Electronic structure of embedded carbon nanotubes

The electronic structure of single-wall carbon nanotubes embedded in a crystal matrix is calculated by means of a linear-augmented cylindrical wave method. A delocalization of the nanotube electrons into the matrix region results in a strong band-structure perturbation. In the case of armchair nanotubes, the delocalization is responsible for a high energy shift of the $\sigma$ states and growth of the electron density of states at the Fermi level. For the semiconducting nanotubes, it causes a decay of the minimum energy gap and the formation of a metallic state. The effect of embedded nanotube metallization correlates with the transport properties of devices with nanotubes encapsulated in a semiconductor crystal.

Figure 1

Nanotube in a matrix (above) and cross section of the electronic potential along the $N0M$ line (below).

Figure 2

Band structure of an embedded (5,5) SWCNT for a barrier parameter ${\epsilon }_m=2$. Here and in Figs. 3, 4, 5: $S_{v1},S_{c1}\text{−}{S}_{c3}$ are the van Hove singularities located between the Brillouin zone center $\Gamma$ and boundary $K;{\Gamma }_{vi}(\pi ∕\sigma ),{\Gamma }_{ci}(\pi ∕\sigma ),K_v\left(\pi \right)$, and $K_c\left(\pi \right)$ stand for $\pi ∕\sigma$ states at the $\Gamma$ and $K$ points. The subscripts $v$ and $c$ refer to the bands of a nonembedded SWCNT;[21, 22, 33] for example, the ${\Gamma }_{v1}\left(\sigma \right)$ state is located below the Fermi level of the nonembedded (5,5) SWCNT, but it is above the Fermi level of the embedded one. The dimensionless barrier parameter ${\epsilon }_m$ is defined as $V_m∕\delta$, where $\delta$ is energy gap between the Fermi level of the SWCNT and the interatomic potential.

Figure 3

DOS of a (5,5) SWCNT vs barrier parameter ${\epsilon }_m$. Here and in Fig. 4, we use Gaussian broadening with a half-width of 0.05 eV. (a) ${\epsilon }_m=\infty$ (nonembedded SWCNT); (b–d) ${\epsilon }_m=6$, 4, and 2, respectively.

Figure 4

Band structure of an embedded (13,0) SWCNT for a barrier parameter ${\epsilon }_m=2$.

Figure 5

DOS of a (13,0) SWCNT for various barrier parameters ${\epsilon }_m$. (a) ${\epsilon }_m=\infty$; (b–d) ${\epsilon }_m=6$, 4, and 2, respectively.

Figure 6

Minimum energy gap $E_{11}$ vs ${\epsilon }_m$ for a (13,0) SWCNT.