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The carbon vacancy in $4H$-SiC is a powerful minority carrier recombinationcenter and a major cause of degradation of SiC-based devices. Despite theextensiveness of the literature regarding the characterization and modeling ofthe defect, many fundamental questions persist. Among them we have the shakyconnection of the EPR data to the electrical measurements, the physical originof the pseudo-Jahn-Teller (pJT) effect, the reasoning for the observedsub-lattice dependence of the paramagnetic states, and the severetemperature-dependence of some hyperfine signals which cannot be accounted forby a thermally-activated dynamic averaging between equivalent JT-distortedstructures. In this work we address these problems by means of semi-local andhybrid density functional calculations. We start by inventorying a total offour vacancy structures. Diamagnetic states have well defined low-energystructures, whereas paramagnetic states display metastability. This richstructural variety is traced back to the filling of electronic states which areshaped by a crystal-field-dependent pJT effect. From calculated minimum energypaths for defect rotation and transformation mechanisms, combined with thecalculated formation energies and electrical levels, we arrived at aconfiguration-coordinate diagram of the defect. The diagram provides us with adetailed first-principles picture of the defect when subject to optical andthermal excitations. The calculated acceptor and donor transitions agree wellwith Z$_{1/2}$ and EH$_{6/7}$ trap energies, respectively. From comparison ofcalculated and measured $U$-values, and correlating the site-dependentformation energies with the relative intensity of the DLTS peaks in as-grownmaterial, we assign Z$_{1}$ (EH$_{6}$) and Z$_{2}$ (EH$_{7}$) signals toacceptor (donor) transitions of carbon vacancies located on the $h$ and $k$sub-lattice sites, respectively.

Theory of the carbon vacancy in $4H$-SiC: crystal field and pseudo Jahn-Teller effects