Electronic structure of [100]-oriented free-standing InAs and InP nanowires with square and rectangular cross sections

We report on a theoretical study of the electronic structure of free-standing InAs and InP nanowires grown along the [100] crystallographic direction, based on an atomistic tight-binding approach. The band structure and wave functions for nanowires with both square (nanowires) and rectangular (nanobelts) cross sections are calculated. A comparison is made between the calculations for InAs, InP, and GaAs nanowires and similar characteristics are found in the band structure and wave functions of the three material types of nanowires. It is found that the nanowires with both square and rectangular cross sections have simple, parabolic conduction bands. However, the characteristics of the valence bands in the nanowires are found to be cross-section aspect-ratio dependent. For the nanowires with a square cross section, the valence bands show rich and complex structures. In particular, the highest valence band of a square nanowire shows a double-maximum structure and has its energy maximum at k not equal 0, giving an indirect nanowire band gap. When the cross section of the nanowires changes from a square to a rectangular type, the top valence bands tend to develop into parabolic bands. For the nanowires with the same cross-section aspect ratio and material type, the valence band structures at different sizes are found to have similar characteristic structures, although the band energies sensitively depend on the nanowire lateral size. The wave functions of the band states of the InAs and InP nanowires at the Gamma point have been calculated. It is found that for the square nanowires the valence band states show complex structures. For the rectangular nanowires with sufficiently large aspect ratios the wave functions of the topmost valence band states show the features predicted by a one-band effective-mass model, in agreement with the fact that these valence bands become good parabolic bands in these rectangular nanowires.