First-principles calculations of charged defects have become a cornerstone of research in semiconductors and insulators by providing insights into their fundamental physical properties. But current standard approach using the so-called jellium model has encountered both conceptual ambiguity and computational difficulty, especially for low-dimensional semiconducting materials. In this Communication, we propose a physical, straightforward, and dimension-independent universal model to calculate the formation energies of charged defects in both three-dimensional (3D) bulk and low-dimensional semiconductors. Within this model, the ionized electrons or holes are placed on the realistic host band-edge states instead of the virtual jellium state, therefore, rendering it not only naturally keeps the supercell charge neutral, but also has clear physical meaning. This realistic model reproduces the same accuracy as the traditional jellium model for most of the 3D semiconducting materials, and remarkably, for the low-dimensional structures, it is able to cure the divergence caused by the artificial long-range electrostatic energy introduced in the jellium model, and hence gives meaningful formation energies of defects in charged state and transition energy levels of the corresponding defects. Our realistic method, therefore, will have significant impact for the study of defect physics in all low-dimensional systems including quantum dots, nanowires, surfaces, interfaces, and 2D materials.
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