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.
Subscribe to Journal
Get full journal access for 1 year
only $3.90 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Kogan, S. M. Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals. Sov. Phys. Solid State 5, 2069–2070 (1964)
Bursian, E. & Zaikovskii, O. I. Changes in curvature of ferroelectric film due to polarization. Sov. Phys. Solid State 10, 1121 (1968)
Tagantsev, A. K. Piezoelectricity and flexoelectricity in crystalline dielectrics. Phys. Rev. B 34, 5883–5889 (1986)
Cross, L. E. Flexoelectric effects: charge separation in insulating solids subjected to elastic strain gradients. J. Mater. Sci. 41, 53–63 (2006)
Zubko, P., Catalan, G. & Tagantsev, A. K. Flexoelectric effect in solids. Annu. Rev. Mater. Res. 43, 387–421 (2013)
Ma, W. & Cross, L. E. Flexoelectricity of barium titanate. Appl. Phys. Lett. 88, 232902 (2006)
Catalan, G. et al. Flexoelectric rotation of polarization in ferroelectric thin films. Nat. Mater. 10, 963–967 (2011)
Lee, D. et al. Giant flexoelectric effect in ferroelectric epitaxial thin films. Phys. Rev. Lett. 107, 057602 (2011)
Lu, H. et al. Mechanical writing of ferroelectric polarization. Science 336, 59–61 (2012)
Tagantsev, A. K. & Yurkov, A. S. Flexoelectric effect in finite samples. J. Appl. Phys. 112, 044103 (2012)
Stengel, M. Microscopic response to inhomogeneous deformations in curvilinear coordinates. Nat. Commun. 4, 2693 (2013)
Stengel, M. Surface control of flexoelectricity. Phys. Rev. B 90, 201112 (2014)
Hong, J. & Vanderbilt, D. First-principles theory of frozen-ion flexoelectricity. Phys. Rev. B 84, 180101 (2011)
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)
Glaister, R. M. Barrier-layer dielectrics. Proc. IEE Part B 109, 423–431 (1962)
Von Hippel, A. Dielectrics and Waves (Artech House, 1995)
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)
Catalan, G. & Scott, J. F. Magnetoelectrics: is CdCr2S4 a multiferroic relaxor? Nature 448, E4–E5 (2007)
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)
Kolodiazhnyi, T. et al. Thermoelectric power, Hall effect, and mobility of n-type BaTiO3 . Phys. Rev. B 68, 085205 (2003)
Heywang, W. Semiconducting barium titanate. J. Mater. Sci. 6, 1214–1226 (1971)
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)
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)
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)
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)
Narvaez, J., Saremi, S., Hong, J., Stengel, M. & Catalan, G. Large flexoelectric anisotropy in paraelectric barium titanate. Phys. Rev. Lett. 115, 037601 (2015)
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)
Garten, L. M. & Trolier-McKinstry, S. Enhanced flexoelectricity through residual ferroelectricity in barium strontium titanate. J. Appl. Phys. 117, 094102 (2015)
Haertling, G. H. Rainbow actuators and sensors: a new smart technology. Proc. SPIE 3040, 81–92 (1997)
Berlincourt, D. & Jaffe, H. Elastic and piezoelectric coefficients of single-crystal barium titanate. Phys. Rev. 111, 143–148 (1958)
Damjanovic, D. Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics. Rep. Prog. Phys. 61, 1267–1324 (1998)
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)
Müller, A. & Härdtl, K. H. Ambipolar diffusion phenomena in BaTiO3 and SrTiO3 . Appl. Phys. A 49, 75–82 (1989)
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)
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)
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)
Chan, N.-H., Sharma, R. K. & Smyth, D. M. Nonstoichiometry in undoped BaTiO3 . J. Am. Ceram. Soc. 64, 556–562 (1981)
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.
The authors declare no competing financial interests.
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.
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.
Total conductivity σ = σelectron + σion measured across the capacitor structure.
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.
About this article
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
Advanced Functional Materials (2020)
Acta Materialia (2020)
Acta Materialia (2020)
Self-powered broadband photo-detection and persistent energy generation with junction-free strained Bi2Te3 thin films
Optics Express (2020)
Advanced Materials Interfaces (2020)