Finite-element analysis of valence band structure and optical properties of quantum-wire arrays on vicinal substrates

The valence subband dispersion of quantum-wire arrays grown on vicinal substrates in GaAs-Al/sub x/Ga/sub 1-x/As material system is calculated using a finite-element method with periodic boundary conditions. The variational functional for the Luttinger-Kohn Hamiltonian is derived using the integration by parts with proper boundary conditions. The validity of this method is confirmed by calculating subband structure of quantum wells and rectangular quantum wires. Along with the electronic band structure, a detailed study of gain in the quantum-wire arrays with rectangular and serpentine shapes is presented, including the effect of coupling between wires and polarization dependence of the momentum matrix element. Finally, these results are compared to those of quantum wells.<
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