An effective capacitance model for computing the electronic properties of charged defects in crystals

By examining how a defect within a crystalline material responds to small changes in its charge state, the electronic properties of an ionized defect can be modeled by an effective work function and capacitance. Such an approach leads to a correction formula to the total energy of a charged periodic system and allows a comparison between the electronic band structure of the ionized defect to its corresponding neutral one. The correction formula can be related to the potential alignment method and Makov-Payne correction widely adopted in charged periodic systems. The new approach suggests both an alternative interpretation and improvements to the popular Makov-Payne and potential alignment scheme. P-doped Si, which has a shallow donor level, and an isolated vacancy in crystalline Si, which has a deep defect level within the Si energy gap, are chosen as prototypical systems to demonstrate our method.