Modeling of strained quantum wires using eight-band k center dot p theory

We have calculated numerically the one-dimensional band structure and densities of states of a V-shaped In0.2Ga0.8As/AlxGa1-xAs single quantum wire using eight-band k . p theory. A finite-difference scheme is used for the calculations. The model includes the realistic orientation, shape, material composition, strain distribution, and piezoelectric charging of the wire. We find a dominant impact of the piezoelectric potential on the band structure and a marked spin splitting of the valence bands. Also, the conduction band is strongly nonparabolic. We propose an efficient procedure to calculate interior eigenvectors from Hamiltonians including conduction-band-valence-band interactions. This algorithm is 20-90 times faster than the best prevailing method and also applies to other Hamiltonians for the modeling of nanostructures, including those occurring in tight-binding or pseudopotential theory.