Image charge interaction correction in charged-defect calculations

Charged-defect calculation using a periodic supercell is a significant class of problems in solid state physics. However, the finite supercell size induces an undesirable long-range image charge Coulomb interaction. Although a variety of methods have been proposed to eliminate such image Coulomb interaction, most of the previous schemes are based on a rough approximation of the defect charge screening. In this work, we present a rigorous derivation of the image charge interaction with a defect screening model where the use of a bulk macroscopic dielectric constant can be avoided. We have verified this approach in comparison with a widely used approach for 12 different defects. Our correction scheme offers a much faster convergence concerning the supercell size for cases with considerable image charge interactions. In those cases, we also found that the nonlinear dielectric screening might play an important role. Our proposed defect screening model will also shed new light on understanding the defect screening properties and can be applied to other defect systems.