Structure and vibrational spectra of carbon clusters in SiC

The electronic, structural, and vibrational properties of small carbon interstitial and antisite clusters are investigated by ab initio methods in $3C$- and $4H-\mathrm{Si}\mathrm{C}$. The defects possess sizable dissociation energies and may be formed via condensation of carbon interstitials, e.g., generated in the course of ion implantation. All considered defect complexes possess localized vibrational modes (LVM’s) well above the SiC bulk phonon spectrum. In particular, the compact antisite clusters exhibit high-frequency LVM’s up to $250\mathrm{meV}$. The isotope shifts resulting from a ${}^{13}\mathrm{C}$ enrichment are analyzed. In the light of these results, the photoluminescence centers $D_{\mathrm{II}}$ and $P-U$ are discussed. The dicarbon antisite is identified as a plausible key ingredient of the $D_{\mathrm{II}}$ center, whereas the carbon split interstitial is a likely origin of the $P-T$ centers. The comparison of the calculated and observed high-frequency modes suggests that the $U$ center is also a carbon-antisite-based defect.

Figure 1

Carbon-interstitial clusters in $3C-\mathrm{Si}\mathrm{C}$. (a) Carbon di-interstitials ${\left({\mathrm{C}}_{\mathrm{sp}}\right)}_{2,\mathrm{lin}}$, ${\left({\mathrm{C}}_{\mathrm{sp}}\right)}_2$, and ${\left({\mathrm{C}}_2\right)}_{\mathrm{hex}}$. (b) Carbon tetra-interstitials ${\left({\mathrm{C}}_{\mathrm{sp}}\right)}_4$ and ${\left[{\left({\mathrm{C}}_2\right)}_{\mathrm{hex}}\right]}_2$.

Figure 2

Carbon di-interstitials in $4H-\mathrm{Si}\mathrm{C}$. (a) linear cubic-cubic di-interstitial ${\left({\mathrm{C}}_{\mathrm{sp}}\right)}_{2,kk,\mathrm{lin}}$, (b) hexagonal-cubic di-interstitial in the cubic plane ${\left({\mathrm{C}}_{\mathrm{sp}}\right)}_{2,hk,\mathrm{cub}}$, (c) cubic-hexagonal di-interstitial in the hexagonal plane ${\left({\mathrm{C}}_{\mathrm{sp}}\right)}_{2,kh,\mathrm{hex}}$. The stacking order of the crystal is highlighted, the cubic and hexagonal planes are marked at the left.

Figure 3

Tetra-interstitial in $4H-\mathrm{Si}\mathrm{C}$ spanning a cubic and a hexagonal plane. The stacking sequence of the crystal is highlighted.

Figure 4

Aggregation of carbon clusters at a carbon antisite in $3C-\mathrm{Si}\mathrm{C}$. (a) Dicarbon antisite ${\left({\mathrm{C}}_2\right)}_{\mathrm{Si}}$, tricarbon antisite ${\left({\mathrm{C}}_3\right)}_{\mathrm{Si}}$, and tetracarbon antisite ${\left({\mathrm{C}}_4\right)}_{\mathrm{Si}}$. (b) Intermediate configurations $I1$ and $I2$ of the tricarbon antisite. (c) Pairing of two dicarbon antisites ${\left[{\left({\mathrm{C}}_2\right)}_{\mathrm{Si}}\right]}_2$.

Figure 5

Isotope shifts of the dicarbon antisite enriched with 30% ${}^{13}\mathrm{C}$. The upper panel shows the splitting of the modes calculated in a 64-site supercell in the Jahn-Teller distorted configuration, the lower in a 216-site supercell with a high-spin-like symmetric configuration. The frequencies of the pure ${}^{12}\mathrm{C}$ case are given in Table .

Figure 6

Pair of dicarbon antisites ${\left[{\left({\mathrm{C}}_2\right)}_{\mathrm{Si}}\right]}_{2,kh}$ in $4H-\mathrm{Si}\mathrm{C}$ spanning cubic and hexagonal sites in the cubic plane. The stacking sequence of the crystal is highlighted.