  For forty years researchers on ferroelectric switching have used the Kay-Dunn
theory to model the thickness-dependence of the coercive field; it works
surprisingly well, despite the fact that it is based upon homogeneous
nucleation and a small-field expansion, neither of which is realized in thin
films. Here we demonstrate that this result can be obtained from a more general
Kolmogorov-Avrami model of (inhomogeneous) nucleation and growth. By including
a correction to the switching field across the dielectric that includes
Thomas-Fermi screening in the metal electrode, we show that our theory
quantitatively describes the coercive fields versus thickness in several
different families of ferroelectric (lead zirconate-titanate [PZT], potassium
nitrate, and polyvinylidenefluoride [PVDF]) over a wide range of thickness (5
decades). This agreement is particularly satisfying in the case of PVDF, as it
indicates that the switching kinetics are domain-wall limited down to 1
nanometer and thus require no new effects.
