Nonparabolicity of the conduction band and the coupled plasmon-phonon modes inn-GaAs

We present the results of a detailed investigation of the infrared reflectivity spectra of $n$-GaAs as a function of doping such that the free-carrier plasma frequency is swept into and away from resonance with the LO-phonon frequency. The variation of the electron effective mass as a function of Fermi energy due to the nonparabolicity of the conduction band is accurately determined. Fits to the experimental data using $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ theory yield the value for the effective mass at the bottom of the conduction band, $m_0^{*}=(0.0665\mathrm{}\pm 0.0010)m_e$. The coupled plasmon-phonon modes are evaluated from the zeros of the real part of the total dielectric function with the variation of the effective mass versus doping included. At low carrier concentrations our data are in good agreement with the Raman scattering data of Mooradian et al., but at high electron concentrations the contributions due to nonparabolicity of the conduction band are significant, as our data demonstrate.