Coupled plasmon–LO-phonon modes in Ga1−xMnxAs

The vibrational and electronic properties of ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ layers with Mn fractions $0<~x<~2.8%,$ grown on GaAs(001) substrates by low-temperature molecular-beam epitaxy, are investigated by micro-Raman spectroscopy and far-infrared (FIR) reflectance spectroscopy. The Raman and FIR spectra are strongly affected by the formation of a coupled mode of the longitudinal optical phonon and the hole plasmon. The spectral line shapes are modeled using a dielectric function where intraband and interband transitions of free holes are included. In addition to the coupled mode, the contributions of a surface depletion layer as well as a symmetry forbidden TO phonon have to be taken into account for the Raman spectra. Values for the hole densities are estimated from a full line-shape analysis of the measured spectra. Annealing at temperatures between 250 and $500\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ results in a decrease of the hole density with increasing annealing temperature and total annealing time. Simultaneously, a reduction of the fraction of Mn atoms on Ga lattice sites is deduced from high-resolution x-ray diffraction.