Charged local defects in extended systems.

The conventional approach to treat charged defects in extended systems in first principles calculations is via the supercell approximation using a neutralizing jellium charge. I explicitly show that errors in the resulting electrostatic potential surface are comparable to a band gap energy in semiconductors, for cell sizes typically used in simulations. I present a method for eliminating divergence of the Coulomb potential in charged supercell calculations that correctly treats the electrostatic potential in the local vicinity of a charged defect, via a mixed boundary condition approach.