Continuous theory of ferroelectric states in ultrathin films with real electrodes

According to a continuous medium theory, in very thin ferroelectric films with real metallic electrodes (or dead layers near the electrodes) the domain structure reduces to sinusoidal distribution of ferroelectric polarization. Such a sinusoidal structure was considered in 1980s for para-ferroelectric phase transition in a capacitor with dead layers near electrode. We give a review of this theory and its further development for the case of real metallic electrodes. The goal of the general theory is to consistently interpret the experimental data in very thin films with real metallic electrodes. This is illustrated on a recent experimental data for 5-30 nm BaTiO3 films with SrRuO3/SrTiO3 electrodes. The screening length by real metallic electrodes is very small small (<1A), but it has a profound effect on ferroelectric properties and its phase behavior. This general theory also allows to formulate the important open problems and show paths towards their solution. In particular, this is a problem of finding parameters of the system, which can sustain the ferroelectric memory over a desired lifetime.