantity compare favorably with recent experiments for GaₗIn₁-ₗP and GaₗIn₁-ₗAs, but not for AlₗIn₁-ₗP, where our calculation does not support the experimental assignment. The ``optical LRO parameter '' can be obtained by fitting our calculated E₆ () to the measured E₆ (), and by expressing the measured E₁₂ () and E₁₃ () in terms of our calculated ₂₅ () and ₒ₎ (). We also provide the calculated x-ray structure factors for ordered alloys that can be used experimentally to deduce independently.