Overtones of interlayer shear modes in the phonon-assisted emission spectrum of hexagonal boron nitride

We address the intrinsic optical properties of hexagonal boron nitride in deep ultraviolet. We show that the fine structure of the phonon replicas arises from overtones involving up to six low-energy interlayer shear modes. These lattice vibrations are specific to layered compounds since they correspond to the shear rigid motion between adjacent layers, with a characteristic energy of about 6–7 meV. We obtain a quantitative interpretation of the multiplet observed in each phonon replica under the assumption of a cumulative Gaussian broadening as a function of the overtone index, and with a phenomenological line broadening taken identical for all phonon types. We show from our quantitative interpretation of the full emission spectrum above 5.7 eV that the energy of the involved phonon mode is $6.8\pm 0.5$ meV, in excellent agreement with temperature-dependent Raman measurements of the low-energy interlayer shear mode in hexagonal boron nitride. We highlight the unusual properties of this material where the optical response is tailored by the phonon group velocities in the middle of the Brillouin zone.

Figure 1

Photoluminescence spectrum in bulk hBN in the deep ultraviolet under two-photon excitation at 3.03 eV, at 10 K. Experimental data (symbols), theoretical fit (red line). $X_{\mu }$ stands for the replica involving the phonon mode $\mu$ in the middle of the Brillouin zone around $T$ points.

Figure 2

Schematic representations, in the single-particle picture of the electronic band structure, of the phonon-assisted recombination processes of the $X_{L{O}_3\left(T\right)}$ line (left part), and of the $X_{L{O}_3\left(T\right)+2E_{2g}}$ one (right part). Inset: top view of the first Brillouin zone with high symmetry points. The green arrows correspond to the $L{O}_3\left(T\right)$ phonon in the middle of the Brillouin zone, and the red arrows to the low-energy interlayer shear phonons of $E_{2g}$ symmetry.

Figure 3

Experimental data (symbols) and fit (solid line) of the phonon-assisted emission spectrum in hBN: (a) without any line-broadening, (b) with a Gaussian broadening identical for each overtone, (c) with a Gaussian cumulative broadening (corresponding to Fig. 1), and (d) with a Lorentzian cumulative broadening. The energy $\mathrm{\Delta }$ of the Raman-active phonons $E_{2g}$ is 6.8 meV. The amplitudes $A_n^{\mu }$ of the different components used in the fits are displayed in Fig. 4.

Figure 4

Normalized weight $A_n^{\mu }$ of the overtones of interlayer shear modes used in Fig. 1, as a function of overtone index $n$, for each type of phonon replicas: $\mathrm{ZA}/{\mathrm{ZO}}_1$ (filled triangle), $\mathrm{TA}/{\mathrm{TO}}_1$ (filled square), $\mathrm{LA}/{\mathrm{LO}}_1$ (filled circle), ${\mathrm{TO}}_2/{\mathrm{TO}}_3$ (open square), ${\mathrm{LO}}_3$ (open circle).

Figure 5

Temperature dependence of the low-energy Raman-active interlayer shear mode energy between 77 K and 600 K (red dots), and value (blue square) of the energy $\mathrm{\Delta }=6.8\pm 0.5$ meV estimated from the fit displayed in Fig. 1. Inset: Raman scattering spectrum in bulk hBN, at 80 K.