Self-Consistently Determining Structures Of Charged Defects And Defect Ionization Energies In Low-Dimensional Semiconductors

Determination of defect ionization energy in low-dimensional semiconductors has been a long-standing unsolved problem in first-principles defect calculations, because the commonly used methods based on the jellium model introduce an unphysical charge density uniformly distributed in the material and vacuum regions, causing the well-known divergence issue of charged defect formation energies. In addition, because of the unphysical jellium charge, how to determine structures of charged defects is also not clear. These two issues pose great challenges in studying defect properties of low-dimensional semiconductors. Here in this work, we combine the jellium framework together with the idea of constraining charge transfer to deal with charged defects in low-dimensional semiconductors by replacing the unphysical jellium background charge density with the band-edge charge density. By doing this, we show that not only the total energy calculation but also the structure relaxation can be self-consistently obtained in one single calculation, thus providing a simple and efficient way to determine the defect ionization energies in low-dimensional semiconductors.