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 ΔEg relative to the random alloy, a crystal field splitting ΔCF at valence-band maximum, as well as an increase of spin-orbit splitting ΔSO. We calculate these quantities for AlₓIn_1-xP, AlₓIn_1-xAs, GaₓIn_1-xP, and GaₓIn_1-xAs 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 ΔE₁₂ (between Γ4,5v and Γ₆ᵥ⁽¹⁾) and ΔE₁₃ (between Γ4,5v and Γ₆ᵥ⁽²⁾) for these materials as a function of the degree {η} of long range order. In the absence of an independent measurement of {η}, experiment is currently able to deduce only the ratio ΔEg/ΔCF. Our LDA-corrected results for this quantity compare favorably with recent experiments for GaₓIn_1-xP and GaₓIn_1-xAs, but not for AlₓIn_1-xP, where our calculation does not support the experimental assignment. The ``optical LRO parameter {η}'' can be obtained by fitting our calculated ΔEg(η) to the measured ΔEg(η), and by expressing the measured ΔE₁₂(η) and ΔE₁₃(η) in terms of our calculated ΔCF(η) and ΔSO(η). We also provide the calculated x-ray structure factors for ordered alloys that can be used experimentally to deduce {η} independently.