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=2kF where q is the phonon wavenumber and kF the Fermi wavenumber. Comparison with other expressions is also given.
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