Breakdown of Pippard ineffectiveness condition for phonon-electron scattering in micro and nanostructures

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Abstract
The Pippard ineffectiveness condition —that electrons strongly scattering from impurities and defects are ineffective in scattering phonons— is based on the assumption that electron scatterers vibrate in the same way as the host lattice. Then the relaxation rate of a low- energy phonon with the wave vector q is 1/τph-e ∼ u2q2l/vF (u and vF are the sound velocity and Fermi velocity, l is the electron mean free path). Boundaries and defects moving differently from host lattice drastically change the character of the interference between scattering processes and increase the phonon-electron coupling. In the presence of the quasistatic potential the phonon relaxation is (q2lL)−1 times faster: 1/τph-e ∼ u2/(vFL )( L is the electron mean free path with respect to scattering from the quasistatic potential). Analogous effect is expected for phonons with ω ∼ 0.01ωD (ωD is the Debye frequency) in conductors with substitutional disorder.