  We study the dielectric response of ferroelectric (FE) thin films with "dead"
dielectric layer at the interface with electrodes. The domain structure
inevitably forms in the FE film in presence of the dead layer. As a result, the
effective dielectric constant of the capacitor $\epsilon_{eff}$ increases
abruptly when the dead layer is thin and, consequently, the pattern of
180-degree domains becomes "soft". We compare the exact results for this
problem with the description in terms of a popular "capacitor" model, which is
shown to give qualitatively incorrect results. We relate the present results to
fatigue observed in thin ferroelectric films.
