Negative capacitance in multidomain ferroelectric superlattices

Abstract

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.

References

  1. 1

    Scott, J. F. & Paz de Araujo, C. A. Ferroelectric memories. Science 246, 1400–1405 (1989)

    ADS  CAS  Google Scholar 

  2. 2

    Naumov, I. I., Bellaiche, L. & Fu, H. Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature 432, 737–740 (2004)

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  3. 3

    Garcia, V. et al. Giant tunnel electroresistance for non-destructive readout of ferroelectric states. Nature 460, 81–84 (2009)

    ADS  CAS  PubMed  Google Scholar 

  4. 4

    Kim, D. J. et al. Ferroelectric tunnel memristor. Nano Lett. 12, 5697–5702 (2012)

    ADS  CAS  PubMed  Google Scholar 

  5. 5

    Bratkovsky, A. M. & Levanyuk, A. P. Very large dielectric response of thin ferroelectric films with the dead layers. Phys. Rev. B 63, 132103 (2001)

    ADS  Google Scholar 

  6. 6

    Salahuddin, S. & Datta, S. Use of negative capacitance to provide voltage amplification for low power nanoscale devices. Nano Lett. 8, 405–410 (2008)

    ADS  CAS  PubMed  Google Scholar 

  7. 7

    Krowne, C. M., Kirchoefer, S. W., Chang, W., Pond, J. M. & Alldredge, L. M. B. Examination of the possibility of negative capacitance using ferroelectric materials in solid state electronic devices. Nano Lett. 11, 988–992 (2011)

    ADS  CAS  PubMed  Google Scholar 

  8. 8

    Fong, D. D. et al. Ferroelectricity in ultrathin perovskite films. Science 304, 1650–1653 (2004)

    ADS  CAS  PubMed  Google Scholar 

  9. 9

    Catalan, G., Jiménez, D. & Gruverman, A. Ferroelectrics: Negative capacitance detected. Nat. Mater. 14, 137–139 (2015)

    ADS  CAS  PubMed  Google Scholar 

  10. 10

    Bratkovsky, A. M. & Levanyuk, A. P. Depolarizing field and “real” hysteresis loops in nanometer-scale ferroelectric films. Appl. Phys. Lett. 89, 253108 (2006)

    ADS  Google Scholar 

  11. 11

    Cano, A. & Jiménez, D. Multidomain ferroelectricity as a limiting factor for voltage amplification in ferroelectric field-effect transistors. Appl. Phys. Lett. 97, 133509 (2010)

    ADS  Google Scholar 

  12. 12

    Luk’yanchuk, I., Pakhomov, A., Sené, A., Sidorkin, A. & Vinokur, V. Terahertz electrodynamics of 180° domain walls in thin ferroelectric films. Preprint at http://arxiv.org/abs/1410.3124 (2014)

  13. 13

    Ponomareva, I., Bellaiche, L. & Resta, R. Dielectric anomalies in ferroelectric nanostructures. Phys. Rev. Lett. 99, 227601 (2007)

    ADS  CAS  PubMed  Google Scholar 

  14. 14

    Stengel, M., Vanderbilt, D. & Spaldin, N. A. Enhancement of ferroelectricity at metal–oxide interfaces. Nat. Mater. 8, 392–397 (2009)

    ADS  CAS  PubMed  Google Scholar 

  15. 15

    Mehta, R. R., Silverman, B. D. & Jacobs, J. T. Depolarization fields in thin ferroelectric films. J. Appl. Phys. 44, 3379–3385 (1973)

    ADS  CAS  Google Scholar 

  16. 16

    Junquera, J. & Ghosez, P. Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422, 506–509 (2003)

    ADS  CAS  PubMed  Google Scholar 

  17. 17

    Khan, A. I. et al. Experimental evidence of ferroelectric negative capacitance in nanoscale heterostructures. Appl. Phys. Lett. 99, 113501 (2011)

    ADS  Google Scholar 

  18. 18

    Appleby, D. J. R. et al. Experimental observation of negative capacitance in ferroelectrics at room temperature. Nano Lett. 14, 3864–3868 (2014)

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  19. 19

    Gao, W. et al. Room-temperature negative capacitance in a ferroelectric–dielectric superlattice heterostructure. Nano Lett. 14, 5814–5819 (2014)

    ADS  CAS  PubMed  Google Scholar 

  20. 20

    Khan, A. I. et al. Negative capacitance in a ferroelectric capacitor. Nat. Mater. 14, 182–186 (2015)

    ADS  CAS  PubMed  Google Scholar 

  21. 21

    Luk’yanchuk, I. A., Lahoche, L. & Sené, A. Universal properties of ferroelectric domains. Phys. Rev. Lett. 102, 147601 (2009)

    ADS  PubMed  Google Scholar 

  22. 22

    Kopal, A., Mokrý, P., Fousek, J. & Bahník, T. Displacements of 180° domain walls in electroded ferroelectric single crystals: the effect of surface layers on restoring force. Ferroelectrics 223, 127–134 (1999)

    CAS  Google Scholar 

  23. 23

    Dawber, M. et al. Tailoring the properties of artificially layered ferroelectric superlattices. Adv. Mater. 19, 4153–4159 (2007)

    CAS  Google Scholar 

  24. 24

    Wojdeł, J. C., Hermet, P., Ljungberg, M. P., Ghosez, P. & Íñiguez, J. First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides. J. Phys. Condens. Matter 25, 305401 (2013)

    PubMed  Google Scholar 

  25. 25

    Blatter, G., Feigel’man, M. V., Geshkenbein, V. B., Larkin, A. I. & Vinokur, V. M. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125–1388 (1994)

    ADS  CAS  Google Scholar 

  26. 26

    De Guerville, F., Luk’yanchuk, I., Lahoche, L. & El Marssi, M. Modeling of ferroelectric domains in thin films and superlattices. Mater. Sci. Eng. B 120, 16–20 (2005)

    Google Scholar 

  27. 27

    Wojdeł, J. C. & Íñiguez, J. Ferroelectric transitions at ferroelectric domain walls found from first principles. Phys. Rev. Lett. 112, 247603 (2014)

    ADS  PubMed  Google Scholar 

  28. 28

    Lichtensteiger, C., Fernandez-Pena, S., Weymann, C., Zubko, P. & Triscone, J.-M. Tuning of the depolarization field and nanodomain structure in ferroelectric thin films. Nano Lett. 14, 4205–4211 (2014)

    ADS  CAS  PubMed  Google Scholar 

  29. 29

    Aguado-Puente, P. & Junquera, J. Ferromagneticlike closure domains in ferroelectric ultrathin films: first-principles simulations. Phys. Rev. Lett. 100, 177601 (2008)

    ADS  PubMed  Google Scholar 

  30. 30

    Warusawithana, M. P. et al. A ferroelectric oxide made directly on silicon. Science 324, 367–370 (2009)

    ADS  CAS  PubMed  Google Scholar 

  31. 31

    Landau, L. & Lifshits, E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phys. Zeitsch. Sow. 8, 153–169 (1935)

    MATH  Google Scholar 

  32. 32

    Kittel, C. Theory of the structure of ferromagnetic domains in films and small particles. Phys. Rev. 70, 965–971 (1946)

    ADS  CAS  Google Scholar 

  33. 33

    Stephanovich, V. A., Luk’yanchuk, I. A. & Karkut, M. G. Domain-enhanced interlayer coupling in ferroelectric/paraelectric superlattices. Phys. Rev. Lett. 94, 047601 (2005)

    ADS  CAS  PubMed  Google Scholar 

  34. 34

    Catalan, G., Schilling, A., Scott, J. F. & Gregg, J. M. Domains in three-dimensional ferroelectric nanostructures: theory and experiment. J. Phys. Condens. Matter 19, 132201 (2007)

    ADS  Google Scholar 

  35. 35

    Sené, A. Theory of Domains and Nonuniform Textures in Ferroelectrics. PhD thesis, Universite de Picardie (2010)

  36. 36

    Zubko, P. et al. Electrostatic coupling and local structural distortions at interfaces in ferroelectric/paraelectric superlattices. Nano Lett. 12, 2846–2851 (2012)

    ADS  CAS  PubMed  Google Scholar 

  37. 37

    Plonka, R., Dittmann, R., Pertsev, N. A., Vasco, E. & Waser, R. Impact of the top-electrode material on the permittivity of single-crystalline Ba0.7Sr0.3TiO3 thin films. Appl. Phys. Lett. 86, 202908 (2005)

    ADS  Google Scholar 

  38. 38

    Stengel, M. & Spaldin, N. A. Origin of the dielectric dead layer in nanoscale capacitors. Nature 443, 679–682 (2006)

    ADS  CAS  PubMed  Google Scholar 

  39. 39

    Catalan, G., O’Neill, D., Bowman, R. M. & Gregg, J. M. Relaxor features in ferroelectric superlattices: a Maxwell–Wagner approach. Appl. Phys. Lett. 77, 3078–3080 (2000)

    ADS  CAS  Google Scholar 

  40. 40

    Ghosez, P., Cockayne, E., Waghmare, U. V. & Rabe, K. M. Lattice dynamics of BaTiO3, PbTiO3, and PbZrO3: a comparative first-principles study. Phys. Rev. B 60, 836–843 (1999)

    ADS  CAS  Google Scholar 

  41. 41

    Bousquet, E. et al. Improper ferroelectricity in perovskite oxide artificial superlattices. Nature 452, 732–736 (2008)

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  42. 42

    Lisenkov, S. & Bellaiche, L. Phase diagrams of BaTiO3/SrTiO3 superlattices from first principles. Phys. Rev. B 76, 020102 (2007)

    ADS  Google Scholar 

  43. 43

    García, A. & Vanderbilt, D. Electromechanical behavior of BaTiO3 from first principles. Appl. Phys. Lett. 72, 2981–2983 (1998)

    ADS  Google Scholar 

  44. 44

    Aguado-Puente, P. & Junquera, J. Structural and energetic properties of domains in PbTiO3/SrTiO3 superlattices from first principles. Phys. Rev. B 85, 184105 (2012)

    ADS  Google Scholar 

  45. 45

    Ponomareva, I., Bellaiche, L. & Resta, R. Relation between dielectric responses and polarization fluctuations in ferroelectric nanostructures. Phys. Rev. B 76, 235403 (2007)

    ADS  Google Scholar 

  46. 46

    Wojdeł, J. C. & Íñiguez, J. Testing simple predictors for the temperature of a structural phase transition. Phys. Rev. B 90, 014105 (2014)

    ADS  Google Scholar 

  47. 47

    Zubko, P. et al. Ferroelectric domains in PbTiO3/SrTiO3 superlattices. Ferroelectrics 433, 127–137 (2012)

    CAS  Google Scholar 

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Acknowledgements

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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Contributions

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). https://doi.org/10.1038/nature17659

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