Coupling of excitons and defect states in boron-nitride nanostructures

The signature of defects in the optical spectra of hexagonal boron nitride (BN) is investigated using many-body perturbation theory. A single BN-sheet serves as a model for different layered BN nanostructures and crystals. In the sheet we embed prototypical defects such as a substitutional impurity, isolated boron and nitrogen vacancies, and the divacancy. Transitions between the deep defect levels and extended states produce characteristic excitation bands that should be responsible for the emission band around $4$ eV, observed in luminescence experiments. In addition, defect bound excitons occur that are consistently treated in our ab initio approach along with the “free” exciton. For defects in strong concentration, the coexistence of both bound and free excitons adds substructure to the main exciton peak and provides an explanation for the corresponding feature in cathodo- and photoluminescence spectra.

Figure 1

Geometry of the defects in BN monolayer with defects: (a) $C_N$; (b) $V_B$; (c) $V_N$; (d) $V_{\mathit{BN}}$. Defect induced changes of BN bond distances are indicated (in atomic units) and have to be compared with the BN distance of the perfect sheet (2.724 a.u.).

Figure 2

Quasiparticle energies of ${\mathrm{C}}_{\text{N}}$, ${\mathrm{V}}_{\text{B}}$, ${\mathrm{V}}_{\text{N}}$, and ${\mathrm{V}}_{\text{BN}}$ as obtained from LDA and ${\mathrm{G}}_0$W${}_0$ calculations: schematic representation of energy position with in the band gap. The filled arrows indicate levels occupied with electrons with spin up or down. Dotted arrows indicate unoccupied states (holes), correspondingly.

Figure 3

Independent-particle absorption spectra (arbitrary units) based on the ${\mathrm{G}}_0{\mathrm{W}}_0$ quasiparticle band structure. In the left panel, the absorption cross section is increased by a factor 15 with respect to the right panel in order to make the defect-related peaks visible.

Figure 4

Optical absorption spectra calculated by the Bethe-Salpeter equation. In the left panels the absorption cross section is increased by a factor of ten in order to make the defect-related peaks visible. Spectra are shown with a broadening of $0.1$ eV (to simulate a typical experimental broadening) and $0.005$ eV (in order to investigate the fine structure of the spectrum).

Figure 5

Amplitude of the different electron-hole pairing entering in the BSE, for the boron vacancy and the BN divacancy, compared with the pure h-BN monolayer.