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Unveiling the double-well energy landscape in a ferroelectric layer


The properties of ferroelectric materials, which were discovered almost a century ago1, have led to a huge range of applications, such as digital information storage2, pyroelectric energy conversion3 and neuromorphic computing4,5. Recently, it was shown that ferroelectrics can have negative capacitance6,7,8,9,10,11, which could improve the energy efficiency of conventional electronics beyond fundamental limits12,13,14. In Landau–Ginzburg–Devonshire theory15,16,17, this negative capacitance is directly related to the double-well shape of the ferroelectric polarization–energy landscape, which was thought for more than 70 years to be inaccessible to experiments18. Here we report electrical measurements of the intrinsic double-well energy landscape in a thin layer of ferroelectric Hf0.5Zr0.5O2. To achieve this, we integrated the ferroelectric into a heterostructure capacitor with a second dielectric layer to prevent immediate screening of polarization charges during switching. These results show that negative capacitance has its origin in the energy barrier in a double-well landscape. Furthermore, we demonstrate that ferroelectric negative capacitance can be fast and hysteresis-free, which is important for prospective applications19. In addition, the Hf0.5Zr0.5O2 used in this work is currently the most industry-relevant ferroelectric material, because both HfO2 and ZrO2 thin films are already used in everyday electronics20. This could lead to fast adoption of negative capacitance effects in future products with markedly improved energy efficiency.

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Fig. 1: Landau–Ginzburg–Devonshire phenomenological model of a ferroelectric.
Fig. 2: Electrical and physical characterization of a ferroelectric Hf0.5Zr0.5O2 layer.
Fig. 3: Electrical measurement of the ferroelectric double-well energy landscape.

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Data availability

The datasets generated and analysed during this study are available from the corresponding author upon reasonable request.


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This project received funding from the Electronic Component Systems for European Leadership Joint Undertaking under grant agreement no. 692519. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and Belgium, Germany, France, Netherlands, Poland and the UK. This work was also supported in part by the EFRE fund of the European Commission and in part by the Free State of Saxony (Germany). P.L. and R.N. acknowledge funding through the Core Program of NIMP (Romanian Ministry for Research and Innovation).

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Nature thanks D. Jiménez, A. Morozovska and L.-E. Wernersson for their contribution to the peer review of this work.

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Authors and Affiliations



M. Hoffmann performed the electrical measurements, analysed the data and wrote the manuscript. F.P.G.F., M. Herzig and B.M. fabricated the samples. T. Mittmann optimized the HZO atomic layer deposition process. P.L. and R.N. performed TEM measurements and analyses. U.S., S.S. and T. Mikolajick supervised the work and discussed the results. S.S. and M. Hoffmann conceived and designed the experiments. All authors commented on the manuscript.

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Correspondence to Michael Hoffmann.

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The authors declare no competing interests.

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Extended data figures and tables

Extended Data Fig. 1 Direct measurement of transient negative capacitance with hysteresis in a TiN/HZO/TiN capacitor.

a, Experimental set-up with resistor in series. See Methods for details. b, Transient applied voltage (VS) and ferroelectric voltage (VF) measured via an oscilloscope. c, Calculated transient current IR flowing through the resistor R. d, Transient charge on the capacitor from integration of IR.

Extended Data Fig. 2 Ferroelectric polarization–electric field hysteresis from transient negative capacitance measurements on TiN/HZO/TiN.

a, Ferroelectric polarization–electric field (PEF) hysteresis calculated from the data in Extended Data Fig. 1b and d. b, c, Grey shaded areas in a are shown at higher magnification; the negative capacitance (NC) regions are shown with blue shading. Negative capacitance is shown for negative (b) and positive (c) electric fields.

Extended Data Fig. 3 HRTEM images of the Ta2O5/HZO/TiN/SiOx/Si heterostructure.

a, High-resolution transmission electron microscopy (HRTEM) images of the Ta2O5/HZO/TiN/SiOx/Si heterostructure. bd, Magnified views of particular areas of a: b, the TiN/SiOx/Si interfaces; c, the HZO/TiN interface; and d, the Ta2O5/HZO interface.

Extended Data Fig. 4 Heterostructure characterization by HAADF-STEM and EELS.

a, Low-magnification HAADF-STEM (high-angle annular dark-field scanning transmission electron microscopy) image of the Ta2O5/HZO/TiN/SiOx/Si heterostructure. The boxed region was analysed by EELS (electron energy-loss spectroscopy). b, EELS maps corresponding to the boxed region in a for the absorption edges N K, O K, Ti L, Hf M and Ta M. The bottom right image was obtained by overlapping the Ti L, Hf M and Ta M maps.

Extended Data Fig. 5 Comparison of theory and experiment of pulsed charge–voltage measurements on TiN/HZO/Ta2O5/TiN samples.

a, Reversibly stored charge Qrev as a function of maximum voltage across the capacitor Vmax as shown in Fig. 3g; solid lines correspond to theoretical calculations using Landau–Ginzburg–Devonshire (LGD) theory. b, Calculated electric field contributions in the ferroelectric layer as a function of Vmax. See main text and Supplementary Information for details of nomenclature. c, Calculated electric field contributions in the dielectric layer as a function of Vmax. See main text and Supplementary Information for details of nomenclature.

Extended Data Fig. 6 Confirmation of hysteresis-free operation and negative capacitance in TiN/HZO/Al2O3/TiN samples.

a, Pulsed charge–voltage hysteresis measurement of a TiN/HZO/Ta2O5/TiN capacitor. See main text for details of nomenclature. Black arrows indicate sweep directions of increasing and decreasing Vmax. b, ‘S’-shaped PEF curve calculated from the data in a as described in Supplementary Information. Black data points and arrows correspond to the increasing Vmax sweep direction, while blue data points and arrows indicate the decreasing Vmax sweep direction. The red line corresponds to LGD theory, and the blue line shows the PEF hysteresis measured on a TiN/HZO/TiN sample. c, ‘S’-shaped PEF curve calculated from pulsed charge–voltage measurements (data points) of a TiN/HZO/Al2O3/TiN capacitor. The red line shows LGD theory calculations. d, Integrating the PEF characteristics in c results in a double-well energy landscape (red curve shows LGD theory) from experimental data (data points).

Extended Data Fig. 7 Investigation of the transition from hysteresis-free negative capacitance to hysteretic switching.

a, Pulsed charge–voltage hysteresis measurement of a TiN/HZO/Ta2O5/TiN capacitor (same as in Fig. 3) for different pulse widths (see key). b, PEF curves calculated from the data in a. Green arrows indicate hysteresis when applying first increasing and then decreasing voltage pulses Vmax. c, Pulsed charge–voltage hysteresis measurement of a TiN/HZO/Al2O3/TiN capacitor with 3-nm Al2O3 for successively increasing maximum pulse voltages (see key). d, PEF curves calculated from the data in c. Arrows indicate hysteresis when applying first increasing and then decreasing voltage pulses Vmax. Clockwise hysteresis is caused by charge-trapping.

Supplementary information

Supplementary Information

This file contains detailed modelling equations of the MFIM capacitor, a description of the extraction of the double-well potential, a discussion of the modelling parameters and a comparison of theoretical and experimental permittivity values of the ferroelectric.

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Hoffmann, M., Fengler, F.P.G., Herzig, M. et al. Unveiling the double-well energy landscape in a ferroelectric layer. Nature 565, 464–467 (2019).

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