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Raman scattering study of background electron density in InN: a hydrodynamical approach to the LO-phonon–plasmon coupled modes

We use a hydrodynamical approach to analyse the long-wavelength LO-phonon–plasmon coupled modes observed in a set of high-quality MBE-grown InN epilayers with electron densities varying over one order of magnitude, from ∼2 × 1018 to ∼2 × 1019 cm−3. The samples were characterized by scanning electron microscopy, x-ray diffraction and Hall measurements. The correlation observed between the E2high mode frequency, and hence residual strain, and the electron density measured in the layers indicates that the differences in background electron density may be associated with threading dislocations. Owing to the low Raman signal, only the L− branch of the coupled modes can be unambiguously observed. The frequency of the L− Raman peak is, however, sensitive enough to the free electron density to allow its determination from lineshape fits to the spectra. These were carried out using an extended hydrodynamical model. Given the small bandgap energy and large conduction band nonparabolicity of InN, suitable expressions for the optical effective mass and mean square velocity that enter the hydrodynamical model were derived. Electron density values extracted from L− lineshape fits agree reasonably well with Hall determinations.