Theory of Oxygen-Boron Vacancy Defect in Cubic Boron Nitride: A Diamond ${\mathrm{NV}}^{-}$ Isoelectronic Center

A color center in $c$-BN which is isoelectronic to diamond ${\mathrm{NV}}^{-}$ is predicted based on first-principles electronic structure calculations using the Heyd-Scuseria-Ernzerhof hybrid functional. The defect consists of a substitutional oxygen and an adjacent boron vacancy (${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$). We find that the ${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$ center is optically accessible with a zero-phonon line of about 1.6 eV. The ${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$ center also shares much of the characteristics of the GC-2 center often observed in $c$-BN. A prominent vibronic coupling peak is predicted to be around 55 meV, which is in excellent agreement with the characteristic phonon frequency (56 meV) observed in the luminescence spectra of the GC-2 center.

Figure 1

Structure of a ${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$ center in $c$-BN. Nitrogen atoms are shown in yellow (light color), boron in blue, and oxygen in red (dark). The boron vacancy ($V_{\mathrm{B}}$) at the center of the tetrahedron is also shown.

Figure 2

Band structures of (a) ${\mathrm{NV}}^{-}$ center in diamond, and (b) ${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$ center in $c$-BN calculated using a 216-atom supercell and the HSE06 functional. The spin resolved defect states ($e$ and $a_1$) are shown in red and blue lines for the majority and minority spins, respectively.

Figure 3

Charge density plots for the minority spin $a_1$ [(a) and (c)] and $e$ [(b) and (d)] defect states for the ${\mathrm{NV}}^{-}$ center in diamond and the ${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$ center in $c$-BN, respectively. Only atoms near the defect center are shown for clarity. The value of the charge density for the isosurface plot is $1.0\times {10}^{-2}e/a_0^3$.

Figure 4

Schematic for the energy versus configuration coordinate $Q$ for two electronic states involved in optical transitions within the Franck-Condon principle.

Figure 5

Identified LVM phonon modes (vertical bars) and projection $|{\eta }_{\alpha }{|}^2$ weighted broadening (dotted line). These LVMs are predicted to be strongly involved in the luminescence of the ${\mathrm{O}}_{\mathrm{N}}-V_{\mathrm{B}}$ center. The inset shows a vibration pattern for a typical $a_1$ LVM.