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temperature and spontaneous polarization along with the increase in the coer-
cive field. Changes in properties occur when the film thickness approaches the
electrode depletion width or the grain size approaches the ferroelectric domain
size [ 84 ].
The extent to which ferroelectric materials can be implemented in future
generations of microelectronic structures is strictly dependent on the influence
of size on the material properties. Several studies have investigated the finite
size effects in ferroelectric materials focusing on a critical lateral size or film
thickness below which ferroelectricity disappears [ 85 ]. The critical thickness of a
ferroelectric thin film with perpendicular polarization comes close to about 1 nm
[ 86 ]. At this value, surface reconstructions need to be considered, because they
may ultimately prevent the emergence of ferroelectricity [ 87 , 88 ]. Regarding the
minimum lateral dimension of a ferroelectric domain, it is important to underline
that for atomic-scale ferroelectric islands the electric field is generally screened
by free external charges that obstruct the inter-domains dipolar interactions.
Recent advances [ 89 ], reveals that this is not an intrinsic behavior of ferroelectric
materials, but an effect of the mechanical and electrical boundary conditions
resulting from the synthesis methods used.
It seems clear that in many of the existing studies, size effects are controlled
by fabrication process rather than intrinsic limits on the stability of the ferroelec-
tric phase. Film thickness, grain size, and lateral size of the ferroelectric material
are parameters that can be tuned within a certain range by an appropriate choice
of processing condition [ 84 ]. Other quantities like the depletion region amplitude
at surfaces, electrode-ferroelectric material interfaces, and grain boundaries can
be manipulated operating on the chemical synthesis or annealing conditions. As
a result, over time, the minimum thickness at which size effects are observed
is continuously dropping. The tremendous number of contributions describing
the size effects in ferroelectric thin films introduce high scatter in the reported
thickness dependence of the high field properties. In particular scaling down
PZT-film thickness while retaining good ferroelectricity has been a topic of great
interest scientifically and this dimension has dramatically decreased during the
past decade [ 90 ].
The achievement of size-independent coercive fields in PZT films down to
60 nm in thickness was reported by Bilodeau et al. [ 91 ]. The switchable polar-
ization dropped somewhat for films below 100 nm in thickness. Below 60 nm
the films were poor electrical insulators. Kim et al. [ 92 ] and Oikawa et al. [ 90 ]
reported the preparation of 70 and 35 nm thick PZT with good ferroelectric
properties. Using mean field theory, Li et al. [ 93 ] were able to calculate the crit-
ical thickness at which perovskite ferroelectric thin films showed a stable polar
phase and applied this theory to PbTiO3 thin films. Song and No [ 94 ] imple-
mented the same approach to PZT thin films, finding that the critical thickness
was approximately 18 nm.
There are also reports that ferroelectricity is stable in films down to much
smaller thicknesses. Tybell et al. [ 95 ] showed that ferroelectricity can be observed
in PZT films as thin as 4 nm [ 96 ] and this statement was confirmed through
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