electronic structure of single-wall silicon nanotubes and silicon nanoribbons: helical symmetry treatment and effect of dimensionality

Helical method of tube formation and Hartree-Fock SCF method modified for periodic solids have been applied in study of electronic properties of single-wall silicon nanotubes (SWSiNT), silicone sheet, and nanoribbons (SiNR). The results obtained for nanotubes in wide diameter range of different helicity types have shown that metallics are only SWSiNTs with diameter up to <6.3 Å due to the effect of curvature, which induces coupling of σ and π orbitals. From the calculated band structure results that, irrespective of helicity, the SWSiNTs of larger diameter are small-gap semiconductors with direct gap between the Dirac-like cones of (π*,π) bands. Gap of SWSiNTs is modulated by fold number of particular tubular rotational axis symmetry and exhibits an oscillatory-decreasing character with increase of the tube diameter. Oscillations are damped and gap decreases toward 0.33 eV for tube diameter ≈116 Å. Irrespective of the width, the SiNRs are small-gap semiconductors, characteristic by oscillatory decreasing gap with increasing ribbon widths. The gap of SWSiNTs and SiNRs is tuneable through modulation of tube diameter or ribbon width, respectively. The SiNRs and SWSiNTs could be fully compatible with contemporary silicon-based microelectronics and could serve as natural junction and active elements in field of nonomicrotechnologies.