Size and orientation dependence in the electronic properties of silicon nanowires

By using first-principles pseudopotential methods, we have studied the electronic properties of hydrogen-passivated silicon nanowires along the [100], [110], and [111] directions with diameter up to 3.40.3em0exnm. It is found that as the diameter decreases, the energy band gaps are distinctly enlarged due to the confinement effect. The valence-band maximum moves down while the conduction-band minimum moves up compared with the bulk. By using the many-body perturbation theory within the $GW$ approximation, we have also investigated the self-energy correction to the energy band gaps. Our calculational results show that, although the band gap values strongly depend on both the diameter and orientation, the $GW$ corrections are mainly dependent on diameter and less sensitive to the growth orientation. The effective mass as a function of diameter is also discussed.