Excitons in germanium nanowires: Quantum confinement, orientation, and anisotropy effects within a first-principles approach

Within a first-principles framework we show how many-body effects crucially modify the electronic and optical properties of free-standing Germanium nanowires. The electron-hole binding energy and probability distribution are found to depend on both wire size and orientation. Moreover, we observe an almost complete compensation of self-energy and excitonic effects for some of the analyzed quantum wires, which we explain as being due to their clusterlike atomic structure.

Figure 1

(Color online) Geometrical structures of the 0.4 nm Ge wires in the [110] (top), [111], and [100] (bottom) directions shown from the side (left) and from the top (right). Large spheres represent Ge atoms; small spheres are hydrogen atoms used to saturate the dangling bonds. The gray isosurface (Ref. 24) gives the probability distribution ${\mid {\psi }_{\mathrm{exc}}(r_r,r_h)\mid }^2$ for finding the electron when the hole is fixed in a given position (the $e\text{−}h$ localization length $L$ is reported for each wire). The hole positions lie on the dashed line in the left panel and are represented by the white crosses in the right panel

Figure 2

Imaginary part of the dielectric function of [110] GeNW (0.4 nm). Left panels: light polarized along the wire axis $\left(x\right)$; right panels: light polarized perpendicularly to this axis $\left(y\right)$. The reader should note the different scale of the vertical axes in the panels.

Figure 3

As Fig. 2, but only for light polarized along the wire axis, for [100] (left panel) and [111] (right panel) GeNWs (0.4 nm).

Figure 4

(Color online) Imaginary part of the dielectric function of the [100] GeNW (0.8 nm) (dashed area) and [100] SiNW (0.8 nm) (solid line) for light polarized along the wire axis $\left(x\right)$.