Competitive interactions between the surface effect and the depolarization field effect on the critical size of ferroelectric perovskite ultrathin films

A competitive interaction exists between the surface effect and the depolarization field effect on the size effect of ferroelectric films, and there exists a crucial film thickness (hs), where the dominant influencing effect changes from the depolarization field effect at larger thickness to the surface effect at smaller thickness. We estimate hs to be ∼20–40 nm, varying with the residual strain, for PbTiO3 films by using a generalized Landau–Ginzburg–Devonshire thermodynamic theory. The calculations are in good agreement with measurements.