Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-11T03:24:08.211Z Has data issue: false hasContentIssue false
  • English
  • Français

Contribution of substrate to converse piezoelectric response of constrained thin films

Published online by Cambridge University Press:  01 October 2004

Lang Chen ,
J-H. Li ,
J. Slutsker ,
J. Ouyang  and
A.L. Roytburd
Lang Chen
Affiliation:
Materials Research Science and Engineering Center, Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742
J-H. Li
Affiliation:
Materials Research Science and Engineering Center, Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742
J. Slutsker
Affiliation:
Materials Research Science and Engineering Center, Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742
J. Ouyang
Affiliation:
Materials Research Science and Engineering Center, Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742
A.L. Roytburd*
Affiliation:
Materials Research Science and Engineering Center, Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742
*
a) Address all correspondence to this author. e-mail: roytburd@wam.umd.edu
Get access

Abstract

The converse piezoelectric response of a thin film constrained by a substrate is analyzed in different geometries under various boundary conditions. We considerthe effects of elastic deformation of the substrate on the total displacement of thefilm surface induced by the electric field. The change of film thickness and the bending curvature of a film/substrate couple are calculated. For a thin film island clamped on a large thick substrate, the theoretical estimation of the piezoresponse, including a local bending in the vicinity of the island/substrate interface, is in agreement with the finite element calculation.

Keywords

PiezoelectricityThin filmTheory
Type
Articles
Information
Journal of Materials Research , Volume 19 , Issue 10 , October 2004 , pp. 2853 - 2858
Copyright
Copyright © Materials Research Society 2004

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Lefki, K. and Dormans, G.J.M.: Measurement of piezoelectric coefficients of ferroelectric thin films. J. Appl. Phys. 76, 1764 (1994).CrossRefGoogle Scholar
2Xu, F., Chu, F. and Trolier-McKinstry, S.: Longitudinal piezoelectric coefficient measurement for bulk ceramics and thin films using pneumatic pressure rig. J. Appl. Phys. 86, 588 (1999).CrossRefGoogle Scholar
3Dubois, M-A. and Muralt, P.: Measurement of the effective transverse piezoelectric coefficient e 31,f of AlN and Pb(Zrx, Ti1-x )O3 thin films. Sens. Actuators A 77, 106 (1999).Google Scholar
4Kholkin, A.L., Wütchrich, C., Taylor, D.V. and Setter, N.: Interferometric measurements of electric field-induced displacements in piezoelectric thin films. Rev. Sci. Instrum. 67, 1935 (1996).CrossRefGoogle Scholar
5Maiwa, H., Christman, J.A., Kim, S.H., Kim, D.J., Maria, J.P., Chen, B., Streiffer, S.K. and Kingon, A.I.: Measurement of piezoelectric displacements of Pb(Zr, Ti)O3 thin films using a double-beam interferometer. Jpn. J. Appl. Phys. Part 1, 38, 5402 (1999).CrossRefGoogle Scholar
6Christman, J.A., Woolcott, R.R., Kingon, A.I. and Nemanich, R.J.: Piezoelectric measurements with atomic force microscopy. Appl. Phys. Lett. 73, 3851 (1998).CrossRefGoogle Scholar
7Roytburd, A.L., Alpay, S.P., Nagarajan, V., Ganpule, C.S., Aggarwal, S., Williams, E.D. and Ramesh, R.: Measurement of internal stresses via the polarization in epitaxial ferroelectric films. Phys. Rev. Lett. 85, 190 (2000).CrossRefGoogle ScholarPubMed
8Buhlman, S., Dwir, B., Baborowski, J. and Muralt, P.: Thermodynamic theory of stress distribution in epitaxial Pb(Zr, Ti)O3 thin films. Appl. Phys. Lett. 75, 3195 (2002).Google Scholar
9Nagarajan, V., Stanishevsky, A., Zhao, T., Chen, L., Melngailis, J., Roytburd, A.L. and Ramesh, R.: Realizing intrinsic piezoresponse in epitaxial submicron lead zirconate titanate capacitors on Si. Appl. Phys. Lett. 81, 4215 (2002).CrossRefGoogle Scholar
10Li, J-H., Chen, L., Nagarajan, V., Ramesh, R. and Roytburd, A.L.: Finite element modeling of piezoresponse in nanostructured ferroelectric films. Appl. Phys. Lett. 84, 2626 (2004).CrossRefGoogle Scholar
11Roytburd, A.L. and Slutsker, J.: Theory of multilayer SMA actuators. Mater. Trans. 43, 1023 (2002).CrossRefGoogle Scholar
12Finot, M. and Suresh, S.: Small and large deformation of thick and thin-film multi-layers: Effects of layer geometry, plasticity and compositional gradients. J. Mech. Phys. Solids 44, 683 (1996).CrossRefGoogle Scholar
13Steinhausen, R., Hauke, T., Seifert, W., Müller, V., Beige, H., Seifert, S. and Löbmann, P. Clamping of piezoelectric thin films on metallic substrates: Influence on the effective piezoelectric Modulus d33. In Proceedings of the 11th IEEE ISAF 98, edited by Colla, Enrico, Damjanovic, Dragan, and Setter, Nava (The Institute of Electrical and Electronic Engineers, Ferroelectrics and Frequency Control Society), Piscataway, NJ (1998), p. 93.Google Scholar
14Barzegar, A., Damjanovic, D., Ledermann, N. and Muralt, P.: Piezoelectric response of thin films determined by charge integration technique: Substrate bending effects. J. Appl. Phys. 93, 4756 (2003).CrossRefGoogle Scholar
15Roytburd, A.L.: Piezoresponse of constrained ferroelectric films. Integr. Ferroelectr. 38, 119 (2001).CrossRefGoogle Scholar
16Hsueh, C-H.: Analyses of edge effects on residual stresses in film strip/substrate systems. J. Appl. Phys. 88, 3022 (2000).CrossRefGoogle Scholar