Quantum-confinement effect on holes in silicon nanowires: Relationship between wave function and band structure

Abstract

The authors theoretically studied the valence band structure and hole effective mass of rectangular cross-sectional Si nanowires (NWs) with the crystal orientation of [110], [111], and [001]. The E–k dispersion and the wave function were calculated using an sp^3d^5s∗ tight-binding method and analyzed with the focus on the nature of p orbitals constituting the subbands. In [110] and [111] nanowires, longitudinal/transverse p orbitals are well separated and longitudinal component makes light (top) subbands and transverse component makes heavy subbands. The heavy subbands are located far below the top light band when NW has square cross-section, but they gain their energy with the increase in the NW width and come near the band edge. This energy shift of heavy bands in [110] NWs shows strong anisotropy to the direction of quantum confinement whereas that in [111] NWs does not have such anisotropy. This anisotropic behavior and the difference among orientations are understandable by the character of the wave function of heavy subbands. Regarding the [001] nanowires, the top valence state is formed by the mixture of longitudinal/transverse p orbitals, which results in heavy effective mass and large susceptibility to lateral-size variation. The correlation of the wave function of hole states between nanowires and bulk is also discussed briefly.