Electronic Structure of Single-Wall Silicon Nanotubes and Silicon Nanoribbons: Helical Symmetry Treatment and Effect of Dimensionality

Abstract

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 singlewall silicon nanotubes (SWSiNT), graphene-like parent 2D-hP silicone sheet and nanoribbons (SiNR). The results obtained for nanotubes of the length of ≈ 358 Å in diameter range ≈ 3.7 Å -116 Å of different helicity-types have shown that only small-diameter SWSiNTs up to < 6.3 Å are metallic due to the effect of curvature which induces coupling of  and  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 ( * , ) bands. Gap of SWSiNTs exhibits, however, an oscillatorydecreasing character with increase of the tube diameter. In the oscillatory series, minima of the gap in "saw-teeth" pattern are reached for helicity numbers m a that are an integer multiple of 3, whilst m a value itself directly determine the fold-number of particular tubular rotational axis symmetry. Oscillations are damped and gap decreases toward ≈ 0.33 eV for tube diameter ≈ 116 Å. 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. 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 nono-micro technologies.-reported method of graphene discovery. Carbon nanotubes formation and theirs stability is directly related to stability of graphene.With valence (s, p x,y,z ) electrons in 3 rd -shell, silicon, though nearest-neighbour of carbon in group IV, exhibits different properties. Most stable crystal form of silicon is diamond-like cF8 structure with sp 3 hybridization, whilst bulk form of graphite-like silicon structure is unknown. That was the main reason of uncertainty about possibility of existence and stability of sp 2 silicone analogue of graphene, i.e. 2D-hP single-layer Si sheet with honeycomb pattern. For a long time, an effort to prepare Si-nanostructures has resulted usually in Si nanowires 3-9 (sp 3 -based structures), rather than to any other form.Since 2002 the first reports on synthesis of large-diameter silicon nanotubes (up to 50nm) have appeared. [10][11][12][13] Experimental evidence of tin-wall and small-diameter silicon nanotubes (  2nm) formation 14,15 came in 2005 and the same authors reported later 16 that parts of less-oxidized Si-nanotubes possess hexagonal character which can be interpreted as a mixture of sp 2 /sp 3 hybridization. Graphene-like pattering has also been reported 17,18 at experimental study of silicon nanoribbons (SiNR). The results of scanning tunnelling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES), published only very re...