The BAC model explains the extreme band-gap bowing observed in InyGa1− yNxAs1−x in terms of an interaction between two levels, one at energy Ec associated with the extended onduction band edge (CBE) states of the InGaAs matrix, and the other at energy EN associated with the localized N impurity states, with the two states linked by a matrix element VNc describing the interaction between them [23]. The CBE energy of Ga(In)NxAs1−x, E−, is then given by the lower eigenvalue of the determinant
FIGURE 3.1
which showed the measured variation in E− and E+ as a function of N composition x in GaNxAs1−x. However, initial pseudopotential calculations found no direct evidence for the upper state, although they do confirm its effect on the conduction band edge, and it has more recently been identified for relatively low N compositions (x<~1%) . To investigate the resonant state, and its behavior, we have developed an accurate sp3s* tight-binding (TB) Hamiltonian to describe the electronic structure of GaInNxAs1−x . This Hamiltonian fully accounts for the observed experimental data, and also gives results in good agreement with pseudopotential calculations. Figure 3.1 shows, for instance, the variation of the band-gap energy across the full alloy range in free-standing GaNxAs1−x, calculated using the sp3s* Hamiltonian: the observed variation matches well that obtained in the literature .
To investigate the resonant state and its behavior, we calculated the electronic structure of ordered GaNxAs1−x supercells . By comparing the calculated CBE states ψc1 and ψc0 in large supercells (Ga864N1As863 and Ga864As864, respectively), we canderive the nitrogen resonant state ψN0 associated with an isolated N atom. In the BAC model, ψc1 is a linear combination of ψc0 and ψN0.
ROSSANA HERNANDEZ
ELECTRONICA DEL ESTADO SOLIDO
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