domingo, 25 de julio de 2010


The k·p and envelope-function methods are widely applied to study III–V semiconductor heterostructures. The strong interaction between the N resonant states and the conduction band edge means that the conventional eight-band k·p method cannot be applied to GaInNAs and related hetero-structures. We must include the interaction between the N resonant states and the conduction band edge to describe the variation of the (zonecenter) conduction-band-edge energy with N. This leads to a modified ten-band k·p Hamiltonian for GaInNAs, with the modified Hamiltonian giving a good description of the conduction-band dispersion over an energy range at least on the order of 200 meV, sufficient for most analyses.

We illustrate this by comparing the band structure of a Ga32As32 and a Ga32N1As31 supercell in Figure a, where the dotted lines show the sp3s* band structure plotted with the spin-orbit interaction Eso set to zero. The GaAs eight-band k·p Hamiltonian reduces to a two-band Hamiltonian for the conduction and light-hole valence bands along the [0,0,1] direction when Eso=0, as illustrated by the thick solid lines, which show the dispersion of these two bands calculated using ψc0 and the light-hole zone-center wavefunction, ψlh0, as the k·p basis states. The k·p matrix elements were found by explicitly evaluating <ψi0|H(kz)|ψj0> using the tight-binding Hamiltonian . We must add the nitrogen resonant state ψN0 to the k·p Hamiltonian for Ga32NAs31. The conduction and light-hole band dispersion are then

found by diagonalizing a 3×3 k·p model. The most general form of this 3×3 Hamiltonian includes k-dependent diagonal and off-diagonal matrix elements linking the ψN0, ψc0. 

The thick solid lines in Figure b show the band structure of Ga32NAs31 calculated, where we evaluate the matrix elements directly using the tightbinding Hamiltonian. This Hamiltonian gives an excellent fit to the conduction-band dispersion within about 200 meV of the band edge. However, it is notable that the N impurity band in Figure b does not correspond to a specific higher-lying conduction b and in the supercell. This is to be expected from our analysis of resonant states in the previous section.


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