Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

First-principles calculations have evolved from mere aids in explaining and supporting experiments to powerful tools for predicting new materials and their properties. In the first part of this review we describe the state-of-the-art computational methodology for calculating the structure and energetics of point defects and impurities in semiconductors. We will pay particular attention to computational aspects which are unique to defects or impurities, such as how to deal with charge states and how to describe and interpret transition levels. In the second part of the review we will illustrate these capabilities with examples for defects and impurities in nitride semiconductors. Point defects have traditionally been considered to play a major role in wide-band-gap semiconductors, and first-principles calculations have been particularly helpful in elucidating the issues. Specifically, calculations have shown that the unintentional n-type conductivity that has often been observed in as-grown GaN cannot be attributed to nitrogen vacancies, but is due to unintentional incorporation of donor impurities. Native point defects may play a role in compensation and in phenomena such as the yellow luminescence, which can be attributed to gallium vacancies. In the section on impurities, specific attention will be focused on dopants. Oxygen, which is commonly present as a contaminant, is a shallow donor in GaN but becomes a deep level in AlGaN due to a DX transition. Magnesium is almost universally used as the p-type dopant, but hole concentrations are still limited. Reasons for this behavior are discussed, and alternative acceptors are examined. Hydrogen plays an important role in p-type GaN, and the mechanisms that underlie its behavior are explained. Incorporating hydrogen along with acceptors is an example of codoping; a critical discussion of codoping is presented. Most of the information available to date for defects and impurities in nitrides has been generated for GaN, but we will also discuss AlN and InN where appropriate. We conclude by summarizing the main points and looking towards the future.

We present total-energy, force, and electronic-structure calculations for Na and K adsorbed in various geometries on an Al(111) surface. The calculations apply density-functional theory together with the local-density approximation and the ab initio pseudopotential formalism. Two adsorbate meshes, namely, (√3 × √3 )R30° and (2×2), are considered and for each of them the geometry of the adlayer relative to the substrate is varied over a wide range of possibilities. By total-energy minimization we determine stable and metastable geometries. For Na we find for both adsorbate meshes that the ordering of the calculated binding energies per adatom is such that the substitutional geometry, where each Na atom replaces a surface Al atom, is most favorable and the on-top position is most unfavorable. The (√3 × √3 )R30° structure has a lower energy than the (2×2) structure. This is shown to be a substrate effect and not an effect of the adsorbate-adsorbate interaction. In contrast to the results for Na, we find for the (√3 × √3 )R30° K adsorption that the calculated adsorption energies for the on-top, threefold hollow, and substitutional sites are equal within the accuracy of our calculation, which is ±0.03 eV. The similarity of the energies of the on-surface adsorption sites is explained as a consequence of the bigger size of K which implies that the adatom experiences a rather small substrate electron-density corrugation. Therefore for potassium the on-top and hollow sites are close in energy already for the unrelaxed Al(111) substrate. Because the relaxation energy of the on-top site is larger than that of the threefold hollow site both sites receive practically the same adsorption energy. The unexpected possibility of surface-substitutional sites is explained as a consequence of the ionic nature of the bonding which, at higher coverages, can develop strongest when the adatom can dive into the substrate as deep as possible. The interesting result of the studied systems is that the difference in bond strengths between the ‘‘normal’’ and substitutional geometries is sufficiently large to kick out a surface Al atom.

In ab initio theory, defects are routinely modeled by supercells with periodic boundary conditions. Unfortunately, the supercell approximation introduces artificial interactions between charged defects. Despite numerous attempts, a general scheme to correct for these is not yet available. We propose a new and computationally efficient method that overcomes limitations of previous schemes and is based on a rigorous analysis of electrostatics in dielectric media. Its reliability and rapid convergence with respect to cell size is demonstrated for charged vacancies in diamond and GaAs.

We have investigated native defects and native defect‐impurity complexes as candidate sources for the yellow luminescence in GaN. Using state‐of‐the‐art first‐principles calculations, we find strong evidence that the Ga vacancy (V_Ga) is responsible. The dependence of the V_Ga formation energy on Fermi level explains why the yellow luminescence is observed only in n‐type GaN. The V_Ga defect level is a deep acceptor state, consistent with recent pressure experiments. Finally we show that the formation of V_Ga is enhanced by the creation of complexes between V_Ga and donor impurities.