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A Ginzburg-Landau model is used to demonstrate how depletion layers give riseto thickness-dependent ferroelectric properties in thin films. It is shown thatfree charge layers at the film-electrode interface can result in an internalelectric field in the bulk of the film even when no external voltage isapplied. At high values of the donor dopant density and small thicknesses, thisinternal electric field can be strong enough to lead to the formation of adomain pattern. This causes a drop in the remnant polarization; a directdemonstration of the important role free charge plays in thin ferroelectricfilms.

Depletion layer-induced size effects in ferroelectric thin films: A Ginzburg-Landau model study