Resonant Raman scattering in cubic and hexagonal boron nitride

S. Reich, A. C. Ferrari, R. Arenal, A. Loiseau, I. Bello, and J. Robertson

Phys. Rev. B 71, 205201 – Published 4 May 2005

Abstract

We measured first- and second-order Raman scattering in cubic and hexagonal boron nitride using excitation energies in the visible and in the UV. The nonresonant first-order Raman susceptibilities for cubic and hexagonal BN are 1 and $10 Å^{2}$ , respectively. Raman scattering is thus very powerful in detecting the hexagonal phase in mixed thin boron nitride films. In cubic BN the constant Raman sucseptibility in the visible and the UV is due to its indirect band gap. For hexagonal BN a Raman enhancement is found at $5.4 eV$ . It is well explained by the energy dependence of the dielectric function of hexagonal BN. The second-order spectrum of cubic boron nitride is in excellent agreement with first-principles calculations of the phonon density of states. In hexagonal BN the overbending of the LO phonon is $\approx 100 {cm}^{- 1}$ , five times larger than in graphite.

Received 25 August 2004

DOI:https://doi.org/10.1103/PhysRevB.71.205201

Authors & Affiliations

S. Reich and A. C. Ferrari

University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom

R. Arenal and A. Loiseau

LEM, ONERA-CNRS, BP72, 92322 Châtillon Cedex, France

I. Bello

Department of Physics and Materials Science, City University of Hong Kong, Hong Kong, China

J. Robertson

University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, United Kingdom

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Vol. 71, Iss. 20 — 15 May 2005

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Images

Figure 1
First-order Raman spectra of (a) cubic and (b) hexagonal boron nitride excited with $λ_{exc} = 244 nm$ . The inset shows the crystal structure of the two BN structures. Note the $A A^{'} A A^{'}$ stacking in the hexagonal type.Reuse & Permissions
Figure 2
(Color online) Theoretical dependence of the Raman cross section in hexagonal BN on laser energy together with the three measured points. ${∣ χ^{'} ∣}^{2} = {∣ d χ ∕ d ω ∣}^{2}$ (full black line) was separated into its real ${∣ χ_{1}^{'} ∣}^{2}$ (red, dashed) and imaginary ${∣ χ_{2}^{'} ∣}^{2}$ (blue, dotted) part. The theoretical and experimental data were multiplied by constant factors to match at $2.41 eV$ . The derivatives were calculated from the dielectric function of hexagonal BN measured by Hoffman et al. (Ref. 53).Reuse & Permissions
Figure 3
Full line: Second-order Raman spectrum of cubic boron nitride excited with $229 nm$ . The gray-shaded areas correspond to the $O_{2}$ $(1556 {cm}^{- 1})$ and $N_{2}$ $(2332 {cm}^{- 1})$ air-related lines and background from the setup. Broken line: Ab initio calculation of the phonon density of states by Karch and Bechstedt (Ref. 59); the frequencies were multiplied by two. Peaks and shoulders in the spectrum were assigned to high-symmetry points and lines in the boron nitride Brillouin zone, see also Table . All structures are well explained as overtones of the phonon density of states. Compared to Fig. 1a the $y$ scale is expanded by a factor of 20.Reuse & Permissions
Figure 4
Second-order Raman scattering in hexagonal boron nitride. The full line is the experimental spectrum. The broken line is the phonon density of states after Kern et al. (Ref. 28); the frequencies were multiplied by 2. For the most prominent features in the second-order spectrum the assignment is indicated, see Table for the measured frequencies and Fig. 5 for the labeling of the branches. Compared to Fig. 1b the $y$ scale is expanded by a factor of 300.Reuse & Permissions
Figure 5
Phonon dispersion of hexagonal boron nitride calculated by Kern et al. (Ref. 28). The phonon branches at the high-symmetry points and lines in the Brillouin zone were assigned to the irreducible representations of the BN group. The numbers correspond to the subscript of the irreducible representation and the +/− sign to the superscript. For example, the two lowest branches at the $M$ point labeled $2^{-}$ and $3^{+}$ belong to the $M_{2}^{-}$ and $M_{3}^{+}$ representation. The degeneracy of these two phonons is accidental. At the high-symmetry points all phonon overtones and the following combinations give rise to in-plane polarized second-order Raman scattering $Γ_{1}^{\pm} \otimes Γ_{5}^{\pm}$ , $Γ_{2}^{\pm} \otimes Γ_{6}^{\pm}$ , $M_{3}^{\pm} \otimes M_{4}^{\pm}$ , $M_{1}^{\pm} \otimes M_{2}^{\pm}$ , $K_{1, 2} \otimes K_{5}$ , and $K_{3, 4} \otimes K_{6}$ .Reuse & Permissions

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