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Electron-confined-phonon interaction in quantum wells: Reformulation of the slab model.

We show that the Fuchs-Kliewer slab model, as used for the description of the electron-phonon Fr\"ohlich interaction in quantum wells and superlattices, can be reformulated in a simple way and it becomes very close to the Huang and Zhu model, based on a lattice-dynamic approach. This simple reformulation answers several questions which have been made over the past few years about the dielectric continuum model, especially those about the existence of a half-wavelength mode of the z component of the relative ionic displacement which has no counterpart in microscopic calculations. We show that in fact this mode does not exist in the reformulated slab model.