Physics and Applications of Dilute Nitrides. An Atomistic View of the Electronic Structure of Mixed Anion III–V Nitrides. Band Anticrossing in III-N-V Alloys. Tight-Binding and k·p Theory of Dilute Nitride Alloys. Electronic Properties of (Ga,In)(N,As)-Based Heterostructures. Theory of Defects in Dilute Nitrides. Growth, Characterization, and Band-Gap Engineering of Dilute Nitrides. GaInNAs Long-Wavelength Lasers.
Overall, clearly demonstrate that the conduction band edge in GaNxAs1−x is being perturbed and pushed downward due to its interaction with a higherlying localized resonant state, centered on the nitrogen atoms. Why, then, has this state not been identified in previous calculations? To answer this question, and to investigate the role of disorder, we extend the tight-binding and two-level model to disordered GaNxAs1−x supercells.
We first consider a set of 1000 atom supercells containing up to 15 randomly distributed N atoms. In these supercells we fit the number, but not the distribution, of NN pairs to the number given statistically, so that each cell contains n isolated N sites and p N-N pairs. For each configuration, we used the GULP molecular relaxation package  to calculate the equilibrium positions of all the atoms, using a parameterized valence-force-field model, while using Végard's law to vary the unit cell basis vectors as a(x)=x aGaN+(1−x) aGaAs. The calculated relaxed bond lengths are in good agreement with those obtained by other authors  who used an ab initio pseudopotential approach.
In a disordered supercell, we can again try to describe the GaNxAs1−x conduction band edge by a Linear Combination of Isolated Nitrogen Resonant States (LCINS) interacting with the unperturbed conduction band edge, ψc0.
H=Ho+ Vn+ Vn-n
where H0 is the Ga500As500 Hamiltonian, ΔVN is the sum of defect potentials associated with the n isolated N atoms, and ΔVNN is the sum of defect Hamiltonians associated with the p N-N pairs. In extension of the approach for ordered structures, we now determine the GaNxAs1−x conduction band edge E− and the N-related conduction-band levels by constructing and solving a (n+2p+1)×(n+2p+1). Hamiltonian matrix involving the GaAs conduction-band-edge wavefunction, and the n+2p N-related states.