Reflection Studies of Coupled Magnetoplasma-Phonon Modes

Far-infrared reflectivity spectra of doped polar semiconductors such as InAs and GaSb exhibit dispersion anomalies which are associated with coupled optical-phonon and plasmon modes and are strongly influenced by magnetic fields. This work examines the behavior of the coupled magnetoplasma-optical-phonon modes as a function of magnetic field. The experimental reflectivity curves, obtained by Fourier transform spectroscopy, are analyzed by means of the Kramers-Kronig relations to obtain the complex dielectric function $\epsilon$. The frequencies and linewidths of the singularities and zeros of $\epsilon$ are obtained from the peaks in the curves of $\mathrm{Im}\left(\epsilon \right)$ and $\mathrm{Im}\left(\frac{1}{\epsilon }\right)$, respectively, and plotted as a function of magnetic field. Using classical equations of motion for lattice ions and conduction electrons, including phenomenological scattering frequencies for both the lattice and the electrons, expressions for the frequencies and effective linewidths of the modes are developed. Theoretical curves of frequency and linewidth versus magnetic field are computed and compared with experiment. Good agreement between theory and experiment is obtained.