Effect of structure, surface passivation, and doping on the electronic properties of Ge nanowires: A first-principles study

We investigate the structural, energetic, and electronic properties of hydrogen-passivated doped and undoped germanium nanowires along [001], [110], and [111] directions, with diameter d up to 3 nm, using ab initio methods. A critical diameter d_c≈2 nm is found, above which all wires have faceted cross sections determined by the symmetry of their axis. The wires possess several electronic properties relevant for sensing and other nanoelectronic applications: (i) Quantum confinement has a substantial effect on the electronic band structure and, hence, the band gap (E_g), which increases with decreasing diameter. (ii) Wires oriented along [110] are found to have a direct E_g, while the wires along [111] are found to have an indirect E_g. Wires along [001] show a crossover from a direct to an indirect E_g as diameter increases, the value of the critical diameter for the transition being 1.3 nm. (iii) The electronic band structure shows a significant response to changes in surface passivation with hydrogen. (iv) Doping of wires with n- and p-type atoms produced a response in the band structure similar to that in a doped bulk crystal.