Skip to main content

Nanomechanics of Ferroelectric Thin Films and Heterostructures

  • Chapter
  • First Online:
Multiscale Materials Modeling for Nanomechanics

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 245))

  • 3416 Accesses

Abstract

The focus of this chapter is to provide basic concepts of how externally applied stresses and strains alter the ferroelectric properties of a material and how to quantitatively evaluate these effects on the phase stability, domain structure, and material properties of ferroelectrics using the phase field method. The chapter starts with a brief introduction of ferroelectrics and the Landau–Devonshire description of ferroelectric transitions and ferroelectric phases in a homogeneous ferroelectric single crystal. Due to the fact that ferroelectric transitions involve changes in crystal structure in conjunction with domain formation, strains and stresses can be produced inside of the material if a ferroelectric transition occurs under physical confinement. These stresses and strains, in turn, affect the domain structure and material ferroelectric properties. Therefore, ferroelectric and mechanical properties are coupled to each other. The ferroelectric–mechanical coupling can be used to engineer the ferroelectric material properties by designing the phase and structure of the material. The following section details the calculations of the stresses, strains, and elastic energy of a thin film containing a single domain, a twinned domain, as well as complicated multidomains that are constrained by the underlying substrate. Furthermore, a phase field model for predicting ferroelectric stable phases and domain structure in a thin film is presented. This phase field model is then used to demonstrate how substrate constraint and temperature be used to obtain interesting ferroelectric domain structures in BaTiO3 films.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. J. Valasek, Piezoelectric and allied phenomena in Rochelle salt. Phys. Rev. 15, 537–538 (1920)

    Google Scholar 

  2. H.F. Kay, P. Vousden, Symmetry changes in barium titanate at low temperatures and their relation to its ferroelectric properties. Philos. Mag. 40, 1019–1040 (1949)

    Article  Google Scholar 

  3. W.J. Merz, The electric and optical behavior of BaTiO3 single-domain crystals. Phys. Rev. 76, 1221–1225 (1949)

    Article  Google Scholar 

  4. Y. Yoneda, T. Okabe, K. Sakaue, H. Terauchi, H. Kasatani, K. Deguchi, Structural characterization of BaTiO3 thin films grown by molecular beam epitaxy. J. Appl. Phys. 83, 2458–2461 (1998)

    Article  Google Scholar 

  5. N.A. Pertsev, A.G. Zembilgotov, A.K. Tagantsev, Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films. Phys. Rev. Lett. 80, 1988–1991 (1998)

    Article  Google Scholar 

  6. K.J. Choi, M. Biegalski, Y.L. Li, A. Sharan, J. Schubert, R. Uecker, P. Reiche, Y.B. Chen, X.Q. Pan, V. Gopalan, L.Q. Chen, D.G. Schlom, C.B. Eom, Enhancement of ferroelectricity in strained BaTiO3 thin films. Science 306, 1005–1009 (2004)

    Article  Google Scholar 

  7. Y.L. Li, L.Q. Chen, Temperature-strain phase diagram for BaTiO3 thin films. Appl. Phys. Lett. 88, 072905 (2006)

    Article  Google Scholar 

  8. D.A. Tenne, X.X. Xi, Y.L. Li, L.Q. Chen, A. Soukiassian, M.H. Zhu, A.R. James, J. Lettieri, D.G. Schlom, W. Tian, X.Q. Pan, Absence of low-temperature phase transitions in epitaxial BaTiO3 thin films. Phys. Rev. B 69, 174101 (2004)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. A.F. Devonshire, Theory of barium titanate 1. Philos. Mag. 40, 1040–1063 (1949)

    Article  Google Scholar 

  11. F. Jona, G. Shirane, Ferroelectric Crystals (Pergamon, Oxford, New York, 1962)

    Google Scholar 

  12. Y.L. Li, L.E. Cross, L.Q. Chen, A phenomenological thermodynamic potential for BaTiO3 single crystals. J. Appl. Phys. 98, 064101 (2005)

    Article  Google Scholar 

  13. A.F. Devonshire, Theory of barium titanate 2. Philos. Mag. 42, 1065–1079 (1951)

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. T. Yamada, Electromechanical properties of oxygen-octahedra ferroelectric crystals. J. Appl. Phys. 43, 328–338 (1972)

    Article  Google Scholar 

  16. V.G. Koukhar, N.A. Pertsev, R. Waser, Thermodynamic theory of epitaxial ferroelectric thin films with dense domain structures. Phys. Rev. B 64, 214103 (2001)

    Article  Google Scholar 

  17. Y.L. Li, S.Y. Hu, Z.K. Liu, L.Q. Chen, Effect of substrate constraint on the stability and evolution of ferroelectric domain structures in thin films. Acta Mater. 50, 395–411 (2002)

    Article  Google Scholar 

  18. Y.L. Li, S.Y. Hu, Z.K. Liu, L.Q. Chen, Phase-field model of domain structures in ferroelectric thin films. Appl. Phys. Lett. 78, 3878–3880 (2001)

    Article  Google Scholar 

  19. Y.L. Li, S.Y. Hu, Z.K. Liu, L.Q. Chen, Effect of electrical boundary conditions on ferroelectric domain structures in thin films. Appl. Phys. Lett. 81, 427–429 (2002)

    Article  Google Scholar 

  20. L.Q. Chen, Phase-field models for microstructure evolution. Annu. Rev. Mater. Res. 32, 113–140 (2002)

    Article  Google Scholar 

  21. Y.L. Li, S. Choudhury, Z.K. Liu, L.Q. Chen, Effect of external mechanical constraints on the phase diagram of epitaxial PbZr1-x Ti x O3 thin films: thermodynamic calculations and phase-field simulations. Appl. Phys. Lett. 83, 1608–1610 (2003)

    Article  Google Scholar 

  22. A. Artemev, Phase field modeling of domain structures and P–E hysteresis in thin ferroelectric layers with deadlayers. Philos. Mag. 90, 89–101 (2010)

    Article  Google Scholar 

  23. A. Artemev, B. Geddes, J. Slutsker, A. Roytburd, Thermodynamic analysis and phase field modeling of domain structures in bilayer ferroelectric thin films. J. Appl. Phys. 103, 074104 (2008)

    Article  Google Scholar 

  24. W.J. Chen, Y. Zheng, B. Wang, Phase field simulations of stress controlling the vortex domain structures in ferroelectric nanosheets. Appl. Phys. Lett. 100, 062901 (2012)

    Article  Google Scholar 

  25. P. Chu, D.P. Chen, J.M. Liu, Multiferroic domain structure in orthorhombic multiferroics of cycloidal spin order: phase field simulations. Appl. Phys. Lett. 101, 042908 (2012)

    Article  Google Scholar 

  26. K. Dayal, K. Bhattacharya, A real-space non-local phase-field model of ferroelectric domain patterns in complex geometries. Acta Mater. 55, 1907–1917 (2007)

    Article  Google Scholar 

  27. W.D. Dong, D.M. Pisani, C.S. Lynch, A finite element based phase field model for ferroelectric domain evolution. Smart Mater. Struct. 21, 094014 (2012)

    Article  Google Scholar 

  28. C. Fang, Phase-field simulation study on size effect of the microstructure evolution of a single-domain barium titanate 2D lattice square. Phys. Status Solidi B 251, 1619–1629 (2014)

    Article  Google Scholar 

  29. T. Koyama, H. Onodera, Phase-field simulation of ferroelectric domain microstructure changes in BatiO3. Mater. Trans. 50, 970–976 (2009)

    Article  Google Scholar 

  30. P.L. Liu, J. Wang, T.Y. Zhang, Y. Li, L.Q. Chen, X.Q. Ma, W.Y. Chu, L.J. Qiao, Effects of unequally biaxial misfit strains on polarization phase diagrams in embedded ferroelectric thin layers: phase field simulations. Appl. Phys. Lett. 93, 132908 (2008)

    Article  Google Scholar 

  31. D.C. Ma, Y. Zheng, C.H. Woo, Phase-field simulation of domain structure for PbTiO3/SrTiO3 superlattices. Acta Mater. 57, 4736–4744 (2009)

    Article  Google Scholar 

  32. G. Sheng, J.X. Zhang, Y.L. Li, S. Choudhury, Q.X. Jia, Z.K. Liu, L.Q. Chen, Domain stability of PbTiO3 thin films under anisotropic misfit strains: phase-field simulations. J. Appl. Phys. 104, 054105 (2008)

    Article  Google Scholar 

  33. Y. Shindo, F. Narita, T. Kobayashi, Phase field simulation on the electromechanical response of poled barium titanate polycrystals with oxygen vacancies. J. Appl. Phys. 117, 234103 (2015)

    Article  Google Scholar 

  34. B. Winchester, P. Wu, L.Q. Chen, Phase-field simulation of domain structures in epitaxial BiFeO3 films on vicinal substrates. Appl. Phys. Lett. 99, 052903 (2011)

    Article  Google Scholar 

  35. P.P. Wu, X.Q. Ma, J.X. Zhang, L.Q. Chen, Phase-field model of multiferroic composites: domain structures of ferroelectric particles embedded in a ferromagnetic matrix. Philos. Mag. 90, 125–140 (2010)

    Article  Google Scholar 

  36. F. Xue, J.J. Wang, G. Sheng, E. Huang, Y. Cao, H.H. Huang, P. Munroe, R. Mahjoub, Y.L. Li, V. Nagarajan, L.Q. Chen, Phase field simulations of ferroelectrics domain structures in PbZr x Ti1-x O3 bilayers. Acta Mater. 61, 2909–2918 (2013)

    Article  Google Scholar 

  37. L.-Q. Chen, Phase-field method of phase transitions/domain structures in ferroelectric thin films: a review. J. Am. Ceram. Soc. 91, 1835–1844 (2008)

    Article  Google Scholar 

  38. L.Q. Chen, J. Shen, Applications of semi-implicit Fourier-spectral method to phase field equations. Comput. Phys. Commun. 108, 147–158 (1998)

    Article  Google Scholar 

  39. J. Fousek, V. Janovec, Orientation of domain walls in twinned ferroelectric crystals. J. Appl. Phys. 40, 135–142 (1969)

    Article  Google Scholar 

  40. J.H. Haeni, P. Irvin, W. Chang, R. Uecker, P. Reiche, Y.L. Li, S. Choudhury, W. Tian, M.E. Hawley, B. Craigo, A.K. Tagantsev, X.Q. Pan, S.K. Streiffer, L.Q. Chen, S.W. Kirchoefer, J. Levy, D.G. Schlom, Room-temperature ferroelectricity in strained SrTiO3. Nature 430, 758–761 (2004)

    Article  Google Scholar 

  41. D.A. Tenne, A. Bruchhausen, N.D. Lanzillotti-Kimura, A. Fainstein, R.S. Katiyar, A. Cantarero, A. Soukiassian, V. Vaithyanathan, J.H. Haeni, W. Tian, D.G. Schlom, K.J. Choi, D.M. Kim, C.B. Eom, H.P. Sun, X.Q. Pan, Y.L. Li, L.Q. Chen, Q.X. Jia, S.M. Nakhmanson, K.M. Rabe, X.X. Xi, Probing nanoscale ferroelectricity by ultraviolet Raman spectroscopy. Science 313, 1614–1616 (2006)

    Article  Google Scholar 

  42. D.G. Schlom, L.-Q. Chen, C.-B. Eom, K.M. Rabe, S.K. Streiffer, J.-M. Triscone, Strain tuning of ferroelectric thin films. Annu. Rev. Mater. Res. 37, 589–626 (2007)

    Article  Google Scholar 

  43. D.G. Schlom, L.-Q. Chen, C.J. Fennie, V. Gopalan, D.A. Muller, X. Pan, R. Ramesh, R. Uecker, Elastic strain engineering of ferroic oxides. MRS Bull. 39, 118–130 (2014)

    Article  Google Scholar 

  44. G. Sheng, J.M. Hu, J.X. Zhang, Y.L. Li, Z.K. Liu, L.Q. Chen, Phase-field simulations of thickness-dependent domain stability in PbTiO3 thin films. Acta Mater. 60, 3296–3301 (2012)

    Article  Google Scholar 

  45. Y.L. Li, S.Y. Hu, L.Q. Chen, Ferroelectric domain morphologies of (001) PbZr1-x Ti x O3 epitaxial thin films. J. Appl. Phys. 97, 034112 (2005)

    Article  Google Scholar 

  46. Y. Cao, G. Sheng, J.X. Zhang, S. Choudhury, Y.L. Li, C.A. Randall, L.Q. Chen, Piezoelectric response of single-crystal PbZr1-x Ti x O3 near morphotropic phase boundary predicted by phase-field simulation. Appl. Phys. Lett. 97, 252904 (2010)

    Article  Google Scholar 

  47. S. Choudhury, Y.L. Li, L.Q. Chen, A phase diagram for epitaxial PbZr1-x Ti x O3 thin films at the bulk morphotropic boundary composition. J. Am. Ceram. Soc. 88, 1669–1672 (2005)

    Article  Google Scholar 

  48. Y.L. Li, S. Choudhury, J.H. Haeni, M.D. Biegalski, A. Vasudevarao, A. Sharan, H.Z. Ma, J. Levy, V. Gopalan, S. Trolier-McKinstry, D.G. Schlom, Q.X. Jia, L.Q. Chen, Phase transitions and domain structures in strained pseudocubic (100) SrTiO3 thin films. Phys. Rev. B 73, 184112 (2006)

    Article  Google Scholar 

  49. J.X. Zhang, Y.L. Li, S. Choudhury, L.Q. Chen, Y.H. Chu, F. Zavaliche, M.P. Cruz, R. Ramesh, Q.X. Jia, Computer simulation of ferroelectric domain structures in epitaxial BiFeO3 thin films. J. Appl. Phys. 103, 094111 (2008)

    Article  Google Scholar 

  50. J.X. Zhang, Y.L. Li, Y. Wang, Z.K. Liu, L.Q. Chen, Y.H. Chu, F. Zavaliche, R. Ramesh, Effect of substrate-induced strains on the spontaneous polarization of epitaxial BiFeO3 thin films. J. Appl. Phys. 101, 114105 (2007)

    Article  Google Scholar 

  51. Y.L. Li, L.Q. Chen, G. Asayama, D.G. Schlom, M.A. Zurbuchen, S.K. Streiffer, Ferroelectric domain structures in SrBi2Nb2O9 epitaxial thin films: electron microscopy and phase-field simulations. J. Appl. Phys. 95, 6332–6340 (2004)

    Article  Google Scholar 

  52. Y.L. Li, S.Y. Hu, D. Tenne, A. Soukiassian, D.G. Schlom, L.Q. Chen, X.X. Xi, K.J. Choi, C.B. Eom, A. Saxena, T. Lookman, Q.X. Jia, Interfacial coherency and ferroelectricity of BaTiO3/SrTiO3 superlattice films. Appl. Phys. Lett. 91, 252904 (2007)

    Article  Google Scholar 

  53. Y.L. Li, S.Y. Hu, D. Tenne, A. Soukiassian, D.G. Schlom, X.X. Xi, K.J. Choi, C.B. Eom, A. Saxena, T. Lookman, Q.X. Jia, L.Q. Chen, Prediction of ferroelectricity in BaTiO3/SrTiO3 superlattices with domains. Appl. Phys. Lett. 91, 112914 (2007)

    Article  Google Scholar 

  54. L. Hong, Y.L. Li, P.P. Wu, L.Q. Chen, Minimum tetragonality in PbTiO3/BaTiO3 ferroelectric superlattices. J. Appl. Phys. 114, 144103 (2013)

    Article  Google Scholar 

  55. L. Hong, P. Wu, Y. Li, V. Gopalan, C.-B. Eom, D.G. Schlom, L.-Q. Chen, Piezoelectric enhancement of (PbTiO3) m /(BaTiO3) n ferroelectric superlattices through domain engineering. Phys. Rev. B 90, 174111 (2014)

    Article  Google Scholar 

  56. S.Y. Hu, L.Q. Chen, A phase-field model for evolving microstructures with strong elastic inhomogeneity. Acta Mater. 49, 1879–1890 (2001)

    Article  Google Scholar 

  57. S.Y. Hu, Y.L. Li, L.Q. Chen, Effect of interfacial dislocations on ferroelectric phase stability and domain morphology in a thin film: a phase-field model. J. Appl. Phys. 94, 2542–2547 (2003)

    Article  Google Scholar 

  58. J.D. Clayton, J. Knap, A phase field model of deformation twinning: nonlinear theory and numerical simulations. Physica D 240, 841–858 (2011)

    Article  Google Scholar 

  59. W. Hong, X. Wang, A phase-field model for systems with coupled large deformation and mass transport. J. Mech. Phys. Solids 61, 1281–1294 (2013)

    Article  Google Scholar 

  60. L. Chen, F. Fan, L. Hong, J. Chen, Y.Z. Ji, S.L. Zhang, T. Zhu, L.Q. Chen, A phase-field model coupled with large elasto-plastic deformation: application to lithiated silicon electrodes. J. Electrochem. Soc. 161, F3164–F3172 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yulan Li .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Li, Y., Hu, S., Chen, LQ. (2016). Nanomechanics of Ferroelectric Thin Films and Heterostructures. In: Weinberger, C., Tucker, G. (eds) Multiscale Materials Modeling for Nanomechanics. Springer Series in Materials Science, vol 245. Springer, Cham. https://doi.org/10.1007/978-3-319-33480-6_15

Download citation

Publish with us

Policies and ethics