Surface Tension and Mismatch Effects in Ferroelectric Thin Film Properties

Abstract

The ferroelectric thin film properties were calculated in phenomenological theory framework. Surface energy that defined boundary conditions for Euler-Lagrange differential equation was written as surface tension energy. The latter was expressed via surface polarization and tension tensor related to mismatch of a substrate and a film lattice constants and thermal expansion coefficients.The additional dependence on the distance from the surfaces of a film appears in the Euler-Lagrange equation coefficients for the most common case of the different conditions on the boundaries film–substrate and film–air. The mismatch effect was shown to shift the critical parameters of the thickness induced phase transition ferroelectric–paraelectric phase, the value and sign being different for the phase transitions of the I-st and II-nd order. The improved by mismatch effects phase diagram and the dielectric permittivity profiles and average values are calculated.The possibility to observe a thickness induced ferroelectric–paraelectric phase transition due mainly to inhomogeneity induced by different mismatch effect on the film two surface is discussed.