Composition dependence of interband transition intensities in GaPN, GaAsN, and GaPAs alloys

Using large (512-atom) pseudopotential supercell calculations, we have investigated the composition dependence of the momentum matrix element Mv,c for transitions between the valence-band maximum and the conduction-band minimum of three semiconductor alloys: GaP_1-xNₓ and GaAs_1-xNₓ, exhibiting large chemical and size differences between their alloyed elements, and GaP_1-xAsₓ, which is a weakly perturbed alloy. In the composition ranges where these alloys have a direct band gap, we find that (i) in GaP_1-xAsₓ, Mv,c is large (like the virtual-crystal value) and nearly composition independent; (ii) in GaAs_1-xNₓ, Mv,c is strongly composition dependent: large for small x and small for large $x;$ and (iii) in GaP_1-xNₓ, Mv,c is only slightly composition dependent and is significantly reduced relative to the virtual-crystal value. The different behavior of GaP_1-xAsₓ, GaP_1-xNₓ, and GaAs_1-xNₓ is traced to the existence/absence of impurity levels at the dilute alloy limits: (a) there are no gap-level impurity states at the x→1 or x→0 limits of GaP_1-xAsₓ, (b) an isolated As impurity in GaN (GaṈ:As) has a deep band gap impurity level but no deep impurity state is found for N in GaAs, and (c) GaṈ:P exhibits a P-localized deep band-gap impurity state and GaP̱:N has an N-localized resonant state. The existence of deep levels leads to wave-function localization in real space, thus to a spectral spread in momentum space and to a reduction of Mv,c. These impurity levels are facilitated by atomic relaxations, as evident by the fact that unrelaxed GaṈ:As and GaṈ:P, show no deep levels, have extended wave functions, and have large interband transition elements.