Quantum confinement effects in Ge [110] nanowires

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 nm in diameter. By placing a 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 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 nm. The valence band maximum scales with diameter D as proportional to D-2.2, and the conduction band scales as proportional to D-0.8.