Scaling of the coercive field with thickness in thin-film ferroelectrics

Motivated by the observed thickness-scaling of the coercive field in ferroelectric films over five decades, we develop a statistical approach towards understanding the conceptual underpinnings of this behavior. Here the scaling exponent is determined by the field-dependence of a known and measured quantity, the nucleation rate per unit area. We end with a discussion of our initial assumptions and point to instances where they could no longer be applicable.