Orientation effects in the electronic and optical properties of germanium quantum wires

We have performed first-principles calculations in order to analyze the influence of spatial orientation on the electronic band structure and optical properties of hydrogenated germanium quantum wires. A quantum confinement-induced direct band gap appears for the (110)-oriented wires, whereas the (100)- and (111)-oriented wires are characterized by an indirect band gap. For the same wire-effective size, an anisotropy in the fundamental band gap $E_g$ with respect to the wire orientation is observed. For (110)-oriented wires, the imaginary part of the dielectric function shows a pronounced peak in the visible energy range with strong dimensionality and polarization dependence.

Figure 1

Germanium quantum wires with the effective size of $0.8\mathrm{nm}$ in the (a) (100), (b) (110), and (c) (111) directions: side view (left) and top view (right). Open circles represent germanium atoms, while dots indicate the hydrogen atoms passivating the dangling bonds at the surface of the wire. Gray-colored circles indicate the germanium atoms belonging to the unit cell.

Figure 2

The electronic band structures of germanium quantum wires for different orientations and effective widths: (a) (100), (b) (110), and (c) (111).

Figure 3

The size dependence of the fundamental band gap in germanium quantum wires.

Figure 4

The calculated imaginary part of the dielectric function polarized in the direction of the wire ($E$ parallel to $z$) and perpendicular to it ($E$ parallel to $x$) for different orientations and different effective widths. The curves are dressed with Lorentzial broadening of $0.1\mathrm{eV}$.