Switching Kinetics at the Nanoscale

Abstract

From the time of domain discovery, the switching kinetics of ferroelectric crystals and thin films has been explained by the domain nucleation and domain dynamics. The domain theory of Kolmogorov-Avrami-Ishibashi (KAI) [1][2][3][4][5][6] successfully explained the switching kinetics of ferroelectric crystals and even thin films with thickness l C 50 nm.A ferroelectric crystal maintains a permanent electric polarization that can be repeatedly switched between two stable states by an external electric field, thus exhibiting a polarization-electric field hysteresis loop ( Fig. 1.3). The hysteresis loops are characterized by the magnitude of the remanent polarization achieved after saturation with a large electric field and by the magnitude of the coercive field, the minimum value of the electric field necessary to reverse, or switch, the polarization state. This coercive field Ec, obtained from LGD mean field theory (Eqs. 4.3, 4.4), is called the intrinsic coercive field, because the switching is homogeneous. From the all previous studies of the kinetics of switching in ferroelectric crystals, it has been apparent that switching is almost invariably an extrinsic process involving the inhomogeneous nucleation of small domains of reversed polarization, usually initiated at crystal boundaries or defects, and subsequent growth of these domains to fill the crystal [7]. Nucleation-limited extrinsic switching is characterized by an exponential increase in the switching rate with increased temperature and electric field, characteristic of an activated process, and is usually achieved with external fields in the range 0.1-50 MV/m. Strictly speaking, extrinsic switching does not have a true threshold coercive field because the activation of nucleation permits switching at arbitrarily small fields, given enough time, but switching experiments are typically carried out with an ac field and so the apparent coercive field is actually a function of frequency. Accordingly this coercive field is called extrinsic.In the absence of nucleation, switching an ideal ferroelectric crystal with uniform polarization requires the application of an enormous coercive field. We call this the intrinsic switching mechanism, and the associated threshold field the intrinsic coercive field [8,9]. The expected value of the intrinsic coercive field is of order 100 MV/m in most ferroelectrics [9]. Intrinsic switching does not occur below the intrinsic coercive field because the constituent crystal dipoles are highly V. Fridkin and S. Ducharme, Ferroelectricity at the Nanoscale, NanoScience and Technology,