Pressure dependence of electronic, vibrational and optical properties of wurtzite-boron nitride

Wurtzite Boron Nitride ($w\mathrm{BN}$) is a wide band gap BN polymorph with unique mechanical properties such as hardness and stiffness. Initially synthesized in 1963 by transforming hexagonal BN ($h\mathrm{BN}$) under high temperature and pressure conditions, $w\mathrm{BN}$ can now be stabilized at atmospheric pressure to obtain high-quality samples. Our first-principles study investigates the electronic, vibrational, and optical properties of $w\mathrm{BN}$ across a broad range of pressures. We account for the electron-hole interaction in the optical response, revealing that this effect is crucial to interpret the available experimental spectra. We also calculate the coupling between excitons and phonons and provide a phonon-assisted emission spectrum, centered around 6.02 eV. Our results hold significant importance for the potential application of $w\mathrm{BN}$ as a dielectric material in BN-based technologies, especially in optoelectronics and harsh environments. We also expect that our prediction could be verified in the future, and it could aid in the identification of $w\mathrm{BN}$ through cathodoluminescence experiments.

Figure 1

Top view (a) and three dimensional structure (b) of wurtzite BN. The atoms in the unit cell are framed by a dotted line in panel (b), lattice parameter $c$ is parallel to the $z$ axis.

Figure 2

Top view and side view of the supercell mapping the $K$ point at $\mathrm{\Gamma }$.

Figure 3

Phonon dispersion of $w\mathrm{BN}$ at 0 kBar calculated in the framework of DFPT.

Figure 4

Phonon eigenmodes at $\mathrm{\Gamma }$ point and their irreducible representations. The $A_1$ eigenmode is intended to be the same for TO and LO modes, while the represented $E_1$ mode corresponds to the TO one, the LO being out of plane with respect to the TO mode.

Figure 5

Top panel: Calculated phonon density of states for 0 (green, solid line) and 200 kBar (orange, dashed line) and experimental phonon density of states (blue, dotted line) extracted from inelastic x-ray scattering in Refs. [43], multiplied by two to make the comparison easier. Bottom panel: Optical phonon frequencies at $\mathrm{\Gamma }$ point in $w\mathrm{BN}$ as a function of hydrostatic pressure. The first three acoustic modes are omitted.

Figure 6

DFT (black points) and QP-corrected electronic (solid blue line) band structure of $w\mathrm{BN}$ at 0 kBar. Arrows highlight the transitions where direct (red) and indirect (violet) gaps occur at QP level. Only four bands above and below the band gap are shown.

Figure 7

QP corrected band structure at 0 kBar (blue solid line) and 200 kBar (red dashed line).

Figure 8

DFT and QP-corrected direct and indirect gaps as a function of pressure.

Figure 9

Quasiparticle (solid black), DFT based independent particle (dashed dotted orange), $\mathit{GW}$ based independent particle (dotted red) spectra of the imaginary part of ${\epsilon }_M$ at 0 kBar. Dashed vertical lines mark the position of the $\mathit{GW}$-corrected and the DFT band gaps in both main figure and inset. Experimental data (dashed blue) are extracted from Ref. [17].

Figure 10

Quasiparticle-corrected direct band gap (blue stars line), first bright exciton level (orange triangles line), and the binding energy (blue dots line) as a function of pressure.

Figure 11

(a) Phonon-assisted luminescence at 0 kBar, when the luminescence has been averaged across the three Cartesian directions. The dotted vertical line indicates the energy of the indirect exciton (iK). In panels (b) and (c) we separated the contributions of the basal plane Cartesian coordinates (average over the $x$ and $y$ directions) and the $z$ axis. In both cases the contributions of single phonon modes have been specified. Note that a couple of phonon modes (the third and the sixth) have a much lower contribution compared to the others and are not shown in the figure.