The effect of dimensional confinement on quantum levels is investigated for hydrogenated Ge [110] nanowires by “density-functional-theory pseudopotential” methods. The energy band dispersion is presented for wires up to $2.8\mathrm{nm}$ in diameter. By placing a ${\mathrm{H}}_2$ molecule in vacuum for reference the bands of the different sized wires are aligned and compared. It is found that for wires with diameters smaller than $3\mathrm{nm}$, confinement strongly affects the shape and energies of the conduction bands. It is found that the energy of the valence-band maximum does not change with diameter once a wire is greater than $2.0\mathrm{nm}$. The valence band maximum scales with diameter $D$ as $\propto D^{-2.2}$, and the conduction band scales as $\propto D^{-0.8}$.

• Received 23 May 2006

DOI:https://doi.org/10.1103/PhysRevB.74.165314