Size effects of static and dynamic polarization in ferroelectric thin film multilayers

Abstract

A thermodynamic theory for the calculation of static and dynamic polarization profiles of ferroelectric thin film multilayers is developed. The free energy functional is written down using a multilayer model in which c-domain layers of the ferroelectric material alternate with a-domain layers of a second ferroelectric materials. We assume that the interfaces are perfectly sharp and that the polarization at these boundaries is zero. The equilibrium polarization profile, its temperature and thickness dependencies were determined from the solutions of the Euler-Lagrange equations. A thickness induced ferroelectric phase transition is shown to exist and its transition temperature and critical layer thickness depend on the domains orientation. The equation determining the time and space dependence of the polarization is proposed and solved. The calculated dispersion law for the nonlinear polarization waves in multilayer structures reveals a critical wave vector or a critical layer thickness, for which the frequency ω = 0, i.e. polarization waves frozen. The calculated polarization profile fits well with measured optic refraction index profile.