  We report piezo-response force microscopy studies of the static and dynamic
properties of domain walls (DWs) in 11 to 36 nm thick films of crystalline
ferroelectric poly(vinylidene-fluoride-trifluorethylene). The DW roughness
exponent {\zeta} ranges from 0.39 to 0.48 and the DW creep exponent {\mu}
varies from 0.20 to 0.28, revealing an unexpected effective dimensionality of
~1.5 that is independent of film thickness. Our results suggest predominantly
2D ferroelectricity in the layered polymer and we attribute the fractal
dimensionality to DW deroughening due to the correlations between the in-plane
and out-of-plane polarization, an effect that can be exploited to achieve high
lateral domain density for developing nanoscale ferroelectrics-based
applications.
