Vibrational Properties of Hexagonal Boron Nitride: Inelastic X-Ray Scattering andAb InitioCalculations

Abstract

The phonon dispersion relations of bulk hexagonal boron nitride have been determined from inelastic x-ray scattering measurements and analyzed by ab initio calculations. Experimental data and calculations show an outstanding agreement and reconcile the controversies raised by recent experimental data obtained by electron-energy loss spectroscopy and second-order Raman scattering. DOI: 10.1103/PhysRevLett.98.095503 PACS numbers: 63.20.Dj, 61.10.Eq, 63.10.+a, 71.15.Mb Besides their intermediate structure between twodimensional sheets and 3D crystals, layered compounds are relevant materials for storage of other compounds [1] and as potential building blocks for nanotubes [2]. Among these materials, graphite and hexagonal boron nitride (h-BN) have drawn most of the attention due to their simple hexagonal structure, their fascinating properties, and the successful realization of carbon-[3] and more recently BN [4 -6] nanotubes. A wide band gap semiconductor, h-BN, has been grown successfully very recently as a single crystal. It exhibits a lasing behavior at 5.8 eV that makes it attractive for optoelectronic applications in the ultraviolet energy range [7].Despite the tremendous effort devoted to the characterization of physical properties of h-BN, the lattice dynamics, responsible for the elastic and thermodynamic properties such as the heat capacity and the thermal expansion, are still under debate. First principles calculations are generally accepted as the most accurate theoretical description of the lattice dynamics [8]. Recently, for h-BN, the validity of state of the art ab initio calculations was put in doubt by two experiments: Rokuta et al. [9] reported the only experimental data available for the phonon dispersion relations by electron-energy loss spectroscopy (EELS) performed on a monolayer of h-BN deposited on a Ni(111) substrate. Among several deviations from ab initio calculations of the lattice dynamics both for a monolayer [10,11] and for bulk h-BN [12,13], the EELS data show a degeneracy at the K point between acoustic (ZA) and optical (ZO) modes polarized along the c axis. The origin of this degeneracy has not been clarified yet. More recently [14], second-order Raman spectra of single crystalline h-BN revealed two features that contested the predictions based on a simple doubling of the energy scale of ab initio calculations for the one-phonon density of states, suggesting deviations up to 40% for the calculated energy of the TA branch in the K-M region. Since h-BN is a relevant material for UV lasing, it is imperative to resolve the existing controversies and critically assess the quality of the ab initio calculations. Furthermore, we need exact information on the lattice dynamics in order to properly understand the contributions due to electron-phonon coupling observed in the cathodoluminescence and absorption spectra of h-BN [7] and BN nanotubes [15,16].In this Letter we address the above discrepancies in the vibrational properties by reporting inelastic x-ray scattering (IXS) measurements...

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

“…[4,6], the five phonon replicas at 5.76, 5.79, 5.86, 5.89, and 5.93 eV had been labeled LO, TO, LA, TA, and ZA, respectively, following the study of the vibrational properties in hBN reported in Ref. [7]. The more detailed study of the hBN phonon dispersion performed in Ref.…”

Interlayer electron–phonon coupling in WSe2/hBN heterostructures

“…The Raman-allowed hBN phonon mode is the E 2g mode at 1,367 cm −1 (refs 26,27 Fig. 2b) is not Raman active, and thus is completely absent in the Raman measurement of pristine hBN 27 . The red curve in Fig.…”

Nature of exciton transitions in hexagonal boron nitride

“…Very large electron-phonon interaction in h-BN has been previously inferred. [25][26][27][28] Other than the strong exciton-phonon interaction, the excitation photon energies used for the PL measurements in our case here ($6.28 emission intensities of the phonon-assisted lines due to the resonant Raman scattering process.…”

“…Values of 6.5 meV and 6.4 meV for the E 2g mode phonon energy of low frequency have been previously deduced, respectively, from a theoretical calculation and Raman scattering experiment. 25,30 This phonon, related to the two BN planes slide against each other, has been termed as a "rigidlayer shear mode." 30 From the relative emission intensities, the 5.763 eV (S4t) and 5.791 eV (S3t) emission lines are, respectively, one phonon replicas (emitting one E 2g phonon of 8 meV) of the 5.771 eV (S4) and 5.799 eV (S3) emission lines.…”

“…Based on previous experimental and theoretical studies, 25,26 we attribute the energy level of 98 meV to the A 2u phonon mode, an out-of-plane vibration at the center of the Brillouin zone (BZ) of h-BN. This means that the emission lines at 5.799 eV (S3)/5.771 eV (S4) are related to the 5.897 eV(S1)/5.869 eV (S2) emission lines through one A 2u phonon of about 98 meV.…”