The first DFT calculations of point defects in silicon carbide,98 dating back to 1988, were burdened by strong limitations in computing time. For this reason, they were performed with relatively small supercells (16 and 32 atoms), largely insufficient basis sets (plane waves with energy up to 28 Ry), and further approximations, namely for the relaxation of atomic positions. Moreover, they were limited to high sym­metry configurations. The results were only qualita­tive; however, it was already clear that vacancies and antisites could be relatively abundant, at equilibrium, with respect to interstitial defects. The authors dared to approach some defect complexes and could predict that antisite pairs and divacancies were bound.

Vacancies were thoroughly studied at the turn of the century.97’99-101 The most prominent result may be the metastability of the silicon vacancy. Indeed, following a suggestion coming from a self-consistent DFT-based tight-binding calculation by Rauls and coworkersy 2 the electron paramagnetic resonance (EPR) spectra of annealed samples of irradiated SiC were measured103 and compared with calculated hyperfine parameters. This showed that silicon vacancies are metastable with regard to a carbon vacancy-carbon antisite complex (Vc—Csi); a fact that has since been consistently confirmed by the other calculations.

Interstitials were less studied than vacancies. One should however mention a study104 devoted to carbon and silicon in interstitials in silicon carbide. Beyond these studies dedicated to one type of defect, very complete and comprehensive work on both vacancies and interstitials was also published. One should cite Bernardini et a/.105 devoted to the formation energies of defects, while Bockstedte eta/.106 goes further as it also covers migration energetics of basic intrinsic defects (vacancies, interstitials, antisites). It is worth noting that in such covalent compounds there are many possible atomic structures for defects as simple as a monointerstitial and that all these structures must be considered in the calculation (see Figure 11).

As examples, the results of these various studies on what concerns formation energies and CTL of vacan­cies are summarized in the following tables.

One can see a general agreement in the formation energies of the neutral defects, especially in the re­cent references. The small differences are related to k-point sampling or cell size in the calculations. Larger discrepancies appear between the various pre­dicted CTL. They relate to the inaccuracy of standard DFT calculations in treating empty or defect states.

A simple example relates directly to the underestima­tion of the band gap: the silicon interstitial (in the Itc configuration) in the neutral state shows up as metallic in standard calculations, the defect states lying inside the conduction band. This fact, on one hand, calls for a better description of the exchange — correlation potential for these configurations; on the other, it makes the convergence with k points and cell size very slow, as has recently been pointed out.107 This drawback of standard DFT-LDA/GGA supercell calculations is common to other defects in SiC. Even when calculated defect states fall within the band gap, their position inside it can be grossly mis­calculated with standard DFT calculations.

The errors produced by standard DFT calcula­tions for the CTL are well known nowadays. The determination of an accurate method to calculate these CTL is an active field of research with works on advanced methods such as GW (e. g., the results on SiO2108) or hybrid functionals.109 For what concerns nuclear materials, and especially SiC, GW correc­tions and excitonic effects will allow further compar­isons with experiments (Table 1).