The Influence Of The Electrical Boundary Conditions On Domain Structures And Properties Of Epitaxial Ferroelectric Thin Films

Based on time-dependent Ginzburg-Landau method,we simulate domain switching of two-dimensional PbTiO3(PTO)ferroelectric thin films under four different surface interdigital electrodes distributions.Also we discuss the constraint on the domain switching of epitaxial ferroelectric thin films with the substrate.And the four different electrodes distributions are(a)both surfaces are symmetrically arranged interdigital electrodes,(b)top surface is covered with interdigital electrode while bottom surface is covered with full electrode,(c)alternative interdigital electrodes distribute on both surfaces and(d)top surface is covered with interdigital electrodes while bottom is not covered with electrode.These electrode distributions could be converted to corresponding electrical boundary conditions of the phase field equations.The simulation results show that there are some special domain structures(vortices,a/c domains,flux-closure structures and close domain structures)due to the change of depolarization electric energy with different surface electrodes.The present results also show that the domain structures in ferroelectric thin films have an obvious size effect with the surface interdigital electrodes.For thin films with the same thickness,the domains tend to form vertical structures near the electrode surface,and form horizontal structures near the no-electrode surface.Namely,there would exist 90° domain walls near the open-circuit electrical zone and form vortices domain;there would be 180° domain walls near the short-circuit electrical zone and form c domain.It would be thought that the expected domain structures(vortices,a/c domains,flux-closure domains,and close domain structures)could be obtained by controlling the surface electrode distributions to obtain ideal ferroelectric propertities in the ferroelectric thin films.Furthermore we use the relatively simple stress function method to calculate the eigenstresses of epitaxial ferroelectric thin films,which is induced by the substrate as domain switching.Based on the phase field method,the domain structures and average polarization of epitaxial ferroelectric thin films under different electrical conditions(short and open circuit electrical conditions)are analyzed.The present results under short electrical boundary show that the critical turning thickness,at which a domain changes to a/c/a domain in PbTiO3 epitaxial ferroelectric thin films,is very close to the result of using the finite element method under the same electrical condition.The numerical results under the open electrical boundary show that the critical thickness of a domain changing to a/c/a domain is much larger than critical thickness under the short electrical boundary.The substrate,which affects the eigenstresses in thin films,leads to two layers of a domain and a/c/a domain in thin films.With the increase of thickness,the polarization increases.When domain structures switch from a domain to a/c/a domain,the average polarization has an obvious increase.