Finite-Size Supercell Correction for Charged Defects at Surfaces and Interfaces

A finite-size supercell correction scheme is introduced for the formation energy of charged defects at surfaces and interfaces. The scheme combines classical electrostatics with the dielectric profile and the electrostatic potential extracted from the electronic-structure calculation. Spurious electrostatic interactions are removed while retaining the dielectric and quantum-mechanical features of the system of interest, which may have no interface (bulk), a single interface or surface, or two interfaces. A pertinent extrapolation scheme validates the proposed corrections. Applications to the charged Cl vacancy at the surface of NaCl and to the dangling bond at the Si(100) surface show that the corrected formation energies are largely independent of the supercell dimensions and of the size of the vacuum region.