  The depolarization fields set up to due to uncompensated surface charges in a
ferroelectric thin film can suppress the ferroelectric phase below a critical
size. Recent experiments show that 180 degree domain structures can help to
stabilize ferroelectricity in films as thin as 3 unit cells. We study the
influence of domain structures on the size-dependent properties of
ferroelectric thin films using time-dependent Ginzburg-Landau theory. The model
incorporates the effect of depolarization field by considering
non-ferroelectric passive layers at the top and bottom surfaces. We show that
the 180 degree domain size decreases as the film thickness is reduced and the
film abruptly becomes paraelectric below a critical size. The 180 degree
domains appear during polarization switching causing a time-dependent
relaxation of the remnant polarization, consistent with recent experiments. The
depolarization-induced domain wall motion significantly alters the shape of the
polarization versus electric field (P-E) loops at small thicknesses.
