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.

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We present total-energy, force, and electronic-structure calculations for Na and K adsorbed in various geometries on an A1(111) surface. The calculations apply density-functional theory together with the local-density approximation and the ab initio pseudopotential formalism. Two adsorbate meshes, namely (&3X &3)R30' and (2X2), 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 (&3X &3)R30' structure has a lower energy than the (2X2) 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 (&3X&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.

Hydrogen strongly affects the electronic and structural properties of many materials. It can bind to defects or to other impurities, often eliminating their electrical activity: this effect of defect passivation is crucial to the performance of many photovoltaic and electronic devices. A fuller understanding of hydrogen in solids is required to support development of improved hydrogen-storage systems, proton-exchange membranes for fuel cells, and high-permittivity dielectrics for integrated circuits. In chemistry and in biological systems, there have also been many efforts to correlate proton affinity and deprotonation with host properties. Here we report a systematic theoretical study (based on ab initio methods) of hydrogen in a wide range of hosts, which reveals the existence of a universal alignment for the electronic transition level of hydrogen in semiconductors, insulators and even aqueous solutions. This alignment allows the prediction of the electrical activity of hydrogen in any host material once some basic information about the band structure of that host is known. We present a physical explanation that connects the behaviour of hydrogen to the line-up of electronic band structures at heterojunctions.