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Frequency-dependent dielectric response of ferroelectric–dielectric junction with negative electric capacitance

Abstract

We calculated the frequency-dependent dielectric response (electric susceptibility) of layered ferroelectric–dielectric junction, biased by the time-dependent harmonic voltage with single frequency \(\omega \). Working point is stabilized, by the charge boundary condition between the layers, in the region with negative electric capacitance. The static susceptibility \(\chi _0\) is negative and the relative dielectric constant \(\epsilon _r\) is smaller than 1, clearly indicating the opposite direction of electric field and polarization in the ferroelectric layer due to the negative electric capacitance. At finite frequencies, this sign is preserved in real part of susceptibility which gains the frequency dependence. Also, frequency-dependent imaginary part arises due to the phase shift between electric field and polarization. The type of that frequency dependence in linear regime is the so-called relaxation (Debye) response, i.e., \(\chi '(\omega )=\chi _0/(1+(\tau \omega )^2)\) and \(\chi ''(\omega )=\chi _0\tau \omega /(1+(\tau \omega )^2)\), where \(\tau \) is the polarization switching time characteristic to ferroelectric material. In particular, we modeled the junction of ferroelectric BaTiO\(_3\) and dielectric Al\(_2\)O\(_3\), taking the experimental values of material parameters, and addressed the role of nonlinearity with respect to result of the linear response theory.

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References

  1. 1.

    S. Salahuddin, S. Datta, Nano Lett. 8, 405 (2008)

    ADS  Article  Google Scholar 

  2. 2.

    A.I. Khan, D. Bhowmik, P. Yu, S.J. Kim, X. Pan, R. Ramesh, S. Salahuddin, Appl. Phys. Lett. 99, 113501 (2011)

    ADS  Article  Google Scholar 

  3. 3.

    R. Tadros-Morgane, G. Vizdrik, B. Martin, H. Kliem, J. Appl. Phys. 109, 014501 (2011)

    ADS  Article  Google Scholar 

  4. 4.

    S. Hrabar, I. Krois, I. Bonic, A. Kiricenko, Appl. Phys. Lett. 99, 2541103 (2011)

    Article  Google Scholar 

  5. 5.

    J. Íñiguez, P. Zubko, I. Luk’yanchuk, A. Cano, Nat. Rev. Mater. 4, 243 (2019)

    ADS  Article  Google Scholar 

  6. 6.

    A. Rusu, A. Saeidi, A.M. Ionescu, Nanotechnology 27, 115201 (2016)

    ADS  Article  Google Scholar 

  7. 7.

    J. Buck, W. Hayt, Engineering Electromagnetics, vol. 7 (McGraw-Hill, New York, 2011)

    Google Scholar 

  8. 8.

    A. Cano, D. Jimenez, Appl. Phys. Lett. 97, 133509 (2010)

    ADS  Article  Google Scholar 

  9. 9.

    T. Mistsui, I. Tatsuzaki, E. Nakamura, An Introduction to the Physics of Ferroelectrics (Gordon and Breach Science Publishers, London, 1976)

    Google Scholar 

  10. 10.

    Y. Akishige, Y. Kamishina, DC electrical resistivity of reduced hexagonal BaTiO3. Ferroelectrics 168(1), 121–125 (1995). https://doi.org/10.1080/00150199508007854

    Article  Google Scholar 

  11. 11.

    J. Li, B. Nagaraj, H. Liang, W. Cao, C.H. Lee, R. Ramesh, Appl. Phys. Lett. 84(7), 1174 (2004)

    ADS  Article  Google Scholar 

  12. 12.

    L.D. Landau, I.M. Khalatnikov, On the anomalous absorption of sound near a second order phase transition point. Dokl. Akad. Nauk 96, 469–472 (1954)

    Google Scholar 

  13. 13.

    T.K. Song, J. Korean Phys. Soc. 46(1), 5–9 (2005)

    Google Scholar 

  14. 14.

    S. Sivasubramanian, A. Widom, Y.N. Srivastava, Physical kinetics of ferroelectric hysteresis. Ferroelectrics 300(1), 43–55 (2004). https://doi.org/10.1080/00150190490442173

    Article  Google Scholar 

  15. 15.

    L.-H. Ong, K.-H. Chew, in Ferroelectrics-Characterization and Modeling, ed. by M. Lallart (InTech, Vienna, 2011), p. 349. ISBN: 978-953-307-455-9

  16. 16.

    S. Miga, J. Dec, W. Kleemann, in Ferroelectrics-Characterization and Modeling, ed. by M. Lallart (InTech, Vienna, 2011) p. 181. ISBN: 978-953-307-455-9

  17. 17.

    L. Dissado, Dielectric response, in Springer Handbook of Electronic and Photonic Materials-Springer Handbooks, ed. by S. Kasap, P. Capper (Springer, Cham, 2017), p. 219. ISBN: 978-3-319-48931-5

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Acknowledgements

This work was supported by the Croatian Science Foundation, Project IP-2016-06-2289, and by the QuantiXLie Centre of Excellence, a project cofinanced by the Croatian Government and European Union through the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme (Grant KK.01.1.1.01.0004). The authors are grateful to K. Jurišić for the fruitful discussions.

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Correspondence to D. Radić.

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Piskač, M., Radić, D. Frequency-dependent dielectric response of ferroelectric–dielectric junction with negative electric capacitance. Eur. Phys. J. Plus 135, 569 (2020). https://doi.org/10.1140/epjp/s13360-020-00578-3

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