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The finite screening length by real metallic electrodes, albeit very small(<1A), results in finite depolarizing field that tends to split the film intodomains. In very thin ferroelectric films the domain structure reduces tosinusoidal distribution of polarization considered first in the 1980s. Wediscuss the phase transition between this structure and a single domain stateand show that it is first order, if it exists at all. The alternativepossibility is that the single domain state at zero bias voltage would bemetastable for all temperatures in most systems. This scenario defines a pathtowards solution to a problem of finding parameters of a system that cansustain the ferroelectric memory over a desired period of time.

Path to finding the critical thickness for memory in thin ferroelectric films