Analysis of magic lengths in growth of supported metallic nanowires

Abstract

Metallic nanowires can exhibit fascinating physical properties. These unique properties often originate primarily from the quantum confinement of free electrons in a potential well, while electron-electron interactions do not play a decisive role. A recent experimental study shows that self-assembled Ir nanowires grown on Ge(001) surface have a strong length preference: the nanowire lengths are an integer multiple of 4.8 nm. In this paper, a free electron-gas model for geometries corresponding to the nanowires is used to analyze the selection of these preferred or magic lengths. The model shows that the inclusion of even numbers of free electrons in an Ir nanowire corresponds to these magic lengths once an electron spillage effect is taken into account. The model also shows that the stability of the nanowire diminishes with its increasing length, and consequently suggests why no long nanowires are observed in experiments. It is also shown that applying generic results for quantum size effects in a nanofilm geometry is not adequate to accurately describe the length selection in the rather different nanowire geometry, where the transverse dimensions smaller than the electron Fermi wavelength. Finally, the monatomic Au chain growth on Ge(001) surface is also analyzed. In contrast to Ir nanowires, the model shows that the stability of an Au chain strongly depends on its electron spillage.