Abrupt Appearance of the Domain Pattern and Fatigue of Thin Ferroelectric Films

Abstract

We study the domain structure in ferroelectric thin films with a 'passive' layer (material with damaged ferroelectric properties) at the interface between the film and electrodes within a continuous medium approximation. An abrupt transition from a monodomain to a polydomain state has been found with the increase of the 'passive' layer thickness d. The domain width changes very quickly at the transition (exponentially with d −2 ). We have estimated the dielectric response dP/dE (the slope of the hysteresis loop) in the 'fatigued' multidomain state and found that it is in agreement with experiment, assuming realistic parameters of the layer. We derive a simple universal relation for the dielectric response, which scales as 1/d, involving only the properties of the passive layer. This relation qualitatively reproduces the evolution of the hysteresis loop in fatigued samples and it could be tested with controlled experiments. It is expected that the coercive field should increase with decreasing lateral size of the film. We believe that specific properties of the domain structure under bias voltage in ferroelectrics with a passive layer can resolve the long-standing 'paradox of the coercive field 77.80.Dj, 84.32.Tt, 85.50.+k Recent studies of thin ferroelectric films have revived interest in properties of the ferroelectric domain structures. It became clear that some basic aspects of these properties remain unexplored, whereas they are of key importance for applications. For instance, the progressive loss of switchable polarization after repeated switching cycles, i.e. polarization fatigue, is a serious problem in device applications of ferroelectrics. In spite of extensive studies, the physics of the fatigue remains poorly understood. Various mechanisms were considered over the years [1][2][3][4][5][6][7][8]. In many cases the deterioration of the switching behavior, like the loss of the coercive force and of the squareness of hysteresis loop, were attributed to the growth of a 'passive layer' at the ferroelectric-electrode interface [1,3,6], or to the pinning of domain walls by defects [2,4]. In this paper, we study the effects of a passive layer (material with damaged ferroelectric properties). We assume an ideal infinite ferroelectric film and treat it within the continuous medium approximation. The model exhibits very interesting properties relevant for real systems.The passive layer leads to the appearance of a depolarizing field in the ferroelectric, so that the system would tend to transform to a polydomain state in order to reduce the field. There is, therefore, a transition between the monodomain state, when the thickness d of the passive layer is zero, to a polydomain state otherwise. What is the nature of this transition? This is the main theoretical question we address in this paper.For a short-circuited infinite ferroelectric plate, as we shall show, the domain structure exists for any value of the passive layer thickness, in disagreement with some earlier results [9]. A surprising feature of the ...

Thickness dependence of intrinsic dielectric response and apparent interfacial capacitance in ferroelectric thin films

“…We assume the film to be in the single-domain state, although the depolarizing field generally favors the formation of 180°domains. 33,34 This model enables us to determine the maximum effect of depolarizing field on the dielectric response of a ferroelectric film. Moreover, the application of an electric field stronger than the coercive field makes the film polarization state uniform on the macroscopic scale.…”

Very large dielectric response of thin ferroelectric films with the dead layers

“…Here C is the capacitance of the electroded FE film of area A, with L the separation between electrodes. Indeed, when the dead layer is thin, the domain width a becomes very large, it grows exponentially with 1/d 2 [1]. The response of this domain structure is very soft, and this should translate into very abrupt increase of the dielectric constant ǫ ef f of the capacitor.…”

“…It has direct bearing on fatigue observed in FE capacitors since in many cases the deterioration of the switching behavior, like the loss of the coercive force and of the squareness of hysteresis loop, were attributed to the growth of a "passive layer" at the ferroelectricelectrode interface [2][3][4][5]. It is of principal importance that the presence of a dead layer, no matter how thin in comparison with thickness of the ferroelectric layer, triggers a formation of the domain structure in FE film [1]. We have shown that when the thickness of the dead layer d is not very small, the apparent (net) polarization P a of the ferroelectric with 180−degree domain walls follows an approximate relation dP a /dE ∝ ǫ g /d, which is in good correspondence with available experimental data (see e.g.…”

“…We have shown recently that the dead layer forming at the interface between ferroelectric (FE) thin film and electrodes has drastic effect on the electric response of a capacitor [1]. It has direct bearing on fatigue observed in FE capacitors since in many cases the deterioration of the switching behavior, like the loss of the coercive force and of the squareness of hysteresis loop, were attributed to the growth of a "passive layer" at the ferroelectricelectrode interface [2][3][4][5].…”

Influence of long-range dipolar interactions on the phase stability and hysteresis shapes of ferroelectric and antiferroelectric multilayers

“…P=e 0 in SI units, " P is total polarization of the system) stabilizes 180°electrical domains [28][29][30] to compensate for the internal depolarization field induced by the variation of the order parameter near interfaces and due to imperfectly screening electrodes. One must keep in mind that the depolarization term in a FE is a function of sample shape and depends on the thickness for the case of a film that is infinite in the plane.…”