Positron annihilation spectroscopy investigation of vacancy clusters in silicon carbide: Combining experiments and electronic structure calculations

The temperature dependence of the point defects in 6$H$-SiC induced by 12-MeV proton irradiation was studied by means of isochronal annealing followed by both positron annihilation spectroscopy and electron paramagnetic resonance measurements. The formation energies and positron lifetimes of various vacancy clusters were calculated to help in the interpretation of the experiments. The combination of the experiments and calculations enabled the identification of a negative silicon vacancy, with the lifetime of 218 ps, which is annealed between 400 ${}^{\circ }$C and 700 ${}^{\circ }$C. This process involves vacancy migration and formation of the $V_{\mathrm{C}}+V_{\mathrm{Si}}$ cluster, with a lifetime of 235 ps. In addition, our calculations confirm the identification of several clusters proposed in previous experimental studies.

Figure 1

EPR spectrum obtained at 300 K with $B\parallel c$ on the proton as-irradiated 6H-SiC CREE crystal. The inset shows the central spectrum and its fit using the $V_{\mathrm{Si}}^{1-}$ model.

Figure 2

Silicon vacancies concentration (not distorted, distorted, sum) as a function of the annealing temperature in the 6H-SiC H${}^{+}$ 12-MeV irradiated crystal.

Figure 3

Measurement temperature dependence of the positron lifetime components obtained for the 12-MeV proton as-irradiated crystals, and after different annealing steps: (a) average lifetime ${\tau }_{\mathrm{av}}$; (b) lifetime ${\tau }_2$ of the longest component; (c) its intensity $I_2$. The uncertainty on the values is close to the symbol size.

Figure 4

Annealing temperature dependence of the positron lifetime components obtained for the 12-MeV proton irradiated crystals for three different measurement temperatures: (a) average lifetime ${\tau }_{\mathrm{av}}$; (b) lifetime ${\tau }_2$ of the longest component; (c) its intensity $I_2$.

Figure 5

Formation energies of various charge states of vacancy complexes calculated in stoichiometric 3$C$-SiC (white background). Results are extrapolated to the top of the 6$H$-SiC gap (gray background).

Figure 6

Formation energies of the most stable charge states of the vacancy complexes studied in stoichiometric 3$C$-SiC (white background). Results are extrapolated to the top of the 6$H$-SiC gap (gray background).

Figure 7

Positron isodensities (solid traced for 70% of the maximum density, transparent for 30%), in red, in $V_{\mathrm{C}}$, $V_{\mathrm{C}}+C_{\mathrm{Si}}$, and $V_{\mathrm{C}}+V_{\mathrm{C}}$, in 3$C$-SiC. Figures were generated using XCRYSDEN [66, 67] program.

Figure 8

Positron isodensities (solid traced for 70% of the maximum density, transparent for 30%), in red, in the defects containing one silicon vacancy, in 3$C$-SiC. Carbon atoms are presented in yellow, silicon atoms in blue. White spheres represent the carbon vacancies. Figures were generated using XCRYSDEN [66, 67] program.

Figure 9

Positron isodensities (solid traced for 70% of the maximum density, transparent for 30%), in red, in the defects containing two silicon vacancies, in 3$C$-SiC. Carbon atoms are presented in yellow, silicon atoms in blue. Carbon and silicon vacancies are represented by white and black spheres, respectively. Figures were generated using XCRYSDEN [66, 67] program.

Figure 10

Positron isodensities (solid traced for 70% of the maximum density, transparent for 30%), in red, in two configurations of a hexavacancy, in 3$C$-SiC. Carbon atoms are presented in yellow, silicon atoms in blue. Carbon and silicon vacancies are represented by white and black spheres, respectively. Figures were generated using XCRYSDEN [66, 67] program.