An expression for the phonon relaxation rate in heavily doped p-type semiconductors with the diamond and the zincblende structures has been derived by extending the formulation obtained previously for heavily doped n-type many-valley semiconductors, where the authors have taken account of the interband hole-phonon interactions, the intraband one and both the deformation potential and the piezoelectric coupling. Explicit expressions for the phonon relaxation rate have been given using an approximation suitable to the small-wavenumber region. Numerical calculations have been performed for a model semiconductor at T=0K. The wavenumber dependence of the phonon relaxation rate is qualitatively different from that obtained previously within a single-band approximation. The shear components of the hole-phonon interaction play an important role in the small-wavenumber region. A contribution of the interband hole-phonon interaction, which can become large for transverse modes, occurs only in a certain wavenumber region and its relative importance depends on the ratio of the light hole mass to the heavy hole one. The phonon relaxation rate via the piezoelectric coupling is smaller than that via the deformation potential one in heavily doped p-type III-V compound semiconductors.
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