Stress Effect on Critical Thickness in Ferroelectric Thin Films
Taking into account surface and stress effects simultaneously we have extended a modified Landau-Devonshire theory to study how stresses between films and substrates affect the critical thickness in ferroelectric thin films. Film thickness-stress phase diagrams have been obtained. The diagrams can interpret why the reported critical thickness varies in a wide range, or even no critical thickness exists in some epitaxial thin films. Our results can also help understand that ferroelectricity can be sustained in a monolayer thin film. Calculation shows that the inverse ferroelectric critical thickness is dependent on stress and temperature linearly. We have got emperical equations to calculate critical thickness under various stresses and temperatures.