Pis'ma v ZhETF, vol. 98, iss. 6, pp. 380-382 © 2013 September 25
Scaling of the coercive field in ferroelectrics at the nanoscale
R. Gaynutdinov, M. Minnekaev+, S. Mitko*, A. Tolstikhina, A. Zenkevich+X, S. Ducharme0, V. Fridkin Shubnikov Institute of Crystallography of the RAS, 119333 Moscow, Russia
+ Moscow Engineering Physics Institute, 115409 Moscow, Russia
*NT-MDT Co., 124482 Moscow, Russia
x National Research Centre "Kurchatov Institute", 123098 Moscow, Russia
° Department of Physics and Astronomy and Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln,
NE68588-0299, USA
Submitted 16 July 2013
The scaling of the coercive field in ferroelectric films at the nanoscale is investigated experimentally. The scaling in the films of copolymer vinylidene fluoride and BaTiO3 with thickness equal by the order of value to the critical domain nucleus size 1-10 nm reveals deviation from the well known Kay and Dunn low. At this thickness region coercive field does not depend on thickness and coincides with Landau-Ginzburg-Devonshire value.
DOI: 10.7868/S0370274X13180070
The Kay and Dunn scaling of coercive field
Ec ~ l-2/3 (1)
is observed for the broad values of thickness l of the ferroelectric films [1]. The relation (1) is caused by the domain dynamics [1,2], which till 1998 was considered as a common mechanism of ferroelectric switching. The mechanism of this switching was successfully explained by theory of Kolmogorov-Avrami-Ishibashi (KAI theory) [3-5].
The application of Langmuir-Blodget film growth method for the first time permitted to obtain ferroelectric copolymer films with thickness in the region l* = 1 — 10 nm [6,7] equal by the order of value to the critical size of domain nucleus [1,8,9]. For example Miller and Weinreich obtained l* « 5 nm [9]. Ferroelectric films with l « l*, investigated in [7], have shown switching. Later in subsequent papers [10-13] have been shown, that copolymer films with thickness l* equal by the order of value to the critical size of domain nucleus reveal homogeneous switching. The homogeneous LGD switching (switching without domains) was never observed before 1998 neither in crystal nor in the films. The results, obtained in [7,10-13], led many authors [1] to the conclusion, that this polymer ferroelectric switching is possibly an exception. But recently the same results were obtained for laser-epitaxial BaTiO3 films with thickness l* = 3—10 nm [14]. These measurements were performed (as for polymeric films) in condenser by means of PFM.
In the present paper we summarize the data about scaling of coercive field both for the ferroelectric copoly-mer and BaTiO3 films at the nanoscale l « l*.
Fig. 1 shows the scaling Ec = Ec(l) for the ferroelectric vinylidene fluoride copolymer P[VDF-TrFE]
1.0
0
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n—✓
0.10
0.01
f H
!K
■ Thin LB films (Ducharme et al. 1999) ♦
• Thick LB films (Blinov et al. 1996)
♦ Thick films other than LB films (Kimura et al. 1986)
♦♦ ♦ ♦
ii_
±J_i..........i.........
1 10 10 10 Thickness (mil)
Fig. 1. Scaling of Ec in copolymer films
films obtained by Langmuir-Blodgett (LB) method [15]. The LB films thinner than 10 nm show Ec = ECth) which does not depend on film thickness l. Thicker LB films (circle symbols) and thick films, obtained by spun method (diamond symbols) show scaling possibly Dunn
Scaling of the coercive field in ferroelectrics at the nanoscale
381
and Kay (1). Correspondingly films in the interval 110 nm reveal LGD homogeneous switching kinetics [10]:
1/2
(2)
where t is switching time, t- is constant, E is switching field, and ECh is LGD coercive field. The homogeneous switching kinetics characterized by the threshold ECh: the switching of ferroelectric film takes place only at E > ECh. At E < ECh there is no switching. On the contrary at l > 10 nm (Kay and Dunn scaling) the copolymer ferroelectric films reveal switching, governed by domain dynamics (KAI mechanism) [5]:
11 t 1 = t0 exp
(3)
where E0 is constant. The results shown on Fig. 1 were obtained in condenser Al-P[VDF-TrFE]-Al by the usual Sawyer-Tower method.
The authors [2] supposed that deviation of these results from (1) are caused by the gap between Al electrodes and copolymer film. But dependence of condenser capacity on the number of LB monolayers (or on the film thickness) did not reveal any gap (Fig. 2 [16]).
40 60 80 100 120 Layers deposited
Fig. 2. Dependence of reciprocal capacity on the number of copolymer monolayers
Here we show the same deviation from (1) for the laser-epitaxial BaTiO3 ultrathin films with l < 10 nm [17,18]. The measurements were performed in condenser Pt-BaTiO3-Cr by means of PFM, which tip contacted one of the electrodes. The electrodes on the surface of BaTiO3 were deposited by lithography and had form of circles with radius of a few microns. Fig. 3 shows hysteresis loops obtained for film thicknesses of 3 (Fig. 3a), 8 (Fig. 3b), and 38 nm (Fig. 3c). The film thickness was measured by Rutherford backscattering spectrometry (RBS) with 2 MeV He++ ions with 10% accuracy
[17,18]. Fig.3 shows also the scaling of Ec = Ec(l) in the region 3-40nm (Fig. 3d). At l > 10nm the scaling follows (1), but at l < 10 nm the coercive field weakly depends on l and its value is near Ec « 108 V/m, what coincides with LGD value ECh. Correspondingly the films with l = 3 and 8 nm reveal homogeneous LGD switching kinetics (2) and thicker films - KAI behavior (3) [14].
Of course ultrathin films with l « l* (in the region of critical domain size) must reveal the existence of two competing polarization reversal mechanisms: domain-driven and homogeneous. One of these mechanisms prevails depending on the thickness and external field. This our conclusion was confirmed recently from the first principles approach [19].
The work in Moscow was performed using the equipment of the Shared Research Center IC RAS and was supported by the Russian Ministry of Education and Science under Contract 11.519.11.3007. Work in the University of Nebraska was supported by the US Department of Energy (DE-FG02-10ER46772) and by National Science Foundation through the Q-SPINS Materials Research Science and Engineering Research Center (DMR-0213808).
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R. Gaynutdinov, M. Minnekaev, S. Mitko et al.
Fig. 3. Hysteresis loops and scaling of the coercive field for the ultrathin BaTiO3 films
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