Structure of the thinnest most stable semiconducting and insulating nanotubes of ${\mathrm{SiO}}_x$ ($x=1$,2)

The ability of silica to form different phases can be used to stabilize its nanostructures. Here we explore the stability of thin nanotubes of ${\mathrm{SiO}}_x$ ($x=1$ and 2) using ab initio calculations with the generalized gradient approximation for the exchange-correlation energy. We find that the pentagonal nanotubes are energetically most stable. The pentagonal SiO nanotube is a semiconductor with the largest calculated band gap of 0.90 eV, which is close to the value for bulk Si. The ${\mathrm{SiO}}_2$ nanotubes are, however, insulating similar to bulk silica and could be promising as the thinnest insulating layers for nanodevices. Our results demonstrate that we can get the most important circuit elements for nanoelectronics, namely semiconducting, as well as insulating nanotubes based on silicon in the subnanometer regime.

Figure 1

(Color online) Optimized unit cells of SiO nanotubes viewed along and perpendicular to the axis of the nanotubes: (a) ${\mathrm{Si}}_{12}{\mathrm{O}}_{12}$ triangular, (b) ${\mathrm{Si}}_{16}{\mathrm{O}}_{16}$ tetragonal, (c) ${\mathrm{Si}}_{20}{\mathrm{O}}_{20}$ pentagonal, and (d) ${\mathrm{Si}}_{24}{\mathrm{O}}_{24}$ hexagonal rings of Si, connected by oxygen atoms. Note that the oxygen atoms in (b) are not aligned; this is due to a symmetric twist in the structure. The corresponding optimized unit cells of infinite ${\mathrm{SiO}}_2$ nanotubes are shown in (e)–(h). In these nanotubes every Si atom is connected with four oxygen atoms.

Figure 2

(Color) Band structures and total and partial densities of states (DOS) of pentagonal infinite nanotube with the effective unit cell: (a) ${\mathrm{Si}}_5{\mathrm{O}}_5$ and (b) ${\mathrm{Si}}_5{\mathrm{O}}_{10}$. Only states near the top of the valence band and the bottom of the conduction bands have been shown. ${\mathrm{O}}^{\prime }$ and O correspond to the oxygen atoms at the bridge sites and in the rings, respectively, in ${\mathrm{SiO}}_2$ nanotubes. The broken line shows the top of the valence band. The spikes in the DOS at the band edges arise due to van Hove singularities that represent the typical features of a one-dimensional system. Red, green, and blue lines represent contributions from $s,p$, and $d$ orbitals. For clarity the scale for the partial DOS of Si has been changed.

Figure 3

(Color) Isosurfaces of (a) the total electronic charge density of SiO (with unit cell ${\mathrm{Si}}_{20}{\mathrm{O}}_{20}$), (b) the excess, and (c) the depletion of charge as compared to the overlapping charge densities of the ${\mathrm{Si}}_{20}$ and ${\mathrm{O}}_{20}$ at the respective positions. The buildup of charge seen on the oxygen atoms is due to the polar nature of $\mathrm{Si}\text{−}\mathrm{O}$ bonds. The corresponding isosurfaces of infinite ${\mathrm{SiO}}_2$ nanotubes (with unit cell ${\mathrm{Si}}_{20}{\mathrm{O}}_{40}$) are shown in (d)–(f).