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Ferroelectric Domains in Thin Films and Superlattices: Results of Numerical Modeling

In micro- and nanoscale ferroelectric samples, a formation 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 samples different from the bulk samples. We present the results of modelling 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. For numerical solution of the problem, we use the finite-element PDE tool-box that allows to work over the entire temperature interval and in a wide region of sample parameters.