  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 new defect screening model where the use of 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. The proposed
new defect screening model will also shed new light on understanding the defect
screening properties and can be applied to other defect systems.
