Contemporary theories of defects and impurities in semiconductors rely to a large extent on supercell calculations within density-functional theory using the approximate local-density approximation ͑LDA͒ or generalized gradient approximation ͑GGA͒ functionals. Such calculations are, however, affected by considerable uncertainties associated with: ͑i͒ the "band-gap problem," which occurs not only in the Kohn-Sham single-particle energies but also in the quasiparticle gap ͑LDA or GGA͒ calculated from total-energy differences, and ͑ii͒ supercell finite-size effects. In the case of the oxygen vacancy in ZnO, uncertainties ͑i͒ and ͑ii͒ have led to a large spread in the theoretical predictions, with some calculations suggesting negligible vacancy concentrations, even under Zn-rich conditions, and others predicting high concentrations. Here, we critically assess ͑i͒ the different methodologies to correct the band-gap problem. We discuss approaches based on the extrapolation of perturbations which open the band gap, and the self-consistent band-gap correction employing the LDA+ U method for d and s states simultaneously. From the comparison of the results of different gap-correction, including also recent results from other literature, we conclude that to date there is no universal scheme for band gap correction in general defect systems. Therefore, we turn instead to classification of different types of defect behavior to provide guidelines on how the physically correct situation in an LDA defect calculation can be recovered. ͑ii͒ Supercell finite-size effects: We performed test calculations in large supercells of up to 1728 atoms, resolving a long-standing debate pertaining to image charge corrections for charged defects. We show that once finite-size effects not related to electrostatic interactions are eliminated, the analytic form of the image charge correction as proposed by Makov and Payne leads to size-independent defect formation energies, thus allowing the calculation of well-converged energies in fairly small supercells. We find that the delocalized contribution to the defect charge ͑i.e., the defect-induced change of the charge distribution͒ is dominated by the dielectric screening response of the host, which leads to an unexpected effective 1 / L scaling of the image charge energy, despite the nominal 1 / L 3 scaling of the third-order term. Based on this analysis, we suggest that a simple scaling of the first order term by a constant factor ͑approximately 2/3͒ yields a simple but accurate image-charge correction for common supercell geometries. Finally, we discuss the theoretical controversy pertaining to the formation energy of the O vacancy in ZnO in light of the assessment of different methodologies in the present work, and we review the present experimental situation on the topic.

Existing defect models for In(2)O(3) and ZnO are inconclusive about the origin of conductivity, nonstoichiometry, and coloration. We apply systematic corrections to first-principles calculated formation energies Delta H, and validate our theoretical defect model against measured defect and carrier densities. We find that (i) intrinsic acceptors ("electron killers") have a high Delta H explaining high n-dopability, (ii) intrinsic donors ("electron producers") have either a high Delta H or deep levels, and do not cause equilibrium-stable conductivity, (iii) the O vacancy V(O) has a low Delta H leading to O deficiency, and (iv) V(O) has a metastable shallow state, explaining the paradoxical coexistence of coloration and conductivity.

Despite the great success that theoretical approaches based on density functional theory have in describing properties of solid compounds, accurate predictions of the enthalpies of formation (∆H f ) of insulating and semiconducting solids still remain a challenge. This is mainly due to incomplete error cancellation when computing the total energy differences between the compound total energy and the total energies of its elemental constituents. In this paper we present an approach based on GGA+U calculations, including the spin-orbit coupling, which involves fitted elemental-phase reference energies (FERE) and which significantly improves the error cancellation with compound total energies resulting in accurate values for the compound enthalpies of formation. We use an extensive set of 252 binary compounds with measured ∆H f values (pnictides, chalcogenides and halides) to obtain FERE energies and show that after the fitting, the 252 enthalpies of formation are reproduced with the mean absolute error MAE=0.054 eV/atom instead of MAE≈0.250 eV/atom resulting from pure GGA calculations. When applied to a set of 55 ternary compounds that were not part of the fitting set the FERE method reproduces their enthalpies of formation with MAE=0.048 eV/atom. Furthermore, we find that contributions to the total energy differences coming from the spin-orbit coupling can be, to a good approximation, separated into purely atomic contributions which do not affect ∆H f . The FERE method, hence, represents a simple and general approach, as it is computationally equivalent to the cost of pure GGA calculations and applies to virtually all insulating and semiconducting compounds, for predicting compound ∆H f values with chemical accuracy. We also show that by providing accurate ∆H f the FERE approach can be applied for accurate predictions of the compound thermodynamic stability or for predictions of Li-ion battery voltages.

Using first-principles electronic structure calculations we identify the anion vacancies in II-VI and chalcopyrite Cu-III-VI 2 semiconductors as a class of intrinsic defects that can exhibit metastable behavior. Specifically, we predict persistent electron photoconductivity (n-type PPC) caused by the oxygen vacancy V O in n-ZnO, and persistent hole photoconductivity (p-type PPC) caused by the Se vacancy V Se in p-CuInSe 2 and p-CuGaSe 2 . We find that V Se in the chalcopyrite materials is amphoteric having two "negative-U" like transitions, i.e. a double-donor transition ε(2+/0) close to the valence band and a double-acceptor transition ε(0/2−) closer to the conduction band. We introduce a classification scheme that distinguishes two types of defects (e.g., donors): type-α, which have a defect-localized-state (DLS) in the gap, and type-β, which have a resonant DLS within the host bands (e.g., conduction band). In the latter case, the introduced carriers (e.g., electrons) relax to the band edge where they can occupy a perturbedhost-state (PHS). Type α is non-conducting, whereas type β is conducting. We identify the neutral anion vacancy as type-α and the doubly positively charged vacancy as type-β. We suggest that illumination changes the charge state of the anion vacancy and leads to a crossover between α-and β-type behavior, resulting in metastability and PPC. In CuInSe 2 , the metastable behavior of V Se is carried over to the (V Se -V Cu ) complex, which we identify as the physical origin of PPC observed experimentally. We explain previous puzzling experimental results in ZnO and CuInSe 2 in the light of this model.

Acceptor-bound holes in oxides often localize asymmetrically at one out of several equivalent oxygen ligands. Whereas Hartree-Fock (HF) theory overly favors such symmetry-broken polaronic holelocalization in oxides, standard local density (LD) calculations suffer from spurious delocalization among several oxygen sites. These opposite biases originate from the opposite curvatures of the energy as a function of the fractional occupation number n, i.e., < 0 in HF and > 0 in LD. We recover the correct linear behavior, = 0, that removes the (de)localization bias by formulating a