Decay of ferroelectric domains formed in the field of an atomic force microscope

Abstract

Ferroelectric domains formed in the electric field of an atomic force microscope decay with time when the reversal voltage is removed. We propose a theory for this process. Dynamic equations describing the time evolution of the domain sizes are constructed and solved. It is shown that the larger the domains, the more stable they are. The time dependences of the domain length and base radius are qualitatively different. The radius of the domain decreases during the decay process, and for a large domain there is a plateau in its time dependence. In contrast to this, the length of the domain first does not decrease but rather grows significantly and then rapidly drops. We introduce the concept of critical radius for the domain stability. Only domains with a radius exceeding the critical radius have a long lifetime, which increases exponentially with the initial domain radius. The calculated value of the critical radius of stability in barium titanate is in reasonable agreement with the experiment. Possible means to stabilize the domains are proposed.

Direct observation of pinning centers in ferroelectrics

“…According to a recently published theory, ferroelectric domains may be stable for several years even in defect-free barium titanate crystal, if their radius exceeds the critical value of around ϳ1 m. 20 It was also found that string-like domains tailored in RbTiOPO 4 and LiNbO 3 crystals using the HVAFM were stable for at least several months. 16,17 However, the domain decay process may be accelerated by increasing the probability for domain walls depinning, done, for example, by heating the sample.…”

Landau-Ginzburg-Devonshire theory for electromechanical hysteresis loop formation in piezoresponse force microscopy of thin films

“…The thermodynamics of domain formation in the tip field has been extensively studies for uniaxial [31,32,33,34,35,36,37,38] and multiaxial [39] ferroelectrics in the rigid ferroelectric approximation. The kinetics of this process was studied by Molotskii et al [40,41]. Recently, a number of studies of thermodynamics of domain formation in the phase-field approximation were reported [17,30,42,43,44].…”

Web-like domain structure formation in barium titanate single crystals

“…These results are in good agreement with the calculated critical radius for domain stability in BTO of 74-100 nm. 22 Note that the formation of domains by ferroelectric domain breakdown is not favorable in BTO crystals due to the high dielectric constant of BTO. 22 Domains fabricated in this study with Ϫ10 and Ϫ20 V pulses decayed rapidly from initial radii of ϳ250 nm and 500 nm, respectively, and while larger domains were more stable, they became smaller after scanning with ac bias overnight.…”

“…22 Note that the formation of domains by ferroelectric domain breakdown is not favorable in BTO crystals due to the high dielectric constant of BTO. 22 Domains fabricated in this study with Ϫ10 and Ϫ20 V pulses decayed rapidly from initial radii of ϳ250 nm and 500 nm, respectively, and while larger domains were more stable, they became smaller after scanning with ac bias overnight. That these domains decayed despite surpassing the critical radius range suggests an incomplete polarization screening of the switched domains on their polar surfaces ͑assuming that the domains extend through the whole sample thickness͒.…”

“…Note that imaging on the subsequent day revealed that the domains had decreased in size, and that the domains formed with pulse magnitudes of Ϫ10 and Ϫ20 V had disappeared. The effects of the domain aspect ratio, 19,20 critical domain radii, 21,22 the ratio between the electrode size and the film thickness, 23 and thermal treatments 24 on domain stability have been the subject of numerous studies. In general, stable domains are ones that exceed a certain critical radius and extend through the thickness of the epitaxial film or crystal, although subsurface layers, defects, and charge injection can play a role in domain stabilization.…”