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

Abstract

The carbon vacancy in 4H-SiC is a powerful minority carrier recombination center in as-grown material and a major cause of degradation of SiC-based devices. Despite the extensiveness and maturity of the literature regarding the characterization and modeling of the defect, many fundamental questions persist. Among them we have the shaky connection of the EPR data to the electrical measurements lacking sub-lattice site resolution, the physical origin of the pseudo-Jahn-Teller effect, the reasoning for the observed sub-lattice dependence of the paramagnetic states, and the severe temperature-dependence of some hyperfine signals which cannot be accounted for by a thermally-activated dynamic averaging between equivalent Jahn-Teller distorted structures. In this work we address these problems by means of semi-local and hybrid density functional calculations. We start by inventorying a total of four different vacancy structures from the analysis of relative energies. Diamagnetic states have well defined low-energy structures, whereas paramagnetic states display metastability. The reasoning for the rich structural variety is traced back to the filling of electronic states which are shaped by a crystal-field-dependent (and therefore site-dependent) pseudo-Jahn-Teller effect. From calculated minimum energy paths for defect rotation and transformation mechanisms, combined with the calculated formation energies and electrical levels, we arrived at a configuration-coordinate diagram of the defect. The diagram provides us with a detailed first-principles picture of the defect when subject to thermal excitations. The calculated acceptor and donor transitions agree well with the binding energies of electrons emitted from the Z 1/2 and EH 6/7 traps, respectively. From the comparison of calculated and measured U -values, and correlating the site-dependent formation energies with the relative intensity of the DLTS peaks in as-grown material, we assign Z1 (EH6) and Z2 (EH7) signals to acceptor (donor) transitions of carbon vacancies located on the h and k sub-lattice sites, respectively * jose.coutinho@ua.pt

Anisotropic and plane-selective migration of the carbon vacancy in SiC: Theory and experiment

“…The electronic self-consistent energy was minimized to a numerical accuracy of 10 −6 eV, while atomic coordinates of stable structures were relaxed by means of a conjugate-gradient algorithm until the largest force was lower than 0.01 eV/Å. The resulting defect structures matched recent semilocal and hybrid DFT calculations [14,19,42].…”

“…First of all, let us identify the number of possible ways a V C defect can jump into a neighboring carbon site. Due to (pseudo-)Jahn-Teller effects, neutral V C adopts tetragonal (D 2d ) and monoclinic (C 1h ) ground state structures in 3C-and 4H-SiC, respectively [14,24,42,57,58]. In the cubic phase, each carbon site has one shell of 12 carbon second neighbors, shown as black haloed spheres in Fig.…”

“…Fortunately, we know that the height of the energy barriers for conversion between equivalent (pseudo-)Jahn-Teller induced alignments, are about 0.3-0.4 eV [14]. Consequently, during vacancy migration, the temperatures are high enough to allow the defect to freely roam around all orientations and effectively show tetrahedral or trigonal symmetry in 3C-and 4H-SiC, respectively.…”

“…In 4H-SiC, and disregarding any departure from the perfect vacancy structure due to pseudo-Jahn-Teller distortions [14], V C may occur in two configurations, namely at pseudocubic and hexagonal sites [V C (k) and V C (h)], essentially differing by some of their second neighbors and more remote ligands. The 3C-SiC cubic phase is isotropic, and only one V C configuration can be found.…”

“…First-principles calculations show that the charge-neutral V C in 4H-SiC has a low formation energy in the range 4.5-5 eV [14,19], partly explaining its prevalence in as-grown (nonirradiated) material, apparently showing a high thermal stability [12,20,21]. It has been shown that reaching the thermodynamic equilibrium of the V C , at, e.g., ∼1500 • C, requires less than 1 h and results in a V C concentration of only ∼10 11 cm −3 [13].…”