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

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 $\left(0.27\mathrm{eV}\right)$ at $\sim 25\%$ of Si concentration. In the Si concentration region of $12–18\%$, both types of nanotubes have less than $0.5\mathrm{eV}$ direct band gaps at the $\Gamma \text{−}\Gamma$ point. The calculation of the chiral (8,2) $\mathrm{SW}{\mathrm{Si}}_{0.15}{\mathrm{C}}_{0.85}\mathrm{NT}$ system gives a similar $\left(0.6\mathrm{eV}\right)$ direct band gap. The regular distribution of Si atoms in the atomic lattice is by $\sim 0.1\mathrm{eV}∕\text{atom}$ 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 $⟨\mathrm{Si}3p\mid r\mid \mathrm{Si}3s⟩$ radial integrals and participation of $\mathrm{Si}3d$ states in chemical bonding in both valence and conductance bands.

Figure 1

The theoretical LDA PW PP PBC, G-type PBE PBC (Ref. 59) DOS and experimental (Ref. 2) STS spectrum of pristine (8,8) SWCNT as well as the LDA PW PP PBC DOS of the pristine (8,8) SWSiCNT. The Fermi level energy is taken as zero for all tubes, except for SWSiCNT with $E_{\text{Fermi}}=-1.12\mathrm{eV}$.

Figure 2

The theoretical LDA PW PP PBC DOS and the correspondent band structures for armchair (4,4), (5,5), (6,6), and (15,15) SWSiCNTs (a) and for chiral [(6,4) and (8,2)] and zigzag (10,0) SWSiCNTs of a similar diameter (b). The Fermi level energy is taken as zero.

Figure 3

(Color online) The theoretical LDA PW PP PBC DOS of a number of Si-substituted (8,8) armchair SWCNT (43.8%, 25.0%, 16.7%, and 5.2% of Si in the unit cells) structures as well as pristine (8,8) SWCNT (0%) and (8,8) SWSiCNT (50%) (the Fermi level is taken as zero). The corresponding atomic lattices of the structures are shown on the right side of the figure [carbon atoms are in yellow (gray) and silicon atoms are in brown (black)].

Figure 4

The band structure of pristine (a) (8,8) SWCNT and (e) (8,8) SWSiCNT as well as 5.2% (b), 16.7% (c), and 25% (d) silicon substituted (8,8) SWCNT. The arrows show the highest/lowest points of valence/conductivity bands. It is clearly seen that the pristine (8,8) SWSiCNT (e) as well as 25% system (b) are indirect band gap semiconductors. The 16.7% system has a narrow direct band gap.

Figure 5

(Color online) The theoretical LDA PW PP PBC DOS of a number of Si-substituted (10,0) zigzag SWCNT (12.5%, 25.0%, and 37.5% of Si in the unit cells) structures as well as pristine (10,0) SWCNT (0%) and (10,0), SWSiCNT (50%). The Fermi level energy is taken as zero. The corresponding atomic lattices of the structures are shown on the right side of the figure [carbon atoms are in yellow (gray) and silicon atoms are in brown (black)].

Figure 6

The concentration dependence of the band gap $E_{\text{gap}}$ of Si-substituted (8,8) (downward triangles) and (10,0) SWCNTs (upward triangles).

Figure 7

The density of the electron states and the band structure of the (8,2) $\mathrm{SW}{\mathrm{Si}}_{0.15}{\mathrm{C}}_{0.85}\mathrm{NT}$ system.