Ferroelectric Thin Film Self-Polarization Induced by Mismatch Effect

Abstract

In present work we consider multi-axial ferroelectrics with the three components of polarization in phenomenological theory framework taking into account the mismatch effect between film and substrate allowing for misfit dislocations and depolarization field. With the help of the variational method we obtained the free energy in the algebraic form with the coefficients dependent on film thickness, mismatch strain, temperature and other parameters. New terms proportional to the misfit strain appeared in the free energy, including built-in electric field originated from piezoelectricity in the vicinity of the surface. As an example we calculated phase diagrams of PZT 50/50 films on different substrates.

Keywords:

• Surface tension
• thin film
• mismatch effect
• phase transition

PACS:

• 77.80.−e
• 77.55.+f
• 68.03.Cd
• 68.35.Gy