Spatially resolved steady-state negative capacitance

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Abstract

Negative capacitance is a newly discovered state of ferroelectric materials that holds promise for electronics applications by exploiting a region of thermodynamic space that is normally not accessible1,2,3,4,5,6,7,8,9,10,11,12,13,14. Although existing reports of negative capacitance substantiate the importance of this phenomenon, they have focused on its macroscale manifestation. These manifestations demonstrate possible uses of steady-state negative capacitance—for example, enhancing the capacitance of a ferroelectric–dielectric heterostructure4,7,14 or improving the subthreshold swing of a transistor8,9,10,11,12. Yet they constitute only indirect measurements of the local state of negative capacitance in which the ferroelectric resides. Spatial mapping of this phenomenon would help its understanding at a microscopic scale and also help to achieve optimal design of devices with potential technological applications. Here we demonstrate a direct measurement of steady-state negative capacitance in a ferroelectric–dielectric heterostructure. We use electron microscopy complemented by phase-field and first-principles-based (second-principles) simulations in SrTiO3/PbTiO3 superlattices to directly determine, with atomic resolution, the local regions in the ferroelectric material where a state of negative capacitance is stabilized. Simultaneous vector mapping of atomic displacements (related to a complex pattern in the polarization field), in conjunction with reconstruction of the local electric field, identify the negative capacitance regions as those with higher energy density and larger polarizability: the domain walls where the polarization is suppressed.

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Fig. 1: Steady-state negative capacitance.
Fig. 2: Identifying the regions of negative permittivity.
Fig. 3: Measurement of local electric field and polarization field using EMPAD-STEM.
Fig. 4: Local permittivity calculated using second-principles and phase-field simulations.

Data availability

All data supporting the findings of this study are available within the paper.

Change history

  • 10 April 2019

    In this Letter, the first name of author Bhagwati Prasad was misspelled Bhagawati. This error has been corrected online.

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Acknowledgements

This work was supported in part by the AFOSR YIP programme, LEAST (one of the SRC/DARPA supported centres within the STARNET initiative), ASCENT (one of the SRC/DARPA supported centres within the JUMP initiative), and the Berkeley Center for Negative Capacitance Transistors and the Multicampus Research Programs and Initiatives (MRPI) of the University of California. Electron microscopy experiments and equipment were supported by the Cornell Center for Materials Research, through the National Science Foundation MRSEC programme, award DMR 1719875. The work at Penn State was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award FG02-07ER46417. Z.J.H. acknowledges support from NSF-MRSEC grant number DMR-1420620 and NSF-MWN grant number DMR-1210588. R.R. and S.D. acknowledge support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, under grant GBMF5307. R.R. also acknowledges funding from the Army Research Office. J.I. acknowledges support from the Luxembourg National Research Fund under grant C15/MS/10458889 NEWALLS. P.G.-F. and J.J. acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through grant number FIS2015-64886-C5-2-P, and P.G.-F. acknowledges support from Ramón y Cajal grant no. RyC-2013-12515.

Reviewer information

Nature thanks D. Jiménez, J. Rondinelli and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information

A.K.Y., K.X.N., D.A.M., R.R. and S.S. designed the research. A.K.Y. performed synthesis and characterization of superlattice films. K.X.N. performed polarization and electric field measurements on superlattice films using EMPAD-STEM. C.T.N. performed atomic-resolution polar displacement mapping on superlattice films using STEM. Z.H. and L.-Q.C. performed phase-field calculations for these superlattice structures. P.G.-F., P.A.-P., J.I. and J.J. performed second-principles calculations for these superlattice structures. D.K., S.C., S.D. and B.P. performed current–voltage measurements. A.K.Y., S.S., C.H., R.R., K.X.N., C.T.N., A.I.K., Z.H., P.G.-F., P.A.-P., J.J., L.-Q.C., D.A.M. and J.I. discussed results and co-wrote the manuscript. S.S. performed the overall supervision of the work. All authors contributed to the discussions and manuscript preparation.

Correspondence to Sayeef Salahuddin.

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Extended data figures and tables

Extended Data Fig. 1 Electron spectrometry of the superlattice.

a, Schematic of the electron microscopy pixel array detector (EMPAD) placed in the diffraction plane to record the full angular scattering distribution from an electron beam focused onto a sample. b, ADF image of the (PbTiO3)12/(SrTiO3)12 superlattice along the [010]pc zone axis. c, d, CBED pattern from the PbTiO3 layer (c) and from the SrTiO3 layer (d).

Extended Data Fig. 2 Electric field and polarization field extracted from TEM measurements.

Left column, x and z components of the electric field, Ex (top) and Ez (bottom); right column, x and z components of the polarization field, Px (top) and Pz (bottom). Ex,z and Px,z are extracted from the 4D STEM measurements of a PbTiO3 multilayer in Extended Data Fig. 1, as discussed in Methods section ‘EMPAD’. The electric field is determined from the center-of-mass shift of the central disk (red disk in Extended Data Fig. 1). The polarization is determined from the center of mass of the Friedel pairs (orange in Extended Data Fig. 1). Field of view, 12 nm.

Extended Data Fig. 3 Vector maps of the electric field and polarization field calculated from phase-field simulations.

Top, polarization field; bottom, electric field.

Extended Data Fig. 4 Illustration of the grids used to obtain the local dielectric constant.

The electrostatic potential is computed at the points of a regular real space grid (blue dots). Then the local electric field components along x and z are computed from finite-difference derivatives at the points of two extra staggered regular grids (green and red points).

Extended Data Fig. 5 Second-principles calculations of the 2D distribution of the inverse of the dielectric constant and the susceptibility.

a, The inverse of the dielectric constant is colour-coded (key at right); b, the susceptibility is colour coded (key at right). Both a and b are overlaid by the polarization vectors, and the green dashed line in both panels shows the line cut used to produce Fig. 4.

Extended Data Fig. 6 Second-principles calculation of the local energy density map overlaid with polarization vectors.

Note that within the PbTiO3 layer (the top where the polarization vectors can be seen more clearly), the core region has a higher energy than the other regions (see colour key at right, in atomic units, a.u.). The core regions are also where the local permittivity is negative. The local energy in the SrTiO3 layer (mostly red) is quite uniform and is equal to the reference energy. Note that the energies shown here are the differences with respect to the reference structure that corresponds to the cubic centrosymmetric phase.

Extended Data Fig. 7 Determination of normalized G.

a, Plot of Ez versus Dz determined from looking at experimentally measured, varying polarization across a vortex and plotting the corresponding electric field (see Fig. 3c). b, Normalized G estimated from a using \(G=\int {E}_{z}{\rm{d}}{D}_{z}\).

Extended Data Fig. 8 Estimation of local permittivity.

Top, z components of polarization (Pz) and of electric field (Ez), plotted against X (position along the lattice). Bottom, permittivity estimated as described in Methods. Permittivity is negative in the regions around the core.

Extended Data Fig. 9 Experimentally measured dielectric constant as a function of voltage.

In red, data are shown for a 100 nm (SrTiO3)12/(PbTiO3)12 superlattice where the existence of vortex states was confirmed. In blue, for comparison, the permittivity (dielectric constant) of a 50 nm SrTiO3 sample is plotted (note that the combined thickness of SrTiO3 in the superlattice is also 50 nm). The black dashed line shows the threshold that needs to be surpassed for capacitance enhancement caused by a stabilized negative capacitance in the PbTiO3 layer. An enhancement in permittivity of almost 3.7 times is observed compared to this threshold.

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Yadav, A.K., Nguyen, K.X., Hong, Z. et al. Spatially resolved steady-state negative capacitance. Nature 565, 468–471 (2019) doi:10.1038/s41586-018-0855-y

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