Enhanced flexoelectric-like response in oxide semiconductors


Flexoelectricity is a property of all dielectric materials whereby they polarize in response to deformation gradients such as those produced by bending1,2,3,4,5. Although it is generally thought of as a property of dielectric insulators, insulation is not a formal requirement: in principle, semiconductors can also redistribute their free charge in response to strain gradients. Here we show that bending a semiconductor not only generates a flexoelectric-like response, but that this response can in fact be much larger than in insulators. By doping single crystals of wide-bandgap oxides to increase their conductivity, their effective flexoelectric coefficient was increased by orders of magnitude. This large response can be explained by a barrier-layer mechanism that remains important even at the macroscale, where conventional (insulator) flexoelectricity otherwise tends to be small. Our results open up the possibility of using semiconductors as active ingredients in electromechanical transducer applications.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Barrier layer model.
Figure 2: Capacitance of BTO.
Figure 3: Effective flexoelectricity of BTO.
Figure 4: Effective flexoelectricity of TiO2 and 0.05%Nb-doped TiO2.


  1. 1

    Kogan, S. M. Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals. Sov. Phys. Solid State 5, 2069–2070 (1964)

    Google Scholar 

  2. 2

    Bursian, E. & Zaikovskii, O. I. Changes in curvature of ferroelectric film due to polarization. Sov. Phys. Solid State 10, 1121 (1968)

    Google Scholar 

  3. 3

    Tagantsev, A. K. Piezoelectricity and flexoelectricity in crystalline dielectrics. Phys. Rev. B 34, 5883–5889 (1986)

    CAS  ADS  Article  Google Scholar 

  4. 4

    Cross, L. E. Flexoelectric effects: charge separation in insulating solids subjected to elastic strain gradients. J. Mater. Sci. 41, 53–63 (2006)

    CAS  ADS  Article  Google Scholar 

  5. 5

    Zubko, P., Catalan, G. & Tagantsev, A. K. Flexoelectric effect in solids. Annu. Rev. Mater. Res. 43, 387–421 (2013)

    CAS  ADS  Article  Google Scholar 

  6. 6

    Ma, W. & Cross, L. E. Flexoelectricity of barium titanate. Appl. Phys. Lett. 88, 232902 (2006)

    ADS  Article  Google Scholar 

  7. 7

    Catalan, G. et al. Flexoelectric rotation of polarization in ferroelectric thin films. Nat. Mater. 10, 963–967 (2011)

    CAS  ADS  Article  Google Scholar 

  8. 8

    Lee, D. et al. Giant flexoelectric effect in ferroelectric epitaxial thin films. Phys. Rev. Lett. 107, 057602 (2011)

    CAS  ADS  Article  Google Scholar 

  9. 9

    Lu, H. et al. Mechanical writing of ferroelectric polarization. Science 336, 59–61 (2012)

    CAS  ADS  Article  Google Scholar 

  10. 10

    Tagantsev, A. K. & Yurkov, A. S. Flexoelectric effect in finite samples. J. Appl. Phys. 112, 044103 (2012)

    ADS  Article  Google Scholar 

  11. 11

    Stengel, M. Microscopic response to inhomogeneous deformations in curvilinear coordinates. Nat. Commun. 4, 2693 (2013)

    ADS  Article  Google Scholar 

  12. 12

    Stengel, M. Surface control of flexoelectricity. Phys. Rev. B 90, 201112 (2014)

    ADS  Article  Google Scholar 

  13. 13

    Hong, J. & Vanderbilt, D. First-principles theory of frozen-ion flexoelectricity. Phys. Rev. B 84, 180101 (2011)

    ADS  Article  Google Scholar 

  14. 14

    Sinclain, D. C., Adams, T. B., Morrison, F. D. & West, A. R. CaCu3Ti4O12: one-step internal barrier layer capacitor. Appl. Phys. Lett. 80, 2153–2155 (2002)

    ADS  Article  Google Scholar 

  15. 15

    Glaister, R. M. Barrier-layer dielectrics. Proc. IEE Part B 109, 423–431 (1962)

    Google Scholar 

  16. 16

    Von Hippel, A. Dielectrics and Waves (Artech House, 1995)

  17. 17

    O’Neill, D., Bowman, R. M. & Gregg, J. M. Dielectric enhancement and Maxwell–Wagner effects in ferroelectric superlattice structures. Appl. Phys. Lett. 77, 1520–1522 (2000)

    ADS  Article  Google Scholar 

  18. 18

    Catalan, G. & Scott, J. F. Magnetoelectrics: is CdCr2S4 a multiferroic relaxor? Nature 448, E4–E5 (2007)

    CAS  ADS  Article  Google Scholar 

  19. 19

    Damjanovic, D., Demartin Maeder, M., Duran Martin, P., Voisard, C. & Setter, N. Maxwell–Wagner piezoelectric relaxation in ferroelectric heterostructures. J. Appl. Phys. 90, 5708–5712 (2001)

    CAS  ADS  Article  Google Scholar 

  20. 20

    Kolodiazhnyi, T. et al. Thermoelectric power, Hall effect, and mobility of n-type BaTiO3 . Phys. Rev. B 68, 085205 (2003)

    ADS  Article  Google Scholar 

  21. 21

    Heywang, W. Semiconducting barium titanate. J. Mater. Sci. 6, 1214–1226 (1971)

    CAS  ADS  Article  Google Scholar 

  22. 22

    Genenko, Y. A., Hirsch, O. & Erhart, P. Surface potential at a ferroelectric grain due to asymmetric screening of depolarization fields. J. Appl. Phys. 115, 104102 (2014)

    ADS  Article  Google Scholar 

  23. 23

    Lee, S. & Randall, C. A. Determination of electronic and ionic conductivity in mixed ionic conductors: HiTEC and in-situ impedance spectroscopy analysis of isovalent and aliovalent doped BaTiO3 . Solid State Ion. 249–250, 86–92 (2013)

    Google Scholar 

  24. 24

    Morozovska, A. N. et al. Thermodynamics of electromechanically coupled mixed ionic-electronic conductors: deformation potential, Vegard strains, and flexoelectric effect. Phys. Rev. B 83, 195313 (2011)

    ADS  Article  Google Scholar 

  25. 25

    Poumellec, B., Marucco, J. F. & Lagnel, F. Electron transport in Ti1–xNbxO2 solid solutions with x < 4%. J. Phys. Chem. Solids 47, 381–385 (1986)

    CAS  ADS  Article  Google Scholar 

  26. 26

    Narvaez, J., Saremi, S., Hong, J., Stengel, M. & Catalan, G. Large flexoelectric anisotropy in paraelectric barium titanate. Phys. Rev. Lett. 115, 037601 (2015)

    ADS  Article  Google Scholar 

  27. 27

    Biancoli, A., Fancher, C. M., Jones, J. L. & Damjanovic, D. Breaking of macroscopic centric symmetry in paraelectric phases of ferroelectric materials and implications for flexoelectricity. Nat. Mater. 14, 224–229 (2015)

    CAS  ADS  Article  Google Scholar 

  28. 28

    Garten, L. M. & Trolier-McKinstry, S. Enhanced flexoelectricity through residual ferroelectricity in barium strontium titanate. J. Appl. Phys. 117, 094102 (2015)

    ADS  Article  Google Scholar 

  29. 29

    Haertling, G. H. Rainbow actuators and sensors: a new smart technology. Proc. SPIE 3040, 81–92 (1997)

    CAS  ADS  Article  Google Scholar 

  30. 30

    Berlincourt, D. & Jaffe, H. Elastic and piezoelectric coefficients of single-crystal barium titanate. Phys. Rev. 111, 143–148 (1958)

    CAS  ADS  Article  Google Scholar 

  31. 31

    Damjanovic, D. Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics. Rep. Prog. Phys. 61, 1267–1324 (1998)

    CAS  ADS  Article  Google Scholar 

  32. 32

    Kaneda, K. et al. Kinetics of oxygen diffusion into multilayer ceramic capacitors during the re-oxidation process and its implications on dielectric properties. J. Am. Ceram. Soc. 94, 3934–3940 (2011)

    CAS  Article  Google Scholar 

  33. 33

    Müller, A. & Härdtl, K. H. Ambipolar diffusion phenomena in BaTiO3 and SrTiO3 . Appl. Phys. A 49, 75–82 (1989)

    ADS  Article  Google Scholar 

  34. 34

    Muller, D. A., Nakagawa, N., Ohtomo, A., Grazul, J. L. & Hwang, H. Y. Atomic-scale imaging of nanoengineered oxygen vacancy profiles in SrTiO3 . Nature 430, 657–661 (2004)

    CAS  ADS  Article  Google Scholar 

  35. 35

    Yang, G. Y., Dickey, E. C., Randall, C. A., Randall, M. S. & Mann, L. A. Modulated and ordered defect structures in electrically degraded Ni–BaTiO3 multilayer ceramic capacitors. J. Appl. Phys. 94, 5990–5996 (2003)

    CAS  ADS  Article  Google Scholar 

  36. 36

    Lee, A. A., Colby, H. H. & Kornyshev, A. A. Statics and dynamics of electroactuation with single-charge-carrier ionomers. J. Phys. Condens. Matter 25, 082203 (2013)

    ADS  Article  Google Scholar 

  37. 37

    Chan, N.-H., Sharma, R. K. & Smyth, D. M. Nonstoichiometry in undoped BaTiO3 . J. Am. Ceram. Soc. 64, 556–562 (1981)

    CAS  Article  Google Scholar 

Download references


This research was funded by an ERC Starting grant from the EU (ERC 308023) and by a national research grant (FIS2013-48668-C2-1-P) from the Spanish MINECO. All research in ICN2 is supported by the Severo Ochoa Excellence Programme (SEV-2013-0295). F.V.-S. thanks MICITT and CONICIT for support during his PhD. We thank D. Torres for the illustration in Fig. 1. Belarre for help with sample polishing and B. Ballesteros for help with the EELS measurements shown in Methods.

Author information




J.N. and G.C. conceived the idea and analysed the results. J.N. and F.V.-S. performed the experiments. G.C. wrote the paper.

Corresponding author

Correspondence to Gustau Catalan.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks E. Eliseev, N. Mathur, D. Vanderbilt and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Effective flexoelectric coefficients of semiconducting crystals of Nb-doped TiO2 (0.05%Nb by weight) as a function of sample thickness.

The red line is a linear fit to the data.

Extended Data Figure 2 EELS analysis.

Top, EELS spectra of a cross-sectional sample of BaTiO3, measured in a transmission electron microscope. There is no monotonic trend as a function of distance to the surface, so no indication that the surface (at least to a depth of 1.4 μm) is any more (or less) oxidized than the bulk. A comparison with the shape of the EELS spectra of SrTiO3−δ (bottom-left; image reproduced from ref. 34, Macmillan Publishers Limited) or BaTiO3−δ (bottom-right; reprinted from ref. 35, with the permission of AIP Publishing) is consistent with δ ≤ 0.14 for our crystals.

Extended Data Figure 3 Consecutive measurements of the flexoelectric coefficient for semiconducting BaTiO3−δ.

Extended Data Figure 4 Conductivity of BaTiO3−δ.

Total conductivity σ = σelectron + σion measured across the capacitor structure.

Extended Data Figure 5 Flexoelectricity of undoped TiO2 and Nb-doped TiO2.

The conducting Nb-doped sample (right) displays an effective flexoelectricity that is >2,000 times larger than the insulating sample (left). Note that the units are nC m−1 and μC m−1 for TiO2 and Nb-TiO2 respectively.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Narvaez, J., Vasquez-Sancho, F. & Catalan, G. Enhanced flexoelectric-like response in oxide semiconductors. Nature 538, 219–221 (2016). https://doi.org/10.1038/nature19761

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Sign up for the Nature Briefing newsletter for a daily update on COVID-19 science.
Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing