Electronic structure of silicon-based nanostructures

We have developed a unifying tight-binding Hamiltonian that can account for the electronic properties of recently proposed Si-based nanostructures, namely, Si graphene-like sheets and Si nanotubes. We considered the $s{p}^3{s}^{*}$ and $s{p}^3$ models up to first- and second-nearest neighbors, respectively. Our results show that the Si graphene-like sheets considered here are metals or zero-gap semiconductors, and that the corresponding Si nanotubes follow the so-called Hamada’s [Phys. Rev. Lett. 68, 1579 (1992)] rule. Comparison to a recent ab initio calculation is made.

Figure 1

(Color online) Lattice of Si (111). (a) Two-dimensional representation of a Si (111) sheet. The atoms labeled as $A$ are all in the $xy$ plane $(z_A=0)$ and all the $B$ atoms are located below the plane $[z=-a∕\left(2\sqrt{6}\right)]$. Hence, the sheet is composed by two atomic planes: one of $A$ atoms and another of $B$ atoms. The $A$ plane is above the $B$ plane. Notice that the $z$ axis points towards the reader. The vectors ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are the two-dimensional basis vectors and the shaded area is the Si (111) unit cell. (b) First-nearest neighbors of Si (111).

Figure 2

Band structure of silicene and of Si (111) obtained from our TB models compared to the ab initio results from Yang and Ni (Ref. 7).

Figure 3

Band structures of Si $h$- and Si $g$-NT’s according to our calculations and to Yang and Ni (Ref. 7). The two-center parameters used in our calculations were taken from Grosso and Piermarocchi (Ref. 20).

Figure 4

(Color online) The $s{p}^2$ and $s{p}^3$ hybridizations in (a) silicene and in (b) Si (111).

Figure 5

(Color online) Band gap of CNT’s and Si $h$-NT’s as a function of their diameters.

Figure 6

(Color online) Effective masses of CNT’s and Si $h$-NT’s as a function of their diameters.