DOI: 10.1063/1.2143129. Scaling of the piezoelectric response in ferroelectric nanostructures: An effective clamping stress model

Scaling of the piezoelectric response in ferroelectric nanostructures: An effective clamping stress model

10.1063/1.2143129

Crossref journal-article

AIP Publishing

Applied Physics Letters (317)

Abstract

It is well understood that due to substrate induced clamping the piezoresponse in thin ferroelectric films is lower than bulk. Recent studies on the effect of lateral scaling have shown that by creating nanostructures one can achieve high piezoelectric constants even in thin films. In this letter we present a simple analytical model, to describe the evolution of the out-of-plane piezoresponse as a function of the device size in 100-nm-thick PbZrxTi1−xO3 thin films. It is shown that by an effective clamping stress analysis, one can successfully map out the size dependence of the piezoelectric constants in thin ferroelectric films. The results of the model are also compared to the predictions made by finite element analysis.

Bibliography

Nagarajan, V. (2005). Scaling of the piezoelectric response in ferroelectric nanostructures: An effective clamping stress model. Applied Physics Letters, 87(24).

Authors 1

V. Nagarajan (first)

References 22 Referenced 36

10.1016/S1359-6454(99)00293-1 / Acta Mater. (2000)
10.1088/0960-1317/10/2/307 / J. Micromech. Microeng. (2000)
10.1063/1.882324 / Phys. Today (1998)
10.1023/B:JECR.0000015661.81386.e6 / J. Electroceram. (2003)
10.1063/1.357693 / J. Appl. Phys. (1994)
10.1063/1.1610242 / J. Appl. Phys. (2003)
10.1557/JMR.2004.0367 / J. Mater. Res. (2004)
10.1103/PhysRevLett.85.190 / Phys. Rev. Lett. (2000)
10.1063/1.125275 / Appl. Phys. Lett. (2002)
10.1063/1.1516857 / Appl. Phys. Lett. (2002)
10.1063/1.1695641 / Appl. Phys. Lett. (2004)
10.1063/1.1823033 / Appl. Phys. Lett. (2004)
10.1063/1.1418002 / J. Appl. Phys. (2001)
10.1109/33.159891 / IEEE Trans. Compon., Hybrids, Manuf. Technol. (1992)
10.1557/JMR.1998.0275 / J. Mater. Res. (1998)
10.1038/nmat800 / Nat. Mater. (2003)
10.1063/1.105075 / Appl. Phys. Lett. (1991)
{'key': '2023073122334704500_c18', 'first-page': '143', 'volume': '55', 'year': '1998', 'journal-title': 'J. Appl. Mech.'} / J. Appl. Mech. (1998)
10.1063/1.1325005 / J. Appl. Phys. (2001)
10.1063/1.1499563 / AIP Conf. Proc. (2002)
10.1103/PhysRevB.59.12771 / Phys. Rev. B (1999)
10.1103/PhysRevLett.80.4321 / Phys. Rev. Lett. (1998)

Dates

Type	When
Created	19 years, 8 months ago (Dec. 7, 2005, 6:15 p.m.)
Deposited	2 years, 1 month ago (July 31, 2023, 6:33 p.m.)
Indexed	1 month ago (July 30, 2025, 6:46 a.m.)
Issued	19 years, 8 months ago (Dec. 8, 2005)
Published	19 years, 8 months ago (Dec. 8, 2005)
Published Online	19 years, 8 months ago (Dec. 8, 2005)
Published Print	19 years, 8 months ago (Dec. 12, 2005)

Funders 0

None

BibTeX

@article{Nagarajan_2005, title={Scaling of the piezoelectric response in ferroelectric nanostructures: An effective clamping stress model}, volume={87}, ISSN={1077-3118}, url={http://dx.doi.org/10.1063/1.2143129}, DOI={10.1063/1.2143129}, number={24}, journal={Applied Physics Letters}, publisher={AIP Publishing}, author={Nagarajan, V.}, year={2005}, month=dec }

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