  We calculate the electron-phonon interaction coefficients for surface
acoustic waves and for phonons in free standing quantum wells. These are used
to derive the inelastic current through a double quantum dot caused by
spontaneous emission of phonons. For the case of the free standing structure
(phonon cavity), we predict a staircase-like inelastic current superimposed by
van Hove singularities. Therefore, the phonon confinement can be detected by
electron transport measurements.
