Nature of the band gap of silicon and germanium nanowires

Nanowires of both Si and Ge have been predicted to have band gaps that are either direct or indirect depending upon the crystallographic direction along which the nanowire is oriented. We use a sp3d5s*sp3d5s* tight binding model to calculate the band structures for both Ge and Si nanowires oriented along the (1 0 0), (1 1 0) and (1 1 1) directions. We show that the nature of the band gap and the variation of the zone centre band gap with nanowire width depends upon the nanowire stacking direction for both Si and Ge nanowires. We then show, by considering bulk unit cells along the (1 0 0), (1 1 0) and (1 1 1) directions, that it is possible to accurately predict whether a nanowire stacked in the same direction as one of these bulk unit cells has a direct or indirect band structure.