Influence of Built-In Internal Electric Field on Ferroelectric Film Properties and Phase Diagram

Abstract

The influence of film-substrate mismatch effect, surface piezoelectric effect caused by broken symmetry on the film surface, surface tension and depolarization field on the ferroelectric film properties was considered in the phenomenological Ginzburg-Landau theory framework. The Euler-Lagrange equations for three polarization components were solved with the help of variational method proposed by us earlier. This approach leads to the free energy in the form of algebraic expression for different powers of polarization components with the coefficients dependent on film thickness, misfit strain, temperature etc. The odd powers of polarization related to built-in electric field normal to the surface originated from misfit strain and piezoelectricity in vicinity of surface appeared in the free energy expansion. The obtained free energy opens the way for the calculation of the ferroelectric film properties by conventional procedure of minimization. The calculations had shown that the built-in field drastically influences all the properties. In particular the smearing of polarization and dielectric permittivity, shift of its maximum temperature, the asymmetry of hysteresis loop were obtained. The latter speaks in favour of statement that the films self-polarization phenomenon originated from built-in field. The calculation of phase diagrams of PZT 50/50 compressive- or tensile-strained films was performed. The temperature behaviour of pyroelectric coefficient and dielectric permittivity lead to the forecast of the electret-like polar state, i.e. existence of pyroelectricity below the critical thickness of ferroelectric-paraelectric phase transitions. The possibility of ferroelectric phase conservation up to monolayer film on substrate for compressive strain was demonstrated.