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Negative capacitance in multidomain ferroelectric superlattices


The stability of spontaneous electrical polarization in ferroelectrics is fundamental to many of their current applications, which range from the simple electric cigarette lighter to non-volatile random access memories1. Research on nanoscale ferroelectrics reveals that their behaviour is profoundly different from that in bulk ferroelectrics, which could lead to new phenomena with potential for future devices2,3,4. As ferroelectrics become thinner, maintaining a stable polarization becomes increasingly challenging. On the other hand, intentionally destabilizing this polarization can cause the effective electric permittivity of a ferroelectric to become negative5, enabling it to behave as a negative capacitance when integrated in a heterostructure. Negative capacitance has been proposed as a way of overcoming fundamental limitations on the power consumption of field-effect transistors6. However, experimental demonstrations of this phenomenon remain contentious7. The prevalent interpretations based on homogeneous polarization models are difficult to reconcile with the expected strong tendency for domain formation8,9, but the effect of domains on negative capacitance has received little attention5,10,11,12. Here we report negative capacitance in a model system of multidomain ferroelectric–dielectric superlattices across a wide range of temperatures, in both the ferroelectric and paraelectric phases. Using a phenomenological model, we show that domain-wall motion not only gives rise to negative permittivity, but can also enhance, rather than limit, its temperature range. Our first-principles-based atomistic simulations provide detailed microscopic insight into the origin of this phenomenon, identifying the dominant contribution of near-interface layers and paving the way for its future exploitation.

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Figure 1: Phenomenological description of negative capacitance.
Figure 2: Temperature dependence of the dielectric permittivities of Pb0.5Sr0.5TiO3–SrTiO3 and PbTiO3–SrTiO3 superlattices.
Figure 3: Results of Monte Carlo simulations of a first-principles-based model for the (8, 2) superlattice.


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We acknowledge financial support from the EPSRC (Grant No. EP/M007073/1; P.Z. and M.H.), the A. G. Leventis Foundation (M.H.); FNR Luxembourg (Grant No. FNR/P12/4853155/Kreisel; J.I.), MINECO-Spain (Grant No. MAT2013-40581-P; J.I. and J.C.W.), the Swiss National Science Foundation Division II (J.-M.T. and S.F.-P.), the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC (Grant No. 319286 (Q-MAC); J.-M.T. and S.F.-P.), and the EU-FP7-ITN project NOTEDEV (Grant No. 607521; I.L.).

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Authors and Affiliations



P.Z., M.H., S.F.-P. and J.-M.T. performed and analysed the experiments. A.S. and I.L. developed the phenomenological theory. J.C.W. and J.I. developed the atomistic models and performed the simulations.

Corresponding authors

Correspondence to Pavlo Zubko or Jorge Íñiguez.

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The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 XRD characterization of the superlattices.

a, Intensity profiles around the (002) substrate reflection for Pb0.5Sr0.5TiO3–SrTiO3 (PST-STO) superlattices. The broad peaks around 2θ = 45.5° correspond to the top and bottom SrRuO3 electrodes. Finite-size oscillations due to the 200-nm superlattice thickness are visible. b, c, XRD domain satellites for Pb0.5Sr0.5TiO3–SrTiO3 (b) and PbTiO3–SrTiO3 (PTO-STO; c) superlattices. Insets, domain periodicities obtained from fitting the Qx line profiles using a sum of two Gaussian functions for the domain satellites and a Lorentzian function for central Bragg peak. The error bars were determined from the 95% confidence bounds for the peak positions obtained from the fits. nd is the number of SrTiO3 layers in the (14, nd) (b) or (5, nd) (c) superlattices; Qx is the in-plane reciprocal-space coordinate.

Extended Data Figure 2 Local polarization distribution at low temperature.

Arrows indicate the dipole component within the plane; we plot arrows for Pb/Sr-centred and Ti-centred dipoles. The colouring indicates the polarization P component along , revealing a low-temperature polar order at the domain walls. PTO, PbTiO3; STO, SrTiO3.

Extended Data Figure 3 Comparison with experiment.

Reciprocal dielectric constant 1/εf of the PbTiO3 layers as a function of temperature T, calculated from the computed total dielectric constants of (8, nd) superlattices using the same analysis as for the experimental data.

Extended Data Figure 4 Interface capacitance contributions.

a, SrRuO3–SrTiO3 interface contribution Ci to the dielectric response. b, Dielectric stiffness 1/εf of the PbTiO3 layers with (blue) and without (red) correcting for the interface capacitance. Grey (a) and blue and pink (b) shading indicates estimated uncertainties obtained from weighted-least-squares linear fits.

Extended Data Figure 5 Dielectric impedance spectroscopy of PbTiO3–SrTiO3 superlattices.

Real (C′; filled circles) and imaginary (C″; open circles) parts of the complex capacitance function C = C′ + iC″ for a (5, 8)30 PbTiO3–SrTiO3 superlattice. For temperatures below about 650 K, the data are well fitted by a single parallel R–C element in series with Rs, as shown by solid curves for the 500 K (blue) and 600 K (orange) data. At higher temperatures, Maxwell–Wagner relaxations appear as the conductivities of some layers increase faster with temperature than others. At 700 K (red), the response is qualitatively captured by a model with two parallel R–C elements in series with each other (dashed red curve), whereas for a quantitative fit three R–C elements are required (solid red curve). The inset shows the arrangement of elements in the generalized equivalent circuit used to fit the data.

Extended Data Figure 6 Temperature evolution of the tetragonality and domain satellites.

Intensity of the XRD domain satellite (filled red circles) and the film tetragonality (c/a; open blue squares) for a (5, 4)28 PbTiO3–SrTiO3 superlattice. The satellite intensity was obtained by integrating the measured intensity of the domain satellites and subtracting the minimum integrated intensity in the paraelectric phase. Vertical blue line marks the temperature at which linear fits to the low- and high-temperature data (blue lines) intersect.

Supplementary information

High temperature fluctuations of the domain structure

Local dipoles (z component) at the mid plane of the PbTiO3 layer in our (8,2) simulated superlattice. The video is constructed from snapshots of a Monte Carlo simulation at 400 K. (MP4 4861 kb)

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Zubko, P., Wojdeł, J., Hadjimichael, M. et al. Negative capacitance in multidomain ferroelectric superlattices. Nature 534, 524–528 (2016).

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