Density of states and localization length in compositionally disordered quantum wires

Electronic states in compositionally disordered quantum wires are studied using a tight-binding Hamiltonian to determine the electronic density of states and localization lengths. The quantum wires are generated using the statistics of the structural roughness extracted from the results of computer simulations of molecular-beam-epitaxy growth of quantum-well wires on a vicinal surface. For monolayer structures, interface roughness and islands strongly suppress the subband structure. The electronic states are found to be localized to within several tens of lattice spacings, which implies severely reduced mobility in narrow quantum wires. Enlargement of the cross section of the wire by depositing additional layers does not improve the subband structure of the density of states. However, the localization lengths will be longer, except for energies near the band edge. The maximum localization length is proportional to the number of layers. Characteristic features of this model in the strong scattering regime, such as a spike in the density of states at the center of the subband and the gap around it, and strong reduction in the localization length for these energies, are observed for a monolayer structure. For multilayer structures spikes also occur at E=±V, but the gap has disappeared.