Band-gap unification of partially Si-substituted single-wall carbon nanotubes

Abstract

The atomic and electronic structure of a set of pristine single wall SiC nanotubes as well as Si-substituted carbon nanotubes and a SiC sheet was studied by the local-density approximation (LDA) plane wave band structure calculations. Consecutive substitution of carbon atoms by Si leads to a gap opening in the energetic spectrum of the metallic (8,8) SWCNT with approximately quadratic dependence of the band gap upon the Si concentration. The same substitution for the semiconductor (10,0) single wall carbon nanotubes (SWCNT) results in a band gap minimum $(0.27\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ at $\ensuremath{\sim}25%$ of Si concentration. In the Si concentration region of $12--18\phantom{\rule{0.2em}{0ex}}%$, both types of nanotubes have less than $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ direct band gaps at the $\ensuremath{\Gamma}\text{\ensuremath{-}}\ensuremath{\Gamma}$ point. The calculation of the chiral (8,2) $\mathrm{SW}{\mathrm{Si}}_{0.15}{\mathrm{C}}_{0.85}\mathrm{NT}$ system gives a similar $(0.6\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ direct band gap. The regular distribution of Si atoms in the atomic lattice is by $\ensuremath{\sim}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\text{atom}$ energetically preferable in comparison with a random distribution. Time dependent density functional theory (DFT) calculations showed that the silicon substitution sufficiently increases (roughly by one order of magnitude) the total probability of optical transitions in the near infrared region, which is caused by the opening of the direct band gap in metallic SWCNTs, the unification of the nature and energy of the band gaps of all SWCNT species, the large values of $⟨\mathrm{Si}3p\ensuremath{\mid}r\ensuremath{\mid}\mathrm{Si}3s⟩$ radial integrals and participation of $\mathrm{Si}3d$ states in chemical bonding in both valence and conductance bands.