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

Abstract

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 $3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, using ab initio methods. A critical diameter ${d}_{c}\ensuremath{\approx}2\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ 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 $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$. (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.