Negative-$U$ carbon vacancy in 4$H$-SiC: Assessment of charge correction schemes and identification of the negative carbon vacancy at the quasicubic site

The carbon vacancy ($V_C$) has been suggested by different studies to be involved in the $Z_1$/$Z_2$ defect-a carrier lifetime killer in SiC. However, the correlation between the $Z_1$/$Z_2$ deep level with $V_C$ is not possible since only the negative carbon vacancy ($V_{\mathrm{C}}^{-}$) at the hexagonal site, $V_{\mathrm{C}}^{-}$($h$), with unclear negative-$U$ behaviors was identified by electron paramagnetic resonance (EPR). Using freestanding $n$-type 4$H$-SiC epilayers irradiated with low energy (250 keV) electrons at room temperature to introduce mainly $V_C$ and defects in the C sublattice, we observed the strong EPR signals of $V_{\mathrm{C}}^{-}$($h$) and another $S$ = 1/2 center. Electron paramagnetic resonance experiments show a negative-$U$ behavior of the two centers and their similar symmetry lowering from $C_{3v}$ to $C_{1h}$ at low temperatures. Comparing the Si and C ligand hyperfine constants observed by EPR and first principles calculations, the new center is identified as $V_{\mathrm{C}}^{-}$($k$). The negative-$U$ behavior is further confirmed by large scale density functional theory supercell calculations using different charge correction schemes. The results support the identification of the lifetime limiting $Z_1$/$Z_2$ defect to be related to acceptor states of the carbon vacancy.

Figure 1

EPR spectra in low-doped ([N] ∼ 1 × 10¹⁴ cm⁻³) n-type 4$H$-SiC layer irradiated by 250 keV electrons to a fluence of ∼7.5 × 10¹⁸ cm⁻² measured for B∥c at 100 K. (a) In darkness, only a weak signal of the SI-1 defect (Ref. [31]) can be observed, whereas (b) under illumination with light of photon energies $h$ν ∼ 3 eV, strong signals of $V_{\mathrm{C}}^{+}$($k$), $V_{\mathrm{C}}^{+}$($h$), $V_{\mathrm{C}}^{-}$($h$), and a new signal, which we will show later to be related to $V_{\mathrm{C}}^{-}$($k$), were observed. Their main lines are shown in the inset and their hf structures are shown in ×10 intensity-scale spectrum.

Figure 2

EPR spectra in a high-doped ([N] ∼ 1.6 × 10¹⁷ cm⁻³) n-type 4$H$-SiC layer irradiated by 250 keV electrons to a fluence of ∼7.5 × 10¹⁸ cm⁻² measured for B∥c at (a) 6 K and (b) 100 K in darkness and (c) at 100 K under illumination with light of photon energies $h$ν ∼ 1.3 eV. The hf structures of $V_{\mathrm{C}}^{-}$($k$) and $V_{\mathrm{C}}^{-}$($h$) are shown in ×10 intensity-scale spectrum. The weak and broad signal at 6 K is from the SI-1 center (Ref. [31]).

Figure 3

EPR spectra in a high-doped n-type 4$H$-SiC layer irradiated by 250 keV electrons to a fluence of ∼7.5 × 10¹⁸ cm⁻² measured for B∥c with low microwave (MW) power (0.1 mW) under illumination with light of photon energies $h$ν ∼ 1.3 eV at (a) 120 K and (b) 140 K. (c) The EPR spectrum of $V_{\mathrm{C}}^{-}$($h$) measured for B∥c at 295 K with high MW power (63.25 mW) showing the Si hf structure due to hf interaction with one ²⁹Si atom occupying one of four nearest Si sites.

Figure 4

Angular dependence of the magnetic field positions of EPR lines (open circles) measured at 140 K with B rotating in the (1$\overline{1}$00) plane. The solid and dashed curves represent the simulated angular dependences for $V_{\mathrm{C}}^{-}$($k$, $C_{3v})$ and $V_{\mathrm{C}}^{-}$($h$, $C_{3v})$, respectively, using Eq. (1) and parameters in Table 1. The angle 0° and 90° correspond to the directions B∥c and B⊥c, respectively.

Figure 5

Angular dependence of the magnetic field positions of $V_{\mathrm{C}}^{-}$($h$, $C_{3v})$ lines (open circles) measured at 295 K with B rotating in the (1$\overline{1}$00) plane. The solid curves represent the simulated angular dependence using Eq. (1) and parameters in Table 1.

Figure 6

EPR spectra in low-energy electron irradiated 4$H$-SiC measured at different temperatures for B∥c under illumination with photon energies $h$ν ∼ 1.3 eV, showing the temperature dependence of the hf structures in the range 30–90 K. The spectra in (a)–(e) are shown in ×10 intensity scale.

Figure 7

Angular dependence of the magnetic field positions of $V_{\mathrm{C}}^{-}$($k$) lines (open circles) measured at 30 K with B rotating in the (1$\overline{1}$00) plane. The upper and lower parts show the angular dependence of the magnetic field positions of the Si_3,4 hf lines, while the middle part shows the corresponding angular dependence of the C_1,2 and Si_5,6 hf lines. The solid curves represent the simulated angular dependence using Eq. (1) and parameters in Table 2.

Figure 8

Defect levels in $V_{\mathrm{C}}^{-}$($k$). After the Jahn-Teller distortion the double degenerate $e$ level splits to $a$′ and $a$″ levels. The unpaired electron occupies the symmetric $a$′ level, which has lower energy than the asymmetric $a$″ level. One of the $a$′ levels lie in the valence band, and the other two are in the band gap, whereas the empty $a$″ sits in the conduction band.

Figure 9

Spin densities for stable (a) and metastable (b) configurations from top view. The silicon and carbon atoms are depicted as yellow (bright) and cyan (dark) balls, respectively. The isovalues are 0.0225 1/Å for the stable geometry and 0.0630 1/Å for the metastable geometry. The distances between the silicon atoms in the basal plane corresponding to the stable (c) and metastable (d) geometries are also shown from top view. The relative stability between the two configurations is indicated. On the red (light grey) silicon atoms high spin density was obtained.

Figure 10

Schematic sketch of the configurations of the negatively charged carbon vacancy at the quasicubic site $V_{\mathrm{C}}^{-}$($k$) in 4$H$-SiC from top view: description of the transition from static Jahn-Teller distortion to the dynamic one as a function of temperature. (a) At lower temperatures, only the stable state exists with static Jahn-Teller distortion with $C_{1h}$ symmetry. (b) At elevated temperatures, the metastable state will also occur beside the stable state. In the case of the metastable state, high spin density was observed on the silicon atom located along the $c$ axis (not shown here: see Si₁ in Fig. 9) and one of the silicon atoms in the basal plane. Assuming low barrier energy between the symmetrically equivalent $C_{1h}$ configurations, the spin density can be high on any of the silicon atoms in the basal plane. That is, the $C_{1h}$ plane will rotate, resulting in an averaged $C_{3v}$ symmetry at higher temperatures.