Phonon attenuation in heavily doped many-valley semiconductors

An expression for the phonon relaxation rate due to the electron-phonon interaction has been derived for heavily doped many-valley semiconductors by solving the equation of motion for the single-particle density matrix within the relaxation time approximation. Detailed calculations have been performed for longitudinal phonons in n-type Ge at 0K. It is shown that acoustic waves which remove the degeneracy of the conduction-band valleys are strongly attenuated for q<or approximately=2k_F where q is the phonon wavenumber and k_F the Fermi wavenumber. Comparison with other expressions is also given.