Density-functional study of atomic and electronic structures of multivacancies in silicon carbide

Abstract

We report the density-functional calculations that provide a firm theoretical framework to identify the multivacancies and unravel the underlying physics in the most stable silicon carbide polytype 4H-SiC. The calculations with the generalized gradient approximation (GGA) for the Si and C monovacancy, ${V}_{\mathrm{Si}}$ and ${V}_{\mathrm{C}}$, have clarified the significantly lower formation energy of the C vacancy accompanied by the efficient pairing relaxation of the surrounding Si dangling bonds. Our GGA calculation also predicts a stable next-neighbor ${V}_{\mathrm{C}}{V}_{\mathrm{C}}$ divacancy which is lower in the formation energy than the usual nearest-neighbor divacancy ${V}_{\mathrm{C}}{V}_{\mathrm{Si}}$ discussed in the past. We also perform the calculations with the hybrid functional and confirm the stability of the next-neighbor ${V}_{\mathrm{C}}{V}_{\mathrm{C}}$ divacancy. Our calculations indeed clarify that it is possible to detect the ${V}_{\mathrm{C}}{V}_{\mathrm{C}}$ with its peculiar hyperfine coupling constants by the electron paramagnetic resonance (EPR) measurements. Based on the structural characteristics and the energetics for the monovacancy, we further propose an extended dangling-bond-counting (EDBC) model to choose the energetically favorable topological network of the vacant sites for the multivacancy. The GGA calculations combined with the EDBC model reveal that ${V}_{3}$ and ${V}_{6}$ are energetically favorable. The stable ${V}_{3}$ is a nearest-neighbor complex of ${V}_{\mathrm{C}}\text{\ensuremath{-}}{V}_{\mathrm{Si}}\text{\ensuremath{-}}{V}_{\mathrm{C}}$, whereas the ${V}_{6}$ is the high-symmetry ${V}_{5}$ (the central ${V}_{\mathrm{Si}}$ surrounded by four ${V}_{\mathrm{C}})$ plus a symmetry-breaking next-neighbor ${V}_{\mathrm{C}}$. We perform the GGA calculations for the electronic structure of such ${V}_{3}$ and ${V}_{6}$ and discuss the possibility of detecting these multivacancies. In particular, the EPR-detected ANN1 center is provisionally identified as the doubly positive trivacancy ${V}_{\mathrm{C}}\text{\ensuremath{-}}{V}_{\mathrm{Si}}\text{\ensuremath{-}}{V}_{\mathrm{C}}$.