  Helical method of tube formation for band structure calculations and
Hartree-Fock self-consistent field method (HF-SCF) modified for periodic solids
have been applied in study of electronic properties of single-wall silicon
nanotubes (SWSiNT), graphene-like parent 2D-hP silicone sheet and nanoribbons
(SiNR). The results obtained for nanotubes of the length of ${\approx}$ 358 \AA
in diameter range ${\approx}$ 3.7 \AA -- 116 \AA of different helicity-types
have shown that only small-diameter SWSiNTs up to} ${\varphi}${6.3 \AA ~ are
metallic due to the effect of curvature which induces coupling
of}{${\sigma}$}{and}{${\pi}$}{orbitals. From the calculated band structures
follow that irrespective of helicity, the SWSiNTs of larger diameter are all
small-gap semiconductors with direct gap between the Dirac-like cones
of}(${\pi}$\textsuperscript{*}, ${\pi}$) bands{.}Gap of SWSiNTs exhibits,
however, an oscillatory-decreasing character with increase of the tube
diameter. In the oscillatory series, minima of the gap in
{\textquotedblleft}saw-teeth{\textquotedblright} pattern are reached for
helicity numbers m \textsubscript{a} that are an integer multiple of 3, whilst
m\textsubscript{a} value itself directly determine the fold-number of
particular tubular rotational axis symmetry. Oscillations are damped and gap
decreases toward {${\approx}$ 0.33 eV} for tube diameter {${\approx}$ 116 \AA
.} {Irrespective of the width, the SiNRs are all 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.

Mesoscale and Nanoscale Physics;Materials Science