Structures of Si and Ge Nanowires in the Subnanometer Range

We report an ab initio investigation of several structures of pristine Si and Ge nanowires with diameters between 0.5 and 2.0 nm. We consider nanowires based on the diamond structure, high-density bulk structures, and fullerenelike structures. Our calculations indicate a transition from $s{p}^3$ geometries to structures with higher coordination, for diameters below 1.4 nm. We find that diamond-structure nanowires are unstable for diameters smaller than 1 nm, undergoing considerable structural transformations towards amorphouslike wires. For diameters between 0.8 and 1 nm, filled-fullerene wires are the most stable. For even smaller diameters ($\sim 0.5\mathrm{nm}$), we find that a simple hexagonal structure is particularly stable for both Si and Ge.

Figure 1

Cross sections of selected Ge nanowire structures labeled according to the parent bulk phase. In (a) and (b), wires derived from the cubic diamond structure, with axis along the (110) direction; in (c), a simple cubic wire; in (d), a $\beta$-tin wire with axis along the bulk $c$ direction; in (e) and (f), simple hexagonal wires with axis along the bulk $c$ direction.

Figure 2

Side view of corrugated Ge nanowire structures. In (a), corrugated wire resulting from a structural instability of a (100) cubic diamond nanowire; in (b), a filled-fullerene nanowire. Inner atoms are shown as green spheres.

Figure 3

First-principles total energies (in $\mathrm{eV}/\mathrm{\text{atom}}$), relative to cd bulk energy, of Ge nanowires as a function of nanowire diameter. Labeling of the structures is explained in the text.

Figure 4

First-principles (DFT) and tight-binding (DMTB) total energies (in $\mathrm{eV}/\mathrm{\text{atom}}$), relative to the cd bulk energy, of Si nanowires as a function of the inverse of the nanowire diameter. The dashed (solid) line shows the curve obtained from a continuum model (see text), parameterized for cd (sh) wires.

Figure 5

Tight-binding energies (in $\mathrm{eV}/\mathrm{\text{atom}}$), of cd Si nanowires oriented along (111), (112), and (110) directions, as a function of inverse nanowire diameter. The dashed line corresponds to a continuum model (see text) parametrized as in Fig. 4.