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# Piezoelectric and pyroelectric effects induced by interface polar symmetry

## Abstract

Interfaces in heterostructures have been a key point of interest in condensed-matter physics for decades owing to a plethora of distinctive phenomena—such as rectification1, the photovoltaic effect2, the quantum Hall effect3 and high-temperature superconductivity4—and their critical roles in present-day technical devices. However, the symmetry modulation at interfaces and the resultant effects have been largely overlooked. Here we show that a built-in electric field that originates from band bending at heterostructure interfaces induces polar symmetry therein that results in emergent functionalities, including piezoelectricity and pyroelectricity, even though the component materials are centrosymmetric. We study classic interfaces—namely, Schottky junctions—formed by noble metal and centrosymmetric semiconductors, including niobium-doped strontium titanium oxide crystals, niobium-doped titanium dioxide crystals, niobium-doped barium strontium titanium oxide ceramics, and silicon. The built-in electric field in the depletion region induces polar structures in the semiconductors and generates substantial piezoelectric and pyroelectric effects. In particular, the pyroelectric coefficient and figure of merit of the interface are over one order of magnitude larger than those of conventional bulk polar materials. Our study enriches the functionalities of heterostructure interfaces, offering a distinctive approach to realizing energy transduction beyond the conventional limitation imposed by intrinsic symmetry.

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## Data availability

The data that support the findings of this study are available at the University of Warwick open access research repository (http://wrap.warwick.ac.uk/136971) or from the corresponding authors upon request. Source data are provided with this paper.

## References

1. Sze, S. M. & Ng, K. K. Physics of Semiconductor Devices (John Wiley & Sons, 2006).

2. Fahrenbruch, A. & Bube, R. Fundamentals of Solar Cells: Photovoltaic Solar Energy Conversion (Academic Press, 1983).

3. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).

4. Gozar, A. et al. High-temperature interface superconductivity between metallic and insulating copper oxides. Nature 455, 782–785 (2008).

5. Livio, M. Why symmetry matters. Nature 490, 472–473 (2012).

6. Mason, W. P. & Baerwald, H. Piezoelectric Crystals and their Applications to Ultrasonics (D. Van Nostrand Company, 1950).

7. Whatmore, R. Pyroelectric devices and materials. Rep. Prog. Phys. 49, 1335–1386 (1986).

8. Nye, J. F. Physical Properties of Crystals: Their Representation by Tensors and Matrices (Oxford Univ. Press, 1985).

9. Bir, G. L. & Pikus, G. E. Symmetry and Strain-induced Effects in Semiconductors (John Wiley & Sons, 1974).

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

11. Zubko, P., Catalan, G., Buckley, A., Welche, P. R. & Scott, J. F. Strain-gradient-induced polarization in SrTiO3 single crystals. Phys. Rev. Lett. 99, 167601 (2007).

12. Narvaez, J., Vasquez-Sancho, F. & Catalan, G. Enhanced flexoelectric-like response in oxide semiconductors. Nature 538, 219–221 (2016).

13. Yang, M.-M., Kim, D. J. & Alexe, M. Flexo-photovoltaic effect. Science 360, 904–907 (2018).

14. Yang, M. M., Iqbal, A. N., Peters, J. J. P., Sanchez, A. M. & Alexe, M. Strain-gradient mediated local conduction in strained bismuth ferrite films. Nat. Commun. 10, 2791 (2019).

15. Meirzadeh, E. et al. Surface pyroelectricity in cubic SrTiO3. Adv. Mater. 31, 1904733 (2019).

16. Cheong, S.-W. SOS: symmetry-operational similarity. npj Quantum Mater. 4, 53 (2019).

17. Papadakis, S., De Poortere, E., Manoharan, H., Shayegan, M. & Winkler, R. J. S. The effect of spin splitting on the metallic behavior of a two-dimensional system. Science 283, 2056–2058 (1999).

18. Wu, S. et al. Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS2. Nat. Phys. 9, 149–153 (2013).

19. Yuan, H. et al. Generation and electric control of spin-valley-coupled circular photogalvanic current in WSe2. Nat. Nanotechnol. 9, 851–857 (2014).

20. Suzuki, S. et al. Fabrication and characterization of Ba1−xKxBiO3/Nb-doped SrTiO3 all-oxide-type Schottky junctions. J. Appl. Phys. 81, 6830–6836 (1997).

21. Kavasov, A. & Tagantsev, A. K. Positive effective Q 12 electrostrictive coefficient in perovskites. J. Appl. Phys. 112, 094106 (2012).

22. Yamada, T., Niizeki, N. & Toyoda, H. Piezoelectric and elastic properties of lithium niobate single crystals. Jpn J. Appl. Phys. 6, 151–155 (1967).

23. Samara, G. A. Pressure and temperature dependences of the dielectric properties of the perovskites BaTiO3 and SrTiO3. Phys. Rev. 151, 378–386 (1966).

24. 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).

25. Kobiakov, I. B. Elastic, piezoelectric and dielectric properties of ZnO and CdS single crystals in a wide range of temperatures. Solid State Commun. 35, 305–310 (1980).

26. Chen, B. et al. Large electrostrictive response in lead halide perovskites. Nat. Mater. 17, 1020–1026 (2018); correction 17, 1164 (2018).

27. Mangalam, R. V. K., Agar, J. C., Damodaran, A. R., Karthik, J. & Martin, L. W. Improved pyroelectric figures of merit in compositionally graded PbZr1−xTixO3 thin films. ACS Appl. Mater. Interfaces 5, 13235–13241 (2013).

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

29. Tagantsev, A. K., Sherman, V. O., Astafiev, K. F., Venkatesh, J. & Setter, N. Ferroelectric materials for microwave tunable applications. J. Electroceram. 11, 5–66 (2003).

30. Schranz, W., Sondergeld, P., Kityk, A. & Salje, E. K. H. Elastic properties of SrTiO3 crystals at ultralow frequencies. Phase Transit. 69, 61–76 (1999).

31. Grimsditch, M. & Ramdas, A. Elastic and elasto-optic constants of rutile from a Brillouin scattering study. Phys. Rev. B 14, 1670–1682 (1976).

32. Mason, W. P. Physical acoustics and the properties of solids. J. Acoust. Soc. Am. 28, 1197–1206 (1956).

33. Kaushal, A., Olhero, S. M., Antunes, P., Ramalho, A. & Ferreira, J. M. F. Structural, mechanical and dielectric properties of Ba0.6Sr0.4TiO3—the benefits of a colloidal processing approach. Mater. Res. Bull. 50, 329–336 (2014).

34. Poindexter, E. & Giardini, A. A. Elastic constant of strontium titanate (SrTiO3). Phys. Rev. 110, 1069 (1958).

35. Wachtman, J. B., Tefft, W. E. & Lam, D. G. Elastic constants of rutile (TiO2). J. Res. Natl Bur. Stand. A 66A, 465–471 (1962).

36. Durán, A., Morales, F., Fuentes, L. & Siqueiros, J. M. Specific heat anomalies at 37, 105 and 455 K in SrTiO3:Pr. J. Phys. Condens. Matter 20, 085219 (2008).

37. Devonshire, A. F. Theory of ferroelectrics. Adv. Phys. 3, 85–130 (1954).

## Acknowledgements

M.A. acknowledges the Theo Murphy Blue-sky Awards of Royal Society. The work was partly supported by the EPSRC (UK) through grant numbers EP/M022706/1, EP/P031544/1 and EP/P025803/1. Z.M. and J.Z. acknowledge the National Natural Science Foundation of China (11772207); Natural Science Foundation of Hebei Province for Distinguished Young Scholar (A2019210204) and Shenzhen Peacock Team Program (KQTD20170810160424889). We acknowledge the discussion with H. Zhang, A. N. Iqbal and F. Zhuge; and the technical support from M. Crosbie.

## Author information

Authors

### Contributions

M.-M.Y. and M.A. conceived the idea, designed the experiments, collected the data and wrote the manuscript. M.-M.Y. developed the theory. Z.-D.L., Z.M. J.Z. and S.P.E. were involved in sample preparation.

### Corresponding authors

Correspondence to Ming-Min Yang or Marin Alexe.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Long-Qing Chen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Electrical-field-engineered symmetry in (001)-oriented Nb:SrTiO3 and Nb:TiO2 crystals.

a, Schematic showing the common group of the $$m\bar{3}m$$ point group and the ∞m group. b, Schematic showing the common group of the 4/mmm point group and the ∞m group. Only the rotation symmetry elements are shown here while the mirror symmetry elements are omitted. The dome symbol represents the intersect operation.

### Extended Data Fig. 2 Microscopic processes of interface piezoelectric and pyroelectric effects.

a, The electric polarization and compensating charges of the Schottky junction in the equilibrium state. b, Charge redistribution when the junction is subjected to a tensile stress. c, The charge redistribution when subjecting to heating. The piezoelectric and pyroelectric effects persist whenever there is a depletion region with a built-in field. However, another factor, that is, the effective barrier, which assures good insulating properties in reverse-bias conditions, is critical for the ability of the junction to deliver displacive current and consequently to output electricity. If the barrier becomes leaky, for example, by further increased temperature, the re-distribution of charge carriers will happen by electron transmission directly cross the interface via either tunnelling or thermionic emission. In this case, the pyroelectric effect might still be there, but it is screened by alternative conducting channels. This is to a certain extent similar to the situation of a solar cell affected by a low shunt resistance.

### Extended Data Fig. 3 Electric characterization of the Al/Nb:SrTiO3/Al and Au/Nb:TiO2 junctions.

a, C−2V curve of the Au/Nb:SrTiO3 junction in a large voltage range. The red dots are the measured data and the blue line is the linear fit near zero voltage. bd, Current–voltage curves of the Al/Nb:SrTiO3/Al (b), Au/Nb:TiO2/Al (c) and Al/Nb:TiO2/Al (d) heterostructures. e, C−2V curve of the Au/Nb:TiO2/Al junction. The red dots are the measured data and the blue line is the linear fit near zero voltage. f, The C−2V curve of the Au/Nb:TiO2/Al junction and its linear fit near zero voltage. Given the dopant density of 3.4 × 1025 m−3 in Nb:TiO2, this fit indicates that the effective permittivity of the Au/Nb:TiO2 junction is 1.02 × 10−9 C V m−1 and a built-in potential of 1.45 V. As we are mainly concerned here with the piezoelectric effect of the Schottky junctions without applying bias (that is, near-zero voltage), the electrical parameters derived by fitting around the zero-voltage bias give a good description of the junction properties and lead to a quantitative prediction of the piezoelectric effect consistent with experimental results.

### Extended Data Fig. 4 Current output by the Nb:SrTiO3 and Nb:TiO2 crystals with Ohmic contacts and charges generated in Schottky junctions.

a, b, Current density generated by the the Al/Nb:SrTiO3/Al heterostructure (a) and the Al/Nb:TiO2/Al heterostructure (b) under the stimuli of external stress. Clearly, the current density waveforms generated in the crystals with Ohmic contacts show not only a low magnitude compared with that shown in Fig. 2 but also an irregular time dependence. This demonstrates both crystals with Ohmic contacts have no piezoelectric effect. c, d, Charge waveforms generated in Au/Nb:SrTiO3/Al junction driven by dynamic stress (c) and temperature (d) by integrating the generated current with respect to time in Figs. 2b, 3a.

### Extended Data Fig. 5 Electric characterization of the Au/Nb:Ba0.6Sr0.4TiO3 junction.

a, Temperature-dependent dielectric constant of the insulating Ba0.6Sr0.4TiO3 ceramic. b, Current density–voltage curve. c, Capacitance–voltage curve of the Au/Nb:Ba0.6Sr0.4TiO3 junction.

### Extended Data Fig. 6 Negligible piezoelectricity in Ohmic contacted ceramics.

a, The current density output by the Au/Nb:Ba0.6Sr0.4TiO3/Ga-In (black line) and Ga-In/Nb:Ba0.6Sr0.4TiO3/Ga-In (red line) driven by sinusoidally varied stress (top). b, The current density generated by the Ga–In/Ba0.6Sr0.4TiO3/Ga–In heterojunctions under sinusoidally varied stress. Note that the current density amplitude observed in both ceramics with only Ohmic contacts are three to four order of magnitude smaller than that generated in the Au/Nb:Ba0.6Sr0.4TiO3 junction, demonstrating the essential role of the Schottky contact in the induced piezoelectric effect.

.

### Extended Data Fig. 8 Converse piezoelectric effect characterization.

a, Schematic showing the measurement setup. b, Force–distance curve of PPP-EFM-50 (Nanosensors) on the Au/Nb:SrTiO3. Z is the distance moved by the AFM tip stage.

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Yang, MM., Luo, ZD., Mi, Z. et al. Piezoelectric and pyroelectric effects induced by interface polar symmetry. Nature 584, 377–381 (2020). https://doi.org/10.1038/s41586-020-2602-4

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• DOI: https://doi.org/10.1038/s41586-020-2602-4

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