Quantum confinement and surface relaxation effects in rutile TiO ₂ nanowires

Spin-polarized density functional theory calculations within the generalized gradient approximation have been applied to investigate the size- and shape-dependent atomic and electronic properties of [001]-oriented rutile TiO ₂ nanowires of rectangular cross section. We find pronounced even-odd oscillation in the formation energy and band structure of the nanowires as a function of the number of TiO ₂ layers, which are largely connected to the presence or absence of a mirror Ti-O plane along either confinement direction. We demonstrate that the relative stability and the oscillation in the band structure characters of the rutile TiO ₂ nanowires arise from the interplay between surface relaxation and quantum confinement effects, which depend on the even-odd parity of the number of TiO ₂ layers and can be tuned separately along each confinement direction.