180° Ferroelectric Domains in Thin Films and Superlattices

In the micro- and nanoscale ferroelectric samples, fort-nation of periodic polarization domains is the efficient mechanism of reducing depolarization field that is produced by the surface bound charges. This makes the physics of these devices different from the bulk samples. We present the results of modeling of ferroelectric domains and domain textures in ferroelectric thin films and periodic paraelectric/ferroelectric superlattices, basing on the self-consistent solution of the coupled electrostatic and Ginzburg-Landau equations. We go beyond the traditionally used low-temperature Kittel approximation (in which the polarization is assumed to be temperature independent and constant across domains) and explore the temperature evolution of the domain-induced properties. We study in detail the evolution of polarization profile P(x, z) in the periodic domains structure as function of the temperature and of the film width and propose the simple interpolation formula that can recover all the regimes of the domain structure, from high temperatures and thin films to low temperatures and thick films.