| Summary: | We use an accurate sp3V* tight-binding Hamiltonian to present a strong case to support the theory of a two-band anti-crossing model describing the electronic structure of GaNxAs1-x and InyGa1-yNxAs1-x alloys, in terms of the interaction between the conduction band edge and a higher-lying band of resonant nitrogen states. For the first time, we derive the functional dependence of the matrix elements of the two-band model and evaluate its parameters α, β and En. The model is shown to be accurate for band gap calculations up to a range of nitrogen composition, x of around 0.1 and is used to calculate other important properties of the alloy throughout this range. We explicitly identify and track the resonant state in GaNxAs1-x even to alloy compositions as large as x=0.25, where we find that the conduction band edge energy can be described analytically assuming independent resonant states up to x~0.03, but interactions between neighbouring resonances must be included for larger x. We find that the resonant state in InyGa1-yNxAs1-x alloys is strongly influenced by its local environment and show that a unique N state exists for each of the five different nearest neighbour configurations. We develop a simple yet accurate model that can describe the InyGa1-yNxAs1-x system with a very large number of randomly distributed N atoms by representing the resonant state for a given x and y as a linear combination of the five unique 'isolated' N states. We use the model to show how a statistical distribution of N states effects the resonant band spectrum and its variation with N and In composition; and show how variations in this distribution can lead to fluctuations in the energy gap and other calculated transition energies. In this we demonstrate the importance of N-N pair states. We carry out a detailed analysis to show how the various components of the defect Hamiltonian that describes the perturbation In a Ga32N1As31 system, affect the values of β and En, and show that in its complete form isoelectronic impurities other than nitrogen only give rise to a minor perturbation in the band structure of III-V compounds. We also find that for a Ga32N1As31 system, the resonant state can be given by an A1-symmetric combination of L and two-thirds Σ states weighted approximately two-to-one. This result also applies to most other A32N1B31 systems. Using this and a generalised form for the A1-symmetric defect Hamiltonian, we derive simple yet accurate expressions for β and En in terms of just two atomic properties and the energy of the L and two-thirds Σ points in the host compound. Finally, we extend the two-band anti-crossing model and derive a multi-band k.P Hamiltonian that describes the band structure of ordered GaNAs systems and of GaNAs with a statistical distribution of N states.
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