Energetics of finite metallic nanowires

The size dependence of the electronic density of states, Fermi energy, and the ionization potential of a finite metallic nanowire is investigated in a free-electron model for Na and Al. A nanowire is modelled by a uniform conductor of a finite length and a square cross-section. Simple relation between the Fermi energy and the depth of a square potential well is employed which yields a correct monotonic size dependence of the ionization potential. It is shown that the ionization potential, as a function of the wire width, oscillates around the values provided by this average dependence. The oscillations in the energetic properties and in the elongation force result from the size quantization of the energy levels.