Interaction of longitudinal-optic phonons with free holes as evidenced in Raman spectra from Be-dopedp-type GaAs

The interaction between small-wave-vector, longitudinal-optic (LO) lattice vibrations and free-hole plasmas in Be-doped p-type GaAs is studied with use of nonresonant, allowed Raman scattering. In contrast to the coupled LO-phonon–plasmon modes, ${\mathrm{\omega }}_{+}$ and ${\mathrm{\omega }}_{\mathrm{-}}$ typically observed in n-type zinc-blende-structure semiconductors, only one mode is observed for hole densities between 1×${10}^{18}$ and 1.6×${10}^{19}$ ${\mathrm{cm}}^{\mathrm{-}3}$. With increasing hole density, this single mode shifts first to higher energies, then back to lower energies, between that of the LO and transverse-optic (TO) phonons, and finally asymptotes at the TO-phonon energy. The observed Raman spectra are accurately fitted with calculated coupled-mode spectra which take into account wave-vector-dependent intra- and inter-valence-band transitions within the heavy- and light-hole bands. Intra-light-hole and inter-heavy- to light-hole transitions are shown to make very significant contributions to the spectra, although they alone cannot account for the novel density dependence of the coupled-mode energy. A detailed analysis of the coupled-mode dependence on wave vector and phenomenological damping reveals that the observed density dependence can, in principle, occur even in a single-component plasma due to two distinctly different physical mechanisms. In the case of the p-type GaAs studied here, it is shown that the novel density dependence is primarily due to the overdamped nature of intra-heavy-hole transitions.