  We propose a new finite-size correction scheme for the formation energy of
charged defects and impurities in one-dimensional systems within density
functional theory. The energy correction in a supercell geometry is obtained by
solving the Poisson equation in a continuum model which is described by an
anistrotropic permittivity tensor, with the defect charge distribution derived
from first-principles calculations. We implement our scheme to study impurities
and dangling bonds in silicon nanowires and demonstrate that the formation
energy of charged defects rapidly converges with the supercell size.
