Ab initio study of the split silicon-vacancy defect in diamond: Electronic structure and related properties

The split silicon-vacancy (SiV) defect in diamond is an electrically and optically active color center. Recently, it has been shown that this color center is bright and can be detected at the single defect level. In addition, the SiV defect shows a nonzero electronic spin ground state that potentially makes this defect an alternative candidate for quantum optics and metrology applications beside the well-known nitrogen-vacancy color center in diamond. However, the electronic structure of the defect, the nature of optical excitations and other related properties are not well understood. Here we present advanced ab initio study on SiV defect in diamond. We determine the formation energies, charge transition levels, and the nature of excitations of the defect. Our study unravels the origin of the dark or shelving state for the negatively charged SiV defect associated with the 1.68-eV photoluminescence center.

Figure 1

The split-vacancy structure of the SiV defect and the calculated spin density in neutral charge state. The isosurface of spin density is 0.05. The defect has $D_{3d}$ symmetry with the symmetry axis of [111] direction. The lattice sites of the missing carbon atoms are depicted by the smallest (pink) balls.

Figure 2

The defect-molecule diagram of the neutral SiV defect in diamond. The irreducible representation of the orbitals under $D_{3d}$ symmetry is shown. The orbitals of the Si-atom and the six carbon dangling bonds of divacancy recombine in diamond where the conduction band (CB) and valence band (VB) are schematically depicted. The $e_g$ orbital is very close to the VB maximum, forming a strong resonance state at the VB edge shown as brown (lighter gray) lines. The $e_u$ level falls in the VB that also forms a strong resonance even deeper in the VB. For the sake of simplicity, the position of the spin-up (majority spin channel) levels are depicted in the spin-polarized DFT calculation.

Figure 3

The electron wave function of $e_u$ and $e_g$ defect states in the neutral SiV defect. Both states are double degenerate, so both $x$ and $y$ components are depicted. Note that $e_u$ states are changing sign upon inversion while $e_g$ states do not, as their irreducible representation indicates. Furthermore, Si orbitals have little contribution in the $e_u$ state but no contribution to the $e_g$ state. The $e_u$ state is resonant with the VB, thus less localized, whereas the localized $e_g$ state lies in the band gap.

Figure 4

The calculated formation energy of SiV defect as a function of the Fermi level in the gap. The crossing points represent the charge transition levels. The chemical potential of Si is taken from cubic silicon carbide in the carbon-rich limit.

Figure 5

Schematic diagram about the electronic structure of the negatively charged SiV defect in diamond. The valence band (VB) resonant states play a crucial role in the excitation. For the sake of the simplicity, the spin polarization of the single-particle levels are not shown. (a) Ground and the bright (optically allowed) excited state. (b) Ground and shelving states when the hole is left on the split VB edge states. (c) Schematic energy level diagram based on HSE06 constraint DFT calculations. Thick red lines indicate strong absorption/emission while the thin red line indicates a weak radiative recombination in the case of the presence of strain which breaks the inversion symmetry of the defect. Orange wavy arrows represent nonradiative recombination down to the ground state.