Shell structure and phase relations in electronic properties of metal nanowires from an electron-gas model

Abstract

The electronic and dynamic properties of metal nanowires are analyzed by using a minimal electron-gas model (EGM), in which the nanowire is treated as a close system with variable Fermi energy as a function of nanowire radius. We show that the planar surface energy and the curvature energy from the EGM are reasonably consistent with those from previous stabilized-jellium-model calculations, especially for metals with low electron densities. The EGM shell structure due to the fillings of quantum-well subbands is similar to that from the stabilized jellium model. The crossings between subbands and Fermi energy level for the metal nanowire correspond to cusps on the chemical-potential curve versus nanowire radius, but inflection points on the surface-free-energy curve versus the radius, as in the case of metal nanofilms. We also find an oscillatory variation in electron density versus radius at the nanowire center with a global oscillation period which approximately equals half Fermi wavelength. Wire string tension, average binding energy, and thermodynamic stability from the EGM are in good agreement with the data from previous first-principles density-functional theory calculations. We also compare our model with those from previous reported free-electron models, in which the nanowire is treated as an open system with a constant Fermi energy. We demonstrate that the fundamental thermodynamic properties depend sensitively on the way that the potential wall is constructed in the models.