InN Thin Film Lattice Dynamics by Grazing Incidence Inelastic X-Ray Scattering

Achieving comprehensive information on thin film lattice dynamics so far has eluded well established spectroscopic techniques. We demonstrate here the novel application of grazing incidence inelastic x-ray scattering combined with ab initio calculations to determine the complete elastic stiffness tensor, the acoustic and low-energy optic phonon dispersion relations of thin wurtzite indium nitride films. Indium nitride is an especially relevant example, due to the technological interest for optoelectronic and solar cell applications in combination with other group III nitrides.

Figure 1

(a) SEM image of the wurtzite InN film. (b) Grazing incidence IXS geometry, where ${\alpha }_i$ and ${\alpha }_f$ are $1.7°$. The $2\theta$ angle determines the total momentum transfer selected by the spectrometer.

Figure 2

Selected IXS spectra for momentum transfer values along the $\Gamma \mathrm{\text{−}}M$ direction of the BZ. The symbols display the experimental data whereas the solid curves represent the best fit to the spectra. Dashed lines are used to indicate the contributions of different excitations and the zero-energy central elastic peak. The solid straight lines are guides to the eye to highlight the different phonon branch dispersions with increasing momentum transfer. The $\xi =0.05$ spectrum intensity has been multiplied by a factor 0.1 to better display the mode dispersion. Note the drastic decrease in TA intensity with increasing momentum transfer.

Figure 3

Acoustic and low-energy optic phonon dispersion relations of wurtzite InN along the main symmetry directions. Open and solid symbols display IXS data corresponding to longitudinal and transverse modes, respectively, except for the solid circles that display IXS data obtained using mixed transverse and longitudinal polarizations. The black (red) curves plot results obtained from LDA (GGA) ab initio calculations. Modes polarized along the $⟨001⟩$ direction of the BZ are represented by (red) squares and dashed lines, whereas in-plane polarized modes are represented by (blue) circles and solid lines. The green diamond at the $\Gamma$ point shows Raman data for the $E_2^{\mathrm{low}}$ mode from Ref 6. Momentum transfers are given in reciprocal lattice units.