Acoustic properties of heavily doped many-valley semiconductors in the weak-localization regime

We have derived expressions for the ultrasonic attenuation coefficient and the sound-velocity change v of heavily doped many-valley semiconductors at low frequencies in the weak-localization regime where any intervalley scattering strength has been taken into account. Quantum corrections due to the effect of localization give a negative contribution to and v and are insensitive to temperature provided that the intervalley scattering time is independent of temperature, while those due to the effect of mutual interaction give a positive contribution to and v and decrease with increasing temperature. The whole behavior of and v, the deviations from classical form for the attenuation coefficient and the sound-velocity change, are determined by the competition between the effects of localization and the effects of mutual interaction mentioned above. The magnitude of and v increase with decreasing intervalley scattering strength. For comparison, expressions for and v in heavily doped single-valley semiconductors have also been derived. The sign of the quantum corrections to and v is the same as that to the electrical conductivity in the many-valley case but opposite in the single-valley case.