Determination of the optical bandgap of the Bernal and rhombohedral boron nitride polymorphs

We report a study of polymorphic boron nitride (BN) samples. We interpret the photoluminescence (PL) line at $6.032\pm 0.005\mathrm{eV}$ that can be recorded at 8 K in $s{p}^2$-bonded BN as being the signature of the excitonic fundamental bandgap of the Bernal BN (bBN) [or graphitic BN (gBN)] polymorph. This is determined by advanced PL measurements combined with x-ray characterizations on pure hexagonal BN (hBN) and on polymorphic crystal samples, later compared with the theoretical predictions of Sponza et al., [Phys. Rev. B 98, 125206 (2018)]. The overall picture is consistent with a direct excitonic fundamental bandgap of the bBN (or gBN) polymorph. This value $d{X}_b=6.032\pm 0.005\mathrm{eV}$ is higher than the indirect bandgap of hBN $(i{X}_h=5.955\pm 0.005\mathrm{eV})$.

Figure 1

Powder diffraction patterns computed for several boron nitride (BN) polytypes, with AA, AA′, AB, and ABC stackings, from bottom to top. The intensity of the main peak at ${27}^{\circ }$ is equal to unity for all phases. The x-ray source is copper.

Figure 2

From bottom to top, the x-ray diffraction $\theta \text{−}2\theta$ diffraction pattern recorded using $\mathrm{Cu}(\mathrm{K}{\alpha }_1+\mathrm{K}{\alpha }_2)$ radiation (1.54186 Å), for three highly (001)-oriented boron nitride (BN) Fe (blue), Fe + V (red) and C + Ni + Cr (green) samples. Asterisks correspond to the $\mathrm{Cu}\left(\mathrm{K}\beta \right)$ (1.39222 Å) and W(LA1) (1.47639 Å) radiations. For C + Ni + Cr, lines supplemental of the {(002), (004), (006)} set are detected and plotted in dark green. The x-ray source is copper.

Figure 3

Magnification of the diffraction feature in the ${40}^{\circ }–{47}^{\circ }$ region to show the existence of both hexagonal (hBN) and rhombohedral boron nitride (rBN) stackings. The structure at $44.5^{\circ }$ is due to a residual of the Ni + Cr flux as well as a second one (not shown) at $51.8^{\circ }$. The x-ray source is copper.

Figure 4

The 8 K macro-photoluminescence (PL) spectra in the 5–6.1 eV range of several samples showing the phonon-assisted transitions typical of hexagonal boron nitride (hBN; blue spectrum), mixed with the undulations linked to rhombohedral boron nitride (rBN) inclusions overlapping with impurities (green and red spectra), as well as signature of the direct bandgap of Bernal boron nitride (bBN), $d{X}_b$ at 6.032 eV. We tentatively identify the 5.72 eV band in C + Ni + Cr as the unresolved analog of the $i{X}_h\text{−}(\mathrm{L}{\mathrm{O}}_{\mathrm{T}}+\mathrm{T}{\mathrm{O}}_{\mathrm{T}})$. Dashed orange lines are guides for the eyes.

Figure 5

Enlarged view of the 8 K macro-photoluminescence (PL) spectra in the 5.7–6.1 eV range that reveals the signature of the direct bandgap of Bernal boron nitride (bBN), $d{X}_b$ at 6.032 eV, as well as its 200 meV phonon-assisted replica (green and red spectra). In blue, the macro-PL of a high-purity hexagonal boron nitride (hBN) crystal. Transitions are labeled according to the convention in the literature. State $T$ sits at the middle of the $\mathrm{\Gamma }K$ direction in the Brillouin zone of hBN.