On the Polarization of M/FE/M structures

The polarization states of a semiconducting ferroelectric film have been analyzed in terms of the Landau-Ginsburg-Devonshire thermodynamic model supplemented with a drift-diffusion equation for electrons. For definiteness, an undoped epitaxial PZT film containing charged oxygen vacancies and electrons is considered. The polar axis is perpendicular to the film plane. It is shown that, for the same parameters and boundary conditions at the contacts, the film can be in one of four basic states: two classical states with positive or negative polarization and two tail-to-tail (TT) and head-to-head (HH) domain states. The condition for the existence of TT and HH domains in a film with finite thickness is obtained. It is shown that the TT and HH domains originate from the unstable part of the theoretical Landau S-curve P(E). The total free energies of different states of the film are compared and the hysteresis loops and the transformation of the HH and TT domains to the classical polarization state under a rectangular voltage pulse are discussed.