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.
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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.
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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
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