Design of a very thin direct-band-gap semiconductor nanotube of germanium with metal encapsulation

Using ab initio total energy calculations we design a very thin semiconducting nanotube of germanium with a direct band gap by encapsulation of $\mathrm{Mo}$ or $\mathrm{W}$. This finding is an outcome of studies of assemblies of ${\mathrm{Ge}}_{18}{\mathrm{Nb}}_2$ clusters into nanotubes. The infinite $\mathrm{Nb}$-doped nanotube is metallic. However, the electronic structure has a significant gap above the Fermi level. When $\mathrm{Nb}$ is replaced by a $Z+1$ element such as $\mathrm{Mo}$ or $\mathrm{W}$, it leads to the formation of a semiconducting nanotube. The atomic structure of these nanotubes is based on a novel alternate prism and antiprism stacking of hexagonal rings of germanium. Such an arrangement is optimal for ${\mathrm{Ge}}_{18}{M}_2$ ($M=\mathrm{Nb}$, $\mathrm{Mo}$, and $\mathrm{W}$) clusters that serve as the building blocks of nanotubes. These results demonstrate that by just changing the $M$ atom in the growth process, we can form metallic, semiconducting, and $n$ or $p$ types of nanotubes, opening new possibilities for nanoscale devices.

Figure 1

(Color online) Optimized structures of clusters and finite nanotubes (a) ${\mathrm{Ge}}_{12}\mathrm{Nb}$, (b) ${\mathrm{Ge}}_{18}{\mathrm{Nb}}_2$, (c) ${\mathrm{Ge}}_{36}{\mathrm{Nb}}_5$, and (d) ${\mathrm{Ge}}_{48}{\mathrm{Nb}}_7$ with three isomers (i) antiprism-prism, (ii) antiprism-antiprism, and (iii) with terminal ${\mathrm{Ge}}_{12}\mathrm{Nb}$ clusters stacked in the prism while the rest stacked in antiprism structures.

Figure 2

(Color online) (a) Optimized unit cell of an infinite nanotube of ${\mathrm{Ge}}_{24}{\mathrm{Nb}}_4$. $\mathrm{W}$-doped nanotube is similar. (b) An isosurface of the total charge density of the ${\mathrm{Ge}}_{24}{\mathrm{Nb}}_4$ nanotube.

Figure 3

Band structures of $\mathrm{Nb}$- and $\mathrm{W}$-doped infinite nanotubes. Dashed line shows the Fermi energy. $E_g$ is the band gap for the $\mathrm{W}$-doped semiconducting nanotube.

Figure 4

(Color) Total and partial densities of states (DOS) of $\mathrm{Nb}$- and $\mathrm{W}$-doped infinite nanotubes obtained by using Gaussian broadening with width of $0.01\mathrm{eV}$. (a) Total DOS, (b) partial DOS of $\mathrm{Ge}$, (c) partial DOS for $\mathrm{Nb}$ atom in the antiprism environment, and (d) partial DOS for the $\mathrm{Nb}$ atom in the prism environment of $\mathrm{Ge}$ atoms. Red, green, and blue lines represent the contributions from $s$, $p$, and $d$ orbitals. Dashed line shows the Fermi energy $\left(E_F\right)$, while for the $\mathrm{W}$-doped semiconducting nanotube the band gap is indicated by an arrow.