Decay of coupled plasmon-phonon modes in heavily doped semiconductors

For comparison with results obtained in recent phonon pulse experiments, we have calculated the relative magnitudes of different decay mechanisms for coupled plasmon-phonon modes in heavily doped GaAs. We find the dominant mechanism for energy loss by the coupled modes to be the direct excitation of bare phonons through second-order dipole moment and third-order anharmonic interactions, resulting in a lifetime of less than 1 ps for the particular material used in the experiments. Other mechanisms, notably lattice viscosity, electron-hole pair creation, rigorously forbidden at absolute zero, and the excitation of two electron-hole pairs, a higher-order effect but allowed at zero temperature, all give significantly smaller contributions to the decay rate. However, collision damping of the electrons through impurity scattering gives a lifetime which is much shorter than the above value, around 0.1 ps, but we note that this is an elastic scattering time, in contrast with the inelastic energy loss process. Linewidths in Raman scattering experiments yield the total scattering rate, which is dominated by the elastic process; currently only the phonon pulse measurements can give information directly on the inelastic process.