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A flexoelectric microelectromechanical system on silicon

Abstract

Flexoelectricity allows a dielectric material to polarize in response to a mechanical bending moment1 and, conversely, to bend in response to an electric field2. Compared with piezoelectricity, flexoelectricity is a weak effect of little practical significance in bulk materials. However, the roles can be reversed at the nanoscale3. Here, we demonstrate that flexoelectricity is a viable route to lead-free microelectromechanical and nanoelectromechanical systems. Specifically, we have fabricated a silicon-compatible thin-film cantilever actuator with a single flexoelectrically active layer of strontium titanate with a figure of merit (curvature divided by electric field) of 3.33 MV−1, comparable to that of state-of-the-art piezoelectric bimorph cantilevers.

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Figure 1: Schematic comparing flexoelectric actuation and piezoelectric bimorph actuation in nanoscale actuators.
Figure 2: Experimental design.
Figure 3: Experimental characterization of flexoelectricity as a function of frequency and electric field.
Figure 4: Comparison of the performance of flexoelectric SrTiO3 with those of state-of-the-art piezoelectric bimorphs.

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References

  1. Kogan, S. Piezoelectric effect during inhomogeneous deformation and acoustic scattering of carriers in crystals. Sov. Phys. Solid State 5, 2069–2079 (1964).

    Google Scholar 

  2. Bursian, E. & Trunov, N. Nonlocal piezoelectric effect. Sov. Phys. Solid State 16, 760–762 (1974).

    Google Scholar 

  3. Gregg, J. M. Stressing ferroelectrics. Science 336, 41–42 (2012).

    Article  Google Scholar 

  4. Majdoub, M., Sharma, P. & Çağin, T. Dramatic enhancement in energy harvesting for a narrow range of dimensions in piezoelectric nanostructures. Phys. Rev. B 78, 121407 (2008).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  7. Cross, E. Lead-free at last. Nature 32, 24–25 (2004).

    Article  Google Scholar 

  8. Dreyfus, R. et al. Microscopic artificial swimmers. Nature 437, 862–865 (2005).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  10. 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. Nature Mater. 14, 224–229 (2014).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Breger, L., Furukawa, T. & Fukada, E. Bending piezoelectricity in polyvinylidene fluoride. Jpn J. Appl. Phys. 15, 2239–2240 (1976).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  14. Bursian, E. & Zaikovskii, O. I. Changes in curvature of ferroelectric film due to polarization. Sov. Phys. Solid State 10, 1121–1124 (1968).

    Google Scholar 

  15. Abdollahi, A., Peco, C., Millán, D., Arroyo, M. & Arias, I. Computational evaluation of the flexoelectric effect in dielectric solids. J. Appl. Phys. 116, 093502 (2014).

    Article  Google Scholar 

  16. Zalesskii, V. G. & Rumyantseva, E. D. Converse flexoelectric effect in the SrTiO3 single crystal. Phys. Solid State 56, 1352–1354 (2014).

    Article  CAS  Google Scholar 

  17. Deng, Q., Liu, L. & Sharma, P. Electrets in soft materials: nonlinearity, size effects, and giant electromechanical coupling. Phys. Rev. E 90, 012603 (2014).

    Article  Google Scholar 

  18. Baek, S.-H. & Eom, C.-B. Epitaxial integration of perovskite-based multifunctional oxides on silicon. Acta Mater. 61, 2734–2750 (2013).

    Article  CAS  Google Scholar 

  19. Cotte, Y., Toy, F., Jourdain, P. & Pavillon, N. Marker-free phase nanoscopy. Nature Photon. 7, 113–117 (2013).

    Article  CAS  Google Scholar 

  20. Colomb, T., Krivec, S. & Hutter, H. Digital holographic reflectometry. Opt. Express 21, 12643–12650 (2013).

    Article  Google Scholar 

  21. Dekkers, M. et al. The significance of the piezoelectric coefficient d31,eff determined from cantilever structures. J. Micromech. Microeng. 23, 025008 (2013).

    Article  Google Scholar 

  22. Narvaez, J. & Catalan, G. Origin of the enhanced flexoelectricity of relaxor ferroelectrics. Appl. Phys. Lett. 104, 162903 (2014).

    Article  Google Scholar 

  23. Wang, P., Du, H., Shen, S., Zhang, M. & Liu, B. Preparation and characterization of ZnO microcantilever for nanoactuation. Nanoscale Res. Lett. 7, 176 (2012).

    Article  CAS  Google Scholar 

  24. Doll, J. C., Petzold, B. C., Ninan, B., Mullapudi, R. & Pruitt, B. L. Aluminum nitride on titanium for CMOS compatible piezoelectric transducers. J. Micromech. Microeng. 20, 025008 (2009).

    Article  Google Scholar 

  25. Baek, S. H. et al. Giant piezoelectricity on Si for hyperactive MEMS. Science 334, 958–961 (2011).

    Article  CAS  Google Scholar 

  26. Zaghloul, U. & Piazza, G. 10–25 NM piezoelectric nano-actuators and NEMS switches for millivolt computational logic. Proc. IEEE Int. Conf. Micro Electro Mech. Syst. 233–236 http://dx.doi.org/10.1109/MEMSYS.2013.6474220 (2013).

  27. Banerjee, N., Koster, G. & Rijnders, G. Submicron patterning of epitaxial PbZr0.52Ti0.48O3 heterostructures. Appl. Phys. Lett. 102, 142909 (2013).

    Article  Google Scholar 

  28. Warusawithana, M. P. et al. A ferroelectric oxide made directly on silicon. Science 324, 367–370 (2009).

    Article  CAS  Google Scholar 

  29. Banerjee, N., Houwman, E. P., Koster, G. & Rijnders, G. Fabrication of piezodriven, free-standing, all-oxide heteroepitaxial cantilevers on silicon. APL Mater. 2, 096103 (2014).

    Article  Google Scholar 

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Acknowledgements

The work at ICN2 was funded by an ERC Starting Grant from the EU (Project No. 308023), a National Plan grant from Spain (FIS2013-48668-C2-1-P) and the Severo Ochoa Excellence programme. The work at Cornell University was supported by the National Science Foundation (Nanosystems Engineering Research Center for Translational Applications of Nanoscale Multiferroic Systems) under grant number EEC-1160504. The authors thank E. Cuche, J. Parent, E. Solanas and Y. Emery for discussions.

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Authors

Contributions

G.C. and U.B. conceived and designed the experiments. N.B. designed and made the cantilevers under the supervision of G.R. U.B. performed and analysed the inverse flexoelectric characterizations under the supervision of G.C. A.A. performed the self-consistent continuum modelling and simulations. Z.W. performed the molecular beam epitaxy growth of the template layer under the supervision of D.S. U.B. and G.C. wrote the paper with the help of all the other authors. All authors discussed the results, commented on the manuscript and gave their approval to the final version of the manuscript.

Corresponding authors

Correspondence to Umesh Kumar Bhaskar or Gustau Catalan.

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The authors declare no competing financial interests.

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Bhaskar, U., Banerjee, N., Abdollahi, A. et al. A flexoelectric microelectromechanical system on silicon. Nature Nanotech 11, 263–266 (2016). https://doi.org/10.1038/nnano.2015.260

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