The wide-band-gap semiconductor GaN is currently of great interest for optoelectronic applications at blue and near-ultraviolet wavelengths, as well as in high-temperature and high-frequency electronics. Since the behaviour of carriers in devices is affected by their interaction with phonons, the lattice-dynamical properties of GaN, i.e., its phonon dispersion and the phonon eigenvectors, are very important and have been studied intensively, mainly by Raman scattering and by theory. Both phenomenological and ab initio approaches have been published. Unfortunately, tests of these theories have been limited to the comparison with Raman data and are thus incomplete even for the mode frequencies at the Brillouin zone centre.

The main reason for the lack of phonon dispersion information in GaN is that single crystals large enough for inelastic neutron scattering do not exist. However, this limitation can now be overcome with inelastic X-ray scattering (IXS) [1,2]. With the availability of dedicated beamlines at third-generation synchrotrons, IXS has developed into a powerful alternative for studying dispersion effects of elementary excitations in solids. As demonstrated here, IXS can even be applied to materials which contain strongly absorbing elements, such as gallium. With X-ray spot sizes in the submillimetre range, IXS is ideal to investigate very small samples. In the specific case of GaN, moreover, even small crystals often do not have sufficient structural quality. We have overcome this obstacle by using small-bulk single crystals obtained from a unique high-pressure growth technique. The widths of rocking scans across Bragg reflections in these crystals were around 0.007 degrees, indicating excellent crystal quality. 

Figure 63
Fig. 63: Phonon dispersion of wurtzite GaN (filled circles: IXS data; solid lines: ab initio lattice-dynamical calculation. The theoretical results have been scaled by a factor of 0.97 in order to obtain optimum agreement with the experiment. The open diamonds at q = 0 are from Raman scattering in the visible.

The data were taken at the ESRF beamline ID28 using excitation energies of 17.79 keV and 15.82 keV with an instrumental resolution of 3.0 meV and 5.5 meV (FWHM), respectively. In a wurtzite-structure GaN single crystal (2 x 3 x 0.2 mm3), we have measured the complete phonon dispersion of the longitudinal optic and acoustic modes along the hexagonal -A direction and several transverse branches along -K-M and -M (Figure 63). As an example, we have determined the energies of the two silent B1 modes, which are neither Raman nor infrared active (zone center frequencies: 40.7 and 85.5 meV). Our data provide important input for fits and tests of lattice-dynamical models. The experiments were guided by calculated scattering intensities and frequencies from our ab initio calculations, and the results agree very well with these predictions. However, we find significant deviations from the predictions of another ab initio theory and phenomenological models. In Figure 64 we show IXS spectra of the backfolded longitudinal-optic phonon branch along -A. The spectra between A1 () and A were measured with scattering vectors Q = G + q, where q = (0, 0, qz) and G = (0, 0, 4); those between A and B1 () were measured with G = (0, 0, 5), in agreement with the selection rules predicted by our ab initio calculations.

Figure 64
Fig. 64: IXS spectra of wurtzite GaN along -A. Values of q z (in units of G z = 2 /c) are given next to each spectrum.

As a conclusion, our data show that the high energy resolution of IXS opens new possibilities for investigations of phonon dispersion in cases where other techniques cannot be applied due to the strong neutron absorption cross section or the small size of the samples, as in the case of wurtzite-GaN reported here.

[1] E. Burkel et al., Europhysics Letters 3, 957 (1987); E. Burkel, Rep. Prog. Phys. 63, 171 (2000).
[2] F. Sette et al., Phys. Rev. Lett. 75, 850 (1995).

Principal Publication and Authors
T. Ruf (a), J. Serrano (a), M. Cardona (a), P. Pavone (b), M. Pabst (b), M. Krisch (c), M. D'Astuto (c), T. Suski (d), I. Grzegory (d) and M. Lesczynski (d), Phys. Rev. Lett. 86, 906 (2001).
(a) Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany)
(b) Universität Regensburg (Germany)
(c) ESRF
(d) Polish Academy of Sciences, Warsaw (Poland)